2024-04-17T07:14:51+02:00
https://www.carmin.tv/fr/oai
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-4-4
2024-04-16T20:46:02+02:00
videos:institution:ihes
videos:collection:misha-gromov-beauty-of-life-seen-through-keyhole-of-mathematics
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-4-4
https://www.carmin.tv/fr/video/beauty-of-life-seen-through-keyhole-of-mathematics-4-4
Beauty of Life seen through Keyhole of Mathematics (4/4)
video/mp4
IHES
We start with reminding basic molecular structures (Crick dogma, genetic code etc.) in living entities and classical examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy on the nature of Life.
Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current and projected numerical data on the human role in ecology of Earth.
2024-04-16T00:00:00+02:00
Misha Gromov
life, bioengineering, Researchers, Graduate Students
en
Misha Gromov : Beauty of Life seen through Keyhole of Mathematics / 19/03/2024 - 16/04/2024
https://www.carmin.tv/uploads/video/video-f8607a03d9ec03afc23fdd44d096ad36.jpg
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-3-4
2024-04-10T16:46:02+02:00
videos:institution:ihes
videos:collection:misha-gromov-beauty-of-life-seen-through-keyhole-of-mathematics
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-3-4
https://www.carmin.tv/fr/video/beauty-of-life-seen-through-keyhole-of-mathematics-3-4
Beauty of Life seen through Keyhole of Mathematics (3/4)
video/mp4
IHES
We start with reminding basic molecular structures (Crick dogma, genetic code etc.) in living entities and classical examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy on the nature of Life.
Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current and projected numerical data on the human role in ecology of Earth.
2024-04-09T00:00:00+02:00
Misha Gromov
life, bioengineering, Researchers, Graduate Students
en
Misha Gromov : Beauty of Life seen through Keyhole of Mathematics / 19/03/2024 - 16/04/2024
https://www.carmin.tv/uploads/video/video-fb4d39da39e960fc6bb3b8378361f4b4.jpg
oai:carmin.tv:reinforcement-learning-an-introduction-and-some-results-1
2024-04-09T19:40:18+02:00
videos:institution:ihes
videos:collection:9e-journee-statistique-et-informatique-pour-la-science-des-donnees-a-paris-saclay
oai:carmin.tv:reinforcement-learning-an-introduction-and-some-results-1
https://www.carmin.tv/fr/video/reinforcement-learning-an-introduction-and-some-results-1
Reinforcement Learning, an Introduction and Some Results
video/mp4
IHES
Reinforcement Learning is the "art" of learning how to act in an environment that is only observed through interactions.
In this talk, I will provide an introduction to this topic starting from the underlying probabilistic model, Markov Decision Process, describing how to learn a good policy (how to pick the actions) when this model is known and when it is unknown. I will stress the impact of the (required) parametrization of the solution, as well as the importance of understanding the inner engine (stochastic approximation).
I will illustrate the variety of questions by describing briefly three different questions:
- How to apply Reinforcement Learning to detect faster an issue during an ultrasound exam ?
- How to solve faster an MDP using better approximation ?
- How to make RL more robust while controlling its sample complexity ?
2024-04-03T00:00:00+02:00
Erwan Le Pennec
reinforcement learning, Stochastic approximation, Robust Reinforcement Learning, Researchers
en
9e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay / The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers. / Evgenii Chzhen, Florence Tupin / 03/04/2024 - 03/04/2024 / https://indico.math.cnrs.fr/event/11698/
https://www.carmin.tv/uploads/video/video-32097e08f4b8a99fa8b5c5762b9885e2.jpg
oai:carmin.tv:contextual-stochastic-bandits-with-budget-constraints-and-fairness-application-1
2024-04-09T19:42:20+02:00
videos:institution:ihes
videos:collection:9e-journee-statistique-et-informatique-pour-la-science-des-donnees-a-paris-saclay
oai:carmin.tv:contextual-stochastic-bandits-with-budget-constraints-and-fairness-application-1
https://www.carmin.tv/fr/video/contextual-stochastic-bandits-with-budget-constraints-and-fairness-application-1
Contextual Stochastic Bandits with Budget Constraints and Fairness Application
video/mp4
IHES
We review the setting and fundamental results of contextual stochastic bandits, where at each round some vector-valued context $x_t$ is observed and $K$ actions are available, each action a providing a stochastic reward with expectation given by some (partially unknown) function of $x_t$ and $a$. The aim is to maximize the cumulative rewards obtained, or equivalently, to minimize the regret. This requires maintaining a good balance between the estimation (a.k.a., exploration) of the function and the exploitation of the estimates built. The literature also considers additional budget constraints (leading to so-called contextual bandits with knapsacks): actions now provide rewards but also costs. The literature also illustrated that costs may model fairness constraints. We will review these two lines of work and briefly describe our own contribution in this respect, related to a more direct strategy, able to handle $\sqrt{T}$ cost constraints over $T$ rounds, which is exactly what is needed for fairness applications. The recent results discussed at the end of the talk will be based on the joint work by Evgenii Chzhen, Christophe Giraud, Zhen Li, and Gilles Stoltz, Small total-cost constraints in contextual bandits with knapsacks, with application to fairness, Neurips, 2023.
2024-04-03T00:00:00+02:00
Gilles Stoltz
Contextual bandits with Knapsacks, Algorithmic fairness, Adaptive stochastic optimization, Researchers
en
9e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay / The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers. / Evgenii Chzhen, Florence Tupin / 03/04/2024 - 03/04/2024 / https://indico.math.cnrs.fr/event/11698/
https://www.carmin.tv/uploads/video/video-60db1d207aafdd88f89bd2bfcba351e0.jpg
oai:carmin.tv:unsupervised-alignment-of-graphs-and-embeddings-fundamental-limits-and-computational-methods-1
2024-04-09T19:41:21+02:00
videos:institution:ihes
videos:collection:9e-journee-statistique-et-informatique-pour-la-science-des-donnees-a-paris-saclay
oai:carmin.tv:unsupervised-alignment-of-graphs-and-embeddings-fundamental-limits-and-computational-methods-1
https://www.carmin.tv/fr/video/unsupervised-alignment-of-graphs-and-embeddings-fundamental-limits-and-computational-methods-1
Unsupervised Alignment of Graphs and Embeddings: Fundamental Limits and Computational Methods
video/mp4
IHES
Aligning two (weighted or unweighted) graphs, or matching two clouds of high-dimensional embeddings, are fundamental problems in machine learning with applications across diverse domains such as natural language processing to computational biology. In this presentation I will introduce the graph alignment problem, which can be viewed as an average-case and noisy version of the graph isomorphism problem. I will talk about the main challenges when the graphs are sparse, give some insights on the fundamental limits, and present efficient algorithms for this task. Then, switching focus on aligning clouds of embeddings, I will delve into the Procrustes-Wassertein problem. We will emphasize differences from the previous graph-to-graph case. Statistical and computational results will be presented to shed light on these emerging questions.
2024-04-03T00:00:00+02:00
Luca Ganassali
Statistical inference in graphs and matrices, Informational and computational thresholds for algorithms on random instances, Researchers
en
9e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay / The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers. / Evgenii Chzhen, Florence Tupin / 03/04/2024 - 03/04/2024 / https://indico.math.cnrs.fr/event/11698/
https://www.carmin.tv/uploads/video/video-d5ac6d25b2c930a83bf2e8bc8f3dab3d.jpg
oai:carmin.tv:learning-with-missing-values-theoretical-insights-and-application-to-health-databases-1
2024-04-09T19:40:46+02:00
videos:institution:ihes
videos:collection:9e-journee-statistique-et-informatique-pour-la-science-des-donnees-a-paris-saclay
oai:carmin.tv:learning-with-missing-values-theoretical-insights-and-application-to-health-databases-1
https://www.carmin.tv/fr/video/learning-with-missing-values-theoretical-insights-and-application-to-health-databases-1
Learning with Missing Values: Theoretical Insights and Application to Health Databases
video/mp4
IHES
Missing values are ubiquitous in many fields such as health, business or social sciences. To date, much of the literature on missing values has focused on imputation as well as inference with incomplete data. In contrast, supervised learning in the presence of missing values has received little attention. In this talk I will explain the challenges posed by missing values in regression and classification tasks. In practice, a common solution consists in imputing the missing values prior to learning. I will show how different baseline methods for handling missing values compare on several large health databases with naturally occurring missing values. We will then examine the theoretical foundations of Impute-then-Regress approaches. Finally, I will present a neural network architecture for learning with missing values that goes beyond the two-stage Impute-then-Regress approaches.
2024-04-03T00:00:00+02:00
Marine Le Morvan
Inference with missing data, Machine learning for health domain, Researchers
en
9e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay / The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers. / Evgenii Chzhen, Florence Tupin / 03/04/2024 - 03/04/2024 / https://indico.math.cnrs.fr/event/11698/
https://www.carmin.tv/uploads/video/video-1e4df2c4ca4afa53cac42fd89a6cc7d6.jpg
oai:carmin.tv:weak-signals-machine-learning-meets-extreme-value-theory-1
2024-04-09T19:41:53+02:00
videos:institution:ihes
videos:collection:9e-journee-statistique-et-informatique-pour-la-science-des-donnees-a-paris-saclay
oai:carmin.tv:weak-signals-machine-learning-meets-extreme-value-theory-1
https://www.carmin.tv/fr/video/weak-signals-machine-learning-meets-extreme-value-theory-1
Weak Signals: machine-learning meets extreme value theory
video/mp4
IHES
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step in learning problems involving observations far away from the center. In the common situation that the components of the vector have different distributions, the rank transformation offers a convenient and robust way of standardizing data in order to build an empirical version of the angular measure based on the most extreme observations. However, the study of the sampling distribution of the resulting empirical angular measure is challenging. It is the purpose of this talk to explain how to establish finite-sample bounds for the maximal deviations between the empirical and true angular measures, uniformly over classes of Borel sets of controlled combi natorial complexity. The bounds are valid with high probability and, up to logarithmic factors, scale as the square root of the effective sample size. The bounds are next applied to provide performance guarantees for two statistical learning procedures tailored to extreme regions of the input space and built upon the empirical angular measure: binary classification in extreme regions through empirical risk minimization and unsupervised anomaly detection through minimum-volume sets of the sphere.
2024-04-03T00:00:00+02:00
Stephan Clémençon
extreme value theory, VC theory, empirical processes, Anomaly Detection, Researchers
en
9e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay / The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers. / Evgenii Chzhen, Florence Tupin / 03/04/2024 - 03/04/2024 / https://indico.math.cnrs.fr/event/11698/
https://www.carmin.tv/uploads/video/video-44cfb67734dd90881c880a17d1ee0853.jpg
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-2-4
2024-04-02T21:26:02+02:00
videos:institution:ihes
videos:collection:misha-gromov-beauty-of-life-seen-through-keyhole-of-mathematics
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-2-4
https://www.carmin.tv/fr/video/beauty-of-life-seen-through-keyhole-of-mathematics-2-4
Beauty of Life seen through Keyhole of Mathematics (2/4)
video/mp4
IHES
We start with reminding basic molecular structures (Crick dogma, genetic code etc.) in living entities and classical examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy on the nature of Life.
Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current and projected numerical data on the human role in ecology of Earth.
2024-04-02T00:00:00+02:00
Misha Gromov
life, bioengineering, Researchers, Graduate Students
en
Misha Gromov : Beauty of Life seen through Keyhole of Mathematics / 19/03/2024 - 16/04/2024
https://www.carmin.tv/uploads/video/video-b17141e76b968f541a3282f83520484f.jpg
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-4-4
2024-04-01T13:06:02+02:00
videos:institution:ihes
videos:collection:gerard-ben-arous-random-matrices-and-dynamics-of-optimization-in-very-high-dimensions
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-4-4
https://www.carmin.tv/fr/video/random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-4-4
Random Matrices and Dynamics of Optimization in Very High Dimensions (4/4)
video/mp4
IHES
Machine learning and Data science algorithms involve in their last stage the need for optimization of complex random functions in very high dimensions. Simple algorithms like Stochastic Gradient Descent (with small batches) are used very effectively. I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized regimes. I will first introduce the whole framework for non-experts, from the structure of the typical tasks to the natural structures of neural nets used in standard contexts. l will then cover briefly the classical and usual context of SGD in finite dimensions. I will then survey recent work with Reza Gheissari (Northwestern), Aukosh Jagannath (Waterloo) giving a general view for the existence of projected “effective dynamics” for “summary statistics” in much smaller dimensions, which still rule the performance of very high dimensional systems, as well . These effective dynamics (as their so-called “critical regime”) define a dynamical system in finite dimensions which may be quite complex, and rules the performance of the learning algorithm. The next step will be to understand how the system finds these “summary statistics”. This is done in the next work with the same authors and with Jiaoyang Huang (Wharton, U-Penn). This is based on a dynamical spectral transition of Random Matrix Theory: along the trajectory of the optimization path, the Gram matix or the Hessian matrix develop outliers which carry these effective dynamics. I will naturally first come back to the Random Matrix Tools needed here (the behavior of the edge of the spectrum and the BBP transition) in a much broader context. And then illustrate the use of this point of view on a few central examples of ML: multilayer neural nets for classification (of Gaussian mixtures), and the XOR examples, for instance.
2024-03-29T00:00:00+01:00
Gérard Ben Arous
machine learning, random matrices, stochastic gradient descent, Optimization in high dimensions, Neural Nets, Researchers, Graduate Students
en
Gérard Ben Arous : Random Matrices and Dynamics of Optimization in Very High Dimensions / 25/03/2024 - 29/03/2024
https://www.carmin.tv/uploads/video/video-b1c060c60d2f46ef61e7e6d8c8ceb766.jpg
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-3-4
2024-03-27T22:36:03+01:00
videos:institution:ihes
videos:collection:gerard-ben-arous-random-matrices-and-dynamics-of-optimization-in-very-high-dimensions
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-3-4
https://www.carmin.tv/fr/video/random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-3-4
Random Matrices and Dynamics of Optimization in Very High Dimensions (3/4)
video/mp4
IHES
Machine learning and Data science algorithms involve in their last stage the need for optimization of complex random functions in very high dimensions. Simple algorithms like Stochastic Gradient Descent (with small batches) are used very effectively. I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized regimes. I will first introduce the whole framework for non-experts, from the structure of the typical tasks to the natural structures of neural nets used in standard contexts. l will then cover briefly the classical and usual context of SGD in finite dimensions. I will then survey recent work with Reza Gheissari (Northwestern), Aukosh Jagannath (Waterloo) giving a general view for the existence of projected “effective dynamics” for “summary statistics” in much smaller dimensions, which still rule the performance of very high dimensional systems, as well . These effective dynamics (as their so-called “critical regime”) define a dynamical system in finite dimensions which may be quite complex, and rules the performance of the learning algorithm. The next step will be to understand how the system finds these “summary statistics”. This is done in the next work with the same authors and with Jiaoyang Huang (Wharton, U-Penn). This is based on a dynamical spectral transition of Random Matrix Theory: along the trajectory of the optimization path, the Gram matix or the Hessian matrix develop outliers which carry these effective dynamics. I will naturally first come back to the Random Matrix Tools needed here (the behavior of the edge of the spectrum and the BBP transition) in a much broader context. And then illustrate the use of this point of view on a few central examples of ML: multilayer neural nets for classification (of Gaussian mixtures), and the XOR examples, for instance.
2024-03-27T00:00:00+01:00
Gérard Ben Arous
machine learning, random matrices, stochastic gradient descent, Optimization in high dimensions, Neural Nets, Researchers, Graduate Students
en
Gérard Ben Arous : Random Matrices and Dynamics of Optimization in Very High Dimensions / 25/03/2024 - 29/03/2024
https://www.carmin.tv/uploads/video/video-d6f837a4b5a2ebe847fa392ee3941392.jpg
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-1-4
2024-03-25T20:16:02+01:00
videos:institution:ihes
videos:collection:gerard-ben-arous-random-matrices-and-dynamics-of-optimization-in-very-high-dimensions
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-1-4
https://www.carmin.tv/fr/video/random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-1-4
Random Matrices and Dynamics of Optimization in Very High Dimensions (1/4)
video/mp4
IHES
Machine learning and Data science algorithms involve in their last stage the need for optimization of complex random functions in very high dimensions. Simple algorithms like Stochastic Gradient Descent (with small batches) are used very effectively. I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized regimes. I will first introduce the whole framework for non-experts, from the structure of the typical tasks to the natural structures of neural nets used in standard contexts. l will then cover briefly the classical and usual context of SGD in finite dimensions. I will then survey recent work with Reza Gheissari (Northwestern), Aukosh Jagannath (Waterloo) giving a general view for the existence of projected “effective dynamics” for “summary statistics” in much smaller dimensions, which still rule the performance of very high dimensional systems, as well . These effective dynamics (as their so-called “critical regime”) define a dynamical system in finite dimensions which may be quite complex, and rules the performance of the learning algorithm. The next step will be to understand how the system finds these “summary statistics”. This is done in the next work with the same authors and with Jiaoyang Huang (Wharton, U-Penn). This is based on a dynamical spectral transition of Random Matrix Theory: along the trajectory of the optimization path, the Gram matix or the Hessian matrix develop outliers which carry these effective dynamics. I will naturally first come back to the Random Matrix Tools needed here (the behavior of the edge of the spectrum and the BBP transition) in a much broader context. And then illustrate the use of this point of view on a few central examples of ML: multilayer neural nets for classification (of Gaussian mixtures), and the XOR examples, for instance.
2024-03-25T00:00:00+01:00
Gérard Ben Arous
machine learning, random matrices, stochastic gradient descent, Optimization in high dimensions, Neural Nets, Researchers, Graduate Students
en
Gérard Ben Arous : Random Matrices and Dynamics of Optimization in Very High Dimensions / 25/03/2024 - 29/03/2024
https://www.carmin.tv/uploads/video/video-457dc4d80a61efc335d77c163cc83804.jpg
oai:carmin.tv:an-introduction-to-super-critical-singularities-3-4
2024-03-15T20:44:01+01:00
videos:institution:ihes
videos:collection:pierre-raphael-une-introduction-aux-singularites-sur-critiques
oai:carmin.tv:an-introduction-to-super-critical-singularities-3-4
https://www.carmin.tv/fr/video/an-introduction-to-super-critical-singularities-3-4
An Introduction to Super Critical Singularities (3/4)
video/mp4
IHES
Lecture 3 : On self similar solutions for compressible Euler
The description of singularity formation for non linear PDE’s is a classical problem with deep physical roots. Immense progress have been done in the last thirty on the understanding of “bubbling” phenomenon for focusing problems. But recently, new mecanisms have been discovered for “defocusing” problems with a deep connection to fluid mechanics. This series of 4 lectures is intended as a graduate class and will propose an introduction to the key results and open problems in the field, as well as a self contained description of the essential steps of the proofs.
2024-03-15T00:00:00+01:00
Pierre Raphaël
Researchers, Graduate Students
en
Pierre Raphael : Une introduction aux singularités sur critiques / 12/03/2024 - 19/03/2024
https://www.carmin.tv/uploads/video/video-4e1c7801935140fc80814395f536b612.jpg
oai:carmin.tv:an-introduction-to-super-critical-singularities-2-4
2024-03-14T19:20:02+01:00
videos:institution:ihes
videos:collection:pierre-raphael-une-introduction-aux-singularites-sur-critiques
oai:carmin.tv:an-introduction-to-super-critical-singularities-2-4
https://www.carmin.tv/fr/video/an-introduction-to-super-critical-singularities-2-4
An Introduction to Super Critical Singularities (2/4)
video/mp4
IHES
Lecture 2 : Front singularities
The description of singularity formation for non linear PDE’s is a classical problem with deep physical roots. Immense progress have been done in the last thirty on the understanding of “bubbling” phenomenon for focusing problems. But recently, new mecanisms have been discovered for “defocusing” problems with a deep connection to fluid mechanics. This series of 4 lectures is intended as a graduate class and will propose an introduction to the key results and open problems in the field, as well as a self contained description of the essential steps of the proofs.
2024-03-14T00:00:00+01:00
Pierre Raphaël
Researchers, Graduate Students
en
Pierre Raphael : Une introduction aux singularités sur critiques / 12/03/2024 - 19/03/2024
https://www.carmin.tv/uploads/video/video-553beed0edfbc69c5b782f36c3a88db5.jpg
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-4-4-2
2024-03-13T10:08:02+01:00
videos:institution:ihes
videos:collection:jonathan-pila-point-counting-and-the-zilber-pink-conjecture
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-4-4-2
https://www.carmin.tv/fr/video/point-counting-and-the-zilber-pink-conjecture-4-4-2
Point-Counting and the Zilber-Pink Conjecture (4/4)
video/mp4
IHES
The Zilber-Pink conjecture is a diophantine finiteness conjecture. It unifies and gives a far-reaching generalization of the classical Mordell-Lang and Andre-Oort conjectures, and is wide open in general.
Point-counting results for definable sets in o-minimal structures provide a strategy for proving suitable cases which has had some success, in particular in its use in proving the Andre-Oort conjecture.
The course will describe the Zilber-Pink conjecture and the point-counting approach to proving cases of it, eventually concentrating on the case of a curve in a power of the modular curve.
We will describe the model-theoretic contexts of the conjectures and techniques, and the essential arithmetic ingredients.
2024-03-12T00:00:00+01:00
Jonathan Pila
Zilber-Pink conjecture, unlikely intersection, o-minimal structure, Researchers, Graduate Students
en
Jonathan Pila : Point-Counting and the Zilber-Pink Conjecture / 20/02/2024 - 12/03/2024
https://www.carmin.tv/uploads/video/video-5d1a3ca93ad33c9ca0aba915e0c86183.jpg
oai:carmin.tv:an-introduction-to-super-critical-singularities-1-4
2024-03-13T10:48:01+01:00
videos:institution:ihes
videos:collection:pierre-raphael-une-introduction-aux-singularites-sur-critiques
oai:carmin.tv:an-introduction-to-super-critical-singularities-1-4
https://www.carmin.tv/fr/video/an-introduction-to-super-critical-singularities-1-4
An Introduction to Super Critical Singularities (1/4)
video/mp4
IHES
Lecture 1 : Energy super critical singularity formation
The description of singularity formation for non linear PDE’s is a classical problem with deep physical roots. Immense progress have been done in the last thirty on the understanding of “bubbling” phenomenon for focusing problems. But recently, new mecanisms have been discovered for “defocusing” problems with a deep connection to fluid mechanics. This series of 4 lectures is intended as a graduate class and will propose an introduction to the key results and open problems in the field, as well as a self contained description of the essential steps of the proofs.
2024-03-12T00:00:00+01:00
Pierre Raphaël
Researchers, Graduate Students
en
Pierre Raphael : Une introduction aux singularités sur critiques / 12/03/2024 - 19/03/2024
https://www.carmin.tv/uploads/video/video-8168f3d71c21cd627f6fab1e84528268.jpg
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-4-4
2024-03-12T19:41:27+01:00
videos:institution:ihes
videos:collection:jonathan-pila-point-counting-and-the-zilber-pink-conjecture
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-4-4
https://www.carmin.tv/fr/video/point-counting-and-the-zilber-pink-conjecture-4-4
Point-Counting and the Zilber-Pink Conjecture (4/4)
video/mp4
IHES
The Zilber-Pink conjecture is a diophantine finiteness conjecture. It unifies and gives a far-reaching generalization of the classical Mordell-Lang and Andre-Oort conjectures, and is wide open in general.
Point-counting results for definable sets in o-minimal structures provide a strategy for proving suitable cases which has had some success, in particular in its use in proving the Andre-Oort conjecture.
The course will describe the Zilber-Pink conjecture and the point-counting approach to proving cases of it, eventually concentrating on the case of a curve in a power of the modular curve.
We will describe the model-theoretic contexts of the conjectures and techniques, and the essential arithmetic ingredients.
2024-03-12T00:00:00+01:00
Jonathan Pila
Zilber-Pink conjecture, unlikely intersection, o-minimal structure, Researchers, Graduate Students
en
Jonathan Pila : Point-Counting and the Zilber-Pink Conjecture / 20/02/2024 - 12/03/2024
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-4-4-1
2024-03-12T20:21:33+01:00
videos:institution:ihes
videos:collection:jonathan-pila-point-counting-and-the-zilber-pink-conjecture
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-4-4-1
https://www.carmin.tv/fr/video/point-counting-and-the-zilber-pink-conjecture-4-4-1
Point-Counting and the Zilber-Pink Conjecture (4/4)
video/mp4
IHES
The Zilber-Pink conjecture is a diophantine finiteness conjecture. It unifies and gives a far-reaching generalization of the classical Mordell-Lang and Andre-Oort conjectures, and is wide open in general.
Point-counting results for definable sets in o-minimal structures provide a strategy for proving suitable cases which has had some success, in particular in its use in proving the Andre-Oort conjecture.
The course will describe the Zilber-Pink conjecture and the point-counting approach to proving cases of it, eventually concentrating on the case of a curve in a power of the modular curve.
We will describe the model-theoretic contexts of the conjectures and techniques, and the essential arithmetic ingredients.
2024-03-12T00:00:00+01:00
Jonathan Pila
Zilber-Pink conjecture, unlikely intersection, o-minimal structure, Researchers, Graduate Students
en
Jonathan Pila : Point-Counting and the Zilber-Pink Conjecture / 20/02/2024 - 12/03/2024
oai:carmin.tv:particle-approximation-of-the-doubly-parabolic-keller-segel-equation-in-the-plane-1
2024-03-12T16:06:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:particle-approximation-of-the-doubly-parabolic-keller-segel-equation-in-the-plane-1
https://www.carmin.tv/fr/video/particle-approximation-of-the-doubly-parabolic-keller-segel-equation-in-the-plane-1
Particle Approximation of the Doubly Parabolic Keller-Segel Equation in the Plane
video/mp4
IHES
In this talk, we study a stochastic system of $N$ particles associated with the parabolic-parabolic Keller-Segel system in the plane. This particle system is singular and non Markovian in that its drift term depends on the past of the particles. When the sensitivity parameter is sufficiently small, we show that this particle system indeed exists for any $N\geq 2$, we show tightness in $N$ of its empirical measure, and that any weak limit point of this empirical measure, as $N\to \infty$, solves some nonlinear martingale problem, which in particular implies that its family of time-marginals solves the parabolic-parabolic Keller-Segel system in some weak sense. The main argument of the proof consists of a "Markovianization" of the interaction kernel: We show that, in some loose sense, the two-by-two path-dependant interaction can be controlled by a two-by-two Coulomb interaction, as in the parabolic-elliptic case. This is a joint work with N. Fournier (Sorbonne Université).
2024-03-08T00:00:00+01:00
Milica Tomašević
Stochastic particle systems, Singular interaction, Non-Markovian processes, Keller-Segel equation, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-e9b9c690e4b688c00297e4f4b1d118c0.jpg
oai:carmin.tv:scaling-limits-of-disordered-systems-1
2024-03-12T16:12:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:scaling-limits-of-disordered-systems-1
https://www.carmin.tv/fr/video/scaling-limits-of-disordered-systems-1
Scaling Limits of Disordered Systems
video/mp4
IHES
I will present some recent results on the scaling limit of disordered systems and some of their consequences. I will mostly focus on the PolandâScheraga model, also known as the pinning model, which is used to describe DNA denaturation: the question is to know wether (and how) disorder affects its phase transition. I will present some results obtained in a generalized (supposedly more realistic) version of the model, in collaboration with Alexandre Legrand (Université Lyon 1).
2024-03-08T00:00:00+01:00
Quentin Berger
disordered systems, critical phenomena, scaling limits, intermediate disorder, disorder relevance, correlated disorder, Poland–Scheraga model, bivariate renewal processes, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-b1fb153a1d35a3cd28bf36167693368e.jpg
oai:carmin.tv:equivalence-of-fluctuations-between-she-and-kpz-equation-in-weak-disorder-regime-1
2024-03-12T16:14:02+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:equivalence-of-fluctuations-between-she-and-kpz-equation-in-weak-disorder-regime-1
https://www.carmin.tv/fr/video/equivalence-of-fluctuations-between-she-and-kpz-equation-in-weak-disorder-regime-1
Equivalence of Fluctuations Between SHE and KPZ Equation in Weak Disorder Regime
video/mp4
IHES
I will The Kardar-Parisi-Zhang (KPZ) equation is a mathematical model that describes the random evolution of interfaces. The equation has become a fundamental model in non-equilibrium statistical physics. Constructing a solution to the KPZ equation in any dimension presents a significant challenge due to its inherent non-linearity. This challenge has resulted in an enduring open problem, particularly in finding solutions in two and higher dimensions. This talk will explore the intriguing connection between the stochastic heat equation (SHE) and the KPZ equation. It offers a rigorous demonstration of the equivalence of fluctuations in these systems in the weak disorder regime for three and higher dimensions. This talk is based on joint work with Stefan Junk (Gakushuin University).
2024-03-08T00:00:00+01:00
Shuta Nakajima
KPZ equation, directed polymer, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-6d30a250e19311b1aa38d105c2110e3e.jpg
oai:carmin.tv:where-do-random-trees-grow-leaves-1
2024-03-12T16:16:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:where-do-random-trees-grow-leaves-1
https://www.carmin.tv/fr/video/where-do-random-trees-grow-leaves-1
Where Do Random Trees Grow Leaves
video/mp4
IHES
Luczak and Winkler (refined by Caraceni and Stauffer) showed that is it possible to create a chain of random binary trees $(T_n : n \geq 1)$ so that $T_{n}$ is uniformly distributed over the set of all binary trees with $n$ leaves and such that $T_{n+1}$ is obtained from $T_{n}$ by adding "on leaf". We show that the location where this leaf must be added is far from being uniformly distributed on $T_n$ but is concentrated on a "fractal" subset of $n^{3(2- \sqrt{3})+o(1)}$ leaves. The full multifractal spectrum of the measure in the continuous setting is computed. Joint work with Alessandra Caraceni and Robin Stephenson.
2024-03-08T00:00:00+01:00
Nicolas Curien
random trees, scaling limits, Markov dynamic, fractal measure, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-eb5fcc25f4345ef859b1039a43d0576a.jpg
oai:carmin.tv:geometric-laplacians-on-self-conformal-fractal-curves-in-the-plane-1
2024-03-12T16:16:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:geometric-laplacians-on-self-conformal-fractal-curves-in-the-plane-1
https://www.carmin.tv/fr/video/geometric-laplacians-on-self-conformal-fractal-curves-in-the-plane-1
Geometric Laplacians on Self-Conformal Fractal Curves in the Plane
video/mp4
IHES
This talk will present the speaker's ongoing work on “geometrically canonical” Laplacians on self-conformal fractal curves in the plane. The main result is that on a given such curve one can construct a family of Laplacians whose heat kernels and eigenvalue asymptotics “respect” the fractal nature of the Euclidean geometry of the curve in certain nice ways. The idea of the construction of such Laplacians originated from the speaker's preceding studies on the case of a circle packing fractal, i.e., a fractal subset of $\mathbb{C}$ whose Lebesgue area is zero and whose complement in the Riemann sphere $\widehat{\mathbb{C}}:=\mathbb{C}\cup\{\infty\}$ is the union of disjoint open disks in $\widehat{\mathbb{C}}$. He has observed that, on a given such fractal, one can explicitly define a Dirichlet form (a quadratic energy functional) by a certain weighted sum of the standard one-dimensional Dirichlet form on each of the circles constituting the fractal, and that this Dirichlet form “respect” the Euclidean geometry of the fractal in the sense that the inclusion map of the fractal into $\mathbb{C}$ is harmonic with respect to this form. The speaker has also proved that such a Dirichlet form is unique for the classical Apollonian gaskets and that, for some concrete families of self-conformal circle packing fractals including the Apollonian gaskets, the associated Laplacian satisfies Weyl's eigenvalue asymptotics involving the Euclidean Hausdorff dimension and measure of the fractal. It would be desirable if one could extend such results to self-conformal fractals which are not circle packing ones, and the talk will present an extension to the simplest case of self-conformal fractal curves in the plane. The key point of the construction of Laplacians is to use (suitable versions of) the harmonic measure in defining the Dirichlet form BUT to use fractional-order Besov seminorms (with respect to the harmonic measure) of the inclusion map into $\mathbb{C}$ in defining the $L^{2}$-inner product for functions on the fractal.
2024-03-08T00:00:00+01:00
Naotaka Kajino
harmonic measure, Laplacian, self-conformal fractal curve, Apollonian gasket, round Sierpinski carpet, Weyl’s eigenvalue asymptotics, Kesten's renewal theorem, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-5d9e19841bf7afcf1ac930bb3692dcd8.jpg
oai:carmin.tv:particle-approximation-of-the-doubly-parabolic-keller-segel-equation-in-the-plane
2024-03-12T10:01:58+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:particle-approximation-of-the-doubly-parabolic-keller-segel-equation-in-the-plane
https://www.carmin.tv/fr/video/particle-approximation-of-the-doubly-parabolic-keller-segel-equation-in-the-plane
Particle Approximation of the Doubly Parabolic Keller-Segel Equation in the Plane
video/mp4
IHES
In this talk, we study a stochastic system of $N$ particles associated with the parabolic-parabolic Keller-Segel system in the plane. This particle system is singular and non Markovian in that its drift term depends on the past of the particles. When the sensitivity parameter is sufficiently small, we show that this particle system indeed exists for any $N\geq 2$, we show tightness in $N$ of its empirical measure, and that any weak limit point of this empirical measure, as $N\to \infty$, solves some nonlinear martingale problem, which in particular implies that its family of time-marginals solves the parabolic-parabolic Keller-Segel system in some weak sense. The main argument of the proof consists of a "Markovianization" of the interaction kernel: We show that, in some loose sense, the two-by-two path-dependant interaction can be controlled by a two-by-two Coulomb interaction, as in the parabolic-elliptic case. This is a joint work with N. Fournier (Sorbonne Université).
2024-03-08T00:00:00+01:00
Milica Tomašević
Stochastic particle systems, Singular interaction, Non-Markovian processes, Keller-Segel equation, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
oai:carmin.tv:scaling-limits-of-disordered-systems
2024-03-11T17:42:50+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:scaling-limits-of-disordered-systems
https://www.carmin.tv/fr/video/scaling-limits-of-disordered-systems
Scaling Limits of Disordered Systems
video/mp4
IHES
I will present some recent results on the scaling limit of disordered systems and some of their consequences. I will mostly focus on the PolandâScheraga model, also known as the pinning model, which is used to describe DNA denaturation: the question is to know wether (and how) disorder affects its phase transition. I will present some results obtained in a generalized (supposedly more realistic) version of the model, in collaboration with Alexandre Legrand (Université Lyon 1).
2024-03-08T00:00:00+01:00
Quentin Berger
disordered systems, critical phenomena, scaling limits, intermediate disorder, disorder relevance, correlated disorder, Poland–Scheraga model, bivariate renewal processes, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
oai:carmin.tv:equivalence-of-fluctuations-between-she-and-kpz-equation-in-weak-disorder-regime
2024-03-12T09:55:53+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:equivalence-of-fluctuations-between-she-and-kpz-equation-in-weak-disorder-regime
https://www.carmin.tv/fr/video/equivalence-of-fluctuations-between-she-and-kpz-equation-in-weak-disorder-regime
Equivalence of Fluctuations Between SHE and KPZ Equation in Weak Disorder Regime
video/mp4
IHES
I will The Kardar-Parisi-Zhang (KPZ) equation is a mathematical model that describes the random evolution of interfaces. The equation has become a fundamental model in non-equilibrium statistical physics. Constructing a solution to the KPZ equation in any dimension presents a significant challenge due to its inherent non-linearity. This challenge has resulted in an enduring open problem, particularly in finding solutions in two and higher dimensions. This talk will explore the intriguing connection between the stochastic heat equation (SHE) and the KPZ equation. It offers a rigorous demonstration of the equivalence of fluctuations in these systems in the weak disorder regime for three and higher dimensions.
This talk is based on joint work with Stefan Junk (Gakushuin University).
2024-03-08T00:00:00+01:00
Shuta Nakajima
KPZ equation, directed polymer, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
oai:carmin.tv:where-do-random-trees-grow-leaves
2024-03-12T09:58:05+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:where-do-random-trees-grow-leaves
https://www.carmin.tv/fr/video/where-do-random-trees-grow-leaves
Where Do Random Trees Grow Leaves
video/mp4
IHES
Luczak and Winkler (refined by Caraceni and Stauffer) showed that is it possible to create a chain of random binary trees $(T_n : n \geq 1)$ so that $T_{n}$ is uniformly distributed over the set of all binary trees with $n$ leaves and such that $T_{n+1}$ is obtained from $T_{n}$ by adding "on leaf". We show that the location where this leaf must be added is far from being uniformly distributed on $T_n$ but is concentrated on a "fractal" subset of $n^{3(2- \sqrt{3})+o(1)}$ leaves. The full multifractal spectrum of the measure in the continuous setting is computed.
Joint work with Alessandra Caraceni and Robin Stephenson.
2024-03-08T00:00:00+01:00
Nicolas Curien
random trees, scaling limits, Markov dynamic, fractal measure, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
oai:carmin.tv:geometric-laplacians-on-self-conformal-fractal-curves-in-the-plane
2024-03-11T17:42:51+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:geometric-laplacians-on-self-conformal-fractal-curves-in-the-plane
https://www.carmin.tv/fr/video/geometric-laplacians-on-self-conformal-fractal-curves-in-the-plane
Geometric Laplacians on Self-Conformal Fractal Curves in the Plane
video/mp4
IHES
This talk will present the speaker's ongoing work on “geometrically canonical” Laplacians on self-conformal fractal curves in the plane. The main result is that on a given such curve one can construct a family of Laplacians whose heat kernels and eigenvalue asymptotics “respect” the fractal nature of the Euclidean geometry of the curve in certain nice ways. The idea of the construction of such Laplacians originated from the speaker's preceding studies on the case of a circle packing fractal, i.e., a fractal subset of $\mathbb{C}$ whose Lebesgue area is zero and whose complement in the Riemann sphere $\widehat{\mathbb{C}}:=\mathbb{C}\cup\{\infty\}$ is the union of disjoint open disks in $\widehat{\mathbb{C}}$. He has observed that, on a given such fractal, one can explicitly define a Dirichlet form (a quadratic energy functional) by a certain weighted sum of the standard one-dimensional Dirichlet form on each of the circles constituting the fractal, and that this Dirichlet form “respect” the Euclidean geometry of the fractal in the sense that the inclusion map of the fractal into $\mathbb{C}$ is harmonic with respect to this form. The speaker has also proved that such a Dirichlet form is unique for the classical Apollonian gaskets and that, for some concrete families of self-conformal circle packing fractals including the Apollonian gaskets, the associated Laplacian satisfies Weyl's eigenvalue asymptotics involving the Euclidean Hausdorff dimension and measure of the fractal. It would be desirable if one could extend such results to self-conformal fractals which are not circle packing ones, and the talk will present an extension to the simplest case of self-conformal fractal curves in the plane. The key point of the construction of Laplacians is to use (suitable versions of) the harmonic measure in defining the Dirichlet form BUT to use fractional-order Besov seminorms (with respect to the harmonic measure) of the inclusion map into $\mathbb{C}$ in defining the $L^{2}$-inner product for functions on the fractal.
2024-03-08T00:00:00+01:00
Naotaka Kajino
harmonic measure, Laplacian, self-conformal fractal curve, Apollonian gasket, round Sierpinski carpet, Weyl’s eigenvalue asymptotics, Kesten's renewal theorem, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
oai:carmin.tv:zeros-of-random-power-series-with-stationary-gaussian-coefficients
2024-03-11T11:26:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:zeros-of-random-power-series-with-stationary-gaussian-coefficients
https://www.carmin.tv/fr/video/zeros-of-random-power-series-with-stationary-gaussian-coefficients
Zeros of Random Power Series with Stationary Gaussian Coefficients
video/mp4
IHES
The zeros of random power series with i.i.d. complex Gaussian coefficients form the determinantal point process associated with the Bergman kernel. As a natural generalization of this model, we are concerned with zeros of Gaussian power series with coefficients being stationary, centered, complex Gaussian process. The zeros of such analytic Gaussian process have special properties. Our main concern is the expected number of zeros in a disk and we compare it with the i.i.d. coefficients case. When the spectral density of the Gaussian process of coefficients is nice, we discuss the precise asymptotic of the expected number of zeros inside the disk of radius $r$ centered at the origin as $r$ tends to the radius of convergence. Also, we discuss the relationships between the intensity of zeros and spectral density.
2024-03-07T00:00:00+01:00
Tomoyuki Shirai
Gaussian power series, Gaussian analytic functions, zeros, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-d41bf45b5ad73d74f57a602a540536cc.jpg
oai:carmin.tv:dunkl-operators-random-matrices-and-hurwitz-numbers
2024-03-11T11:28:02+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:dunkl-operators-random-matrices-and-hurwitz-numbers
https://www.carmin.tv/fr/video/dunkl-operators-random-matrices-and-hurwitz-numbers
Dunkl Operators, Random Matrices and Hurwitz Numbers
video/mp4
IHES
This talk is concerned with selected probabilistic aspects of Dunkl operators. In the first part, I'll revisit Cepa and Lepingle study of particles on the real line then I'll show how it extends to radial Dunkl processes associated to reduced root sytems. In the second part, I'll talk about the reflected Brownian motion in Weyl chambers. In this respect, I'll exhibit its construction using folding operators and provide the Tanaka-type formula it satisfies. The last part is devoted to the mysterious occurrence of simple Hurwitz numbers in the expression of the Dunkl interwining operator and in particular in the generalized Bessel function (HCIZ integral).
2024-03-07T00:00:00+01:00
Nizar Demni
Processus de Dunkl radial, systemes de particules, Matrices aleatoires, Nombres de Hurwitz simples, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-922fb387072a98b7ba2a75ad03ac7456.jpg
oai:carmin.tv:outliers-of-perturbations-of-banded-toeplitz-matrices
2024-03-11T11:34:02+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:outliers-of-perturbations-of-banded-toeplitz-matrices
https://www.carmin.tv/fr/video/outliers-of-perturbations-of-banded-toeplitz-matrices
Outliers of Perturbations of Banded Toeplitz Matrices
video/mp4
IHES
Let $T_n({\bf a})$ be a $n\times n$ Toeplitz matrix with symbol ${\bf a}\colon \mathbb S^1 \to \mathbb{C}$ given by the Laurent polynomial ${\bf a}(\lambda) = \sum_{k=-r}^s a_k \lambda^k$. We consider the matrix
$$
M_n = T_n({\bf a}) + \sigma \frac{X_n}{\sqrt{n}},
$$
where $\sigma >0$ and $X_n$ is some noise matrix whose entries are centered i.i.d. random variables of unit variance. When $n$ goes to infinity, the empirical spectral distribution of $M_n$ converges towards a probability measure $\beta_\sigma$ on $\mathbb{C}$. The objective of this talk is to describe, when $n$ is large, the eigenvalues of $M_n$ in closed regions of $\mathbb{C} \backslash \mbox{support}(\beta_\sigma)$ which we will call the outlier eigenvalues.
This is a joint work with Charles Bordenave and Fran\c{c}ois Chapon.
2024-03-07T00:00:00+01:00
Mireille Capitaine
random matrices, Outliers, Banded Toeplitz matrices, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-b722bce4610a8a95b143757c50341eec.jpg
oai:carmin.tv:an-exact-solution-of-the-macroscopic-fluctuation-theory
2024-03-12T10:02:51+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:an-exact-solution-of-the-macroscopic-fluctuation-theory
https://www.carmin.tv/fr/video/an-exact-solution-of-the-macroscopic-fluctuation-theory
An Exact Solution of the Macroscopic Fluctuation Theory
video/mp4
IHES
The Macroscopic Fluctuation Theory (MFT) is a framework proposed by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim for diffusive interacting particle systems, in which large deviations functions can be obtained by solving a system of nonlinear PDEs. In this talk, we shall present an exact solution of the MFT for a paradigmatic process, the simple exclusion process, derived by using Inverse Scattering Theory.
2024-03-07T00:00:00+01:00
Kirone Mallick
large deviations, non-equilibrium processes, macroscopic fluctuations, inverse scattering, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-28027f288e1f0ecf90ce9666299289c5.jpg
oai:carmin.tv:regularity-structures-for-quasilinear-singular-spdes
2024-03-12T10:38:54+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:regularity-structures-for-quasilinear-singular-spdes
https://www.carmin.tv/fr/video/regularity-structures-for-quasilinear-singular-spdes
Regularity Structures for Quasilinear Singular SPDEs
video/mp4
IHES
I will give an overview of the tools of regularity structures for the study of semilinear and quasilinear parabolic singular stochastic PDEs. No previous knowledge of the domain is needed.
2024-03-07T00:00:00+01:00
Ismael Bailleul
EDPS singulières quasi-linéaires, structures de régularités, équation renormalisée, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-39bfe017bca2a37716985921d7cd30f9.jpg
oai:carmin.tv:random-models-on-regularity-integrability-structures
2024-03-12T10:02:35+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:random-models-on-regularity-integrability-structures
https://www.carmin.tv/fr/video/random-models-on-regularity-integrability-structures
Random Models on Regularity-Integrability Structures
video/mp4
IHES
In the study of singular SPDEs, it has been a challenging problem to obtain a simple proof of a general probabilistic convergence result (BPHZ theorem). Differently from Chandra and Hairer's Feynman diagram approach, Linares, Otto, Tempelmayr, and Tsatsoulis recently proposed an inductive proof based on the spectral gap inequality by using their multiindex language. Inspired by their approach, Hairer and Steele also obtained an inductive proof by using the regularity structure language. In this talk, we introduce an extension of the regularity structure including integrability exponents, and provide a simpler proof of BPHZ theorem.
This talk is based on a joint work with Ismael Bailleul (Université de Bretagne Occidentale).
2024-03-07T00:00:00+01:00
Masato Hoshino
Regularity Structures, renormalisation, Singular stochastic PDEs, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-72d748517b1901e6a62c1e7d41e7f4a5.jpg
oai:carmin.tv:global-solutions-to-quadratic-systems-of-stochastic-reaction-diffusion-equations-in-space-dimension-
2024-03-12T11:26:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:global-solutions-to-quadratic-systems-of-stochastic-reaction-diffusion-equations-in-space-dimension-
https://www.carmin.tv/fr/video/global-solutions-to-quadratic-systems-of-stochastic-reaction-diffusion-equations-in-space-dimension-
Global Solutions to Quadratic Systems of Stochastic Reaction-Diffusion Equations in Space-Dimension Two
video/mp4
IHES
With Marta Leocata (LUISS, Roma), we study stochastic perturbations to systems of reaction-diffusion equations, the structure of the noise being deduced from the modeling of chemical reactions in a diffusive regime. I will explain in this talk how to establish the existence of global solutions for four-species quadratic systems in space-dimension two.
2024-03-07T00:00:00+01:00
Julien Vovelle
entropy, global existence, reaction-diffusion equations, diffusion-approximation, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-d542155bc9da16e93e351cc8c3b13033.jpg
oai:carmin.tv:global-solutions-to-quadratic-systems-of-stochastic-reaction-diffusion-equations-in-space-dimensio-1
2024-03-11T17:42:50+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:global-solutions-to-quadratic-systems-of-stochastic-reaction-diffusion-equations-in-space-dimensio-1
https://www.carmin.tv/fr/video/global-solutions-to-quadratic-systems-of-stochastic-reaction-diffusion-equations-in-space-dimensio-1
Global Solutions to Quadratic Systems of Stochastic Reaction-Diffusion Equations in Space-Dimension Two
video/mp4
IHES
With Marta Leocata (LUISS, Roma), we study stochastic perturbations to systems of reaction-diffusion equations, the structure of the noise being deduced from the modeling of chemical reactions in a diffusive regime. I will explain in this talk how to establish the existence of global solutions for four-species quadratic systems in space-dimension two.
2024-03-07T00:00:00+01:00
Julien Vovelle
entropy, global existence, reaction-diffusion equations, diffusion-approximation, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
oai:carmin.tv:dominated-representations-intersections-and-large-deviations-1
2024-03-12T10:15:29+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:dominated-representations-intersections-and-large-deviations-1
https://www.carmin.tv/fr/video/dominated-representations-intersections-and-large-deviations-1
Dominated Representations, Intersections and Large Deviations
video/mp4
IHES
We show that mean distortions and growth rates determine rough similarity classes of hyperbolic metrics in groups, and discuss its relation to the rigidity of dominated representations and concentration phenomena for counting measures on large balls.
Joint work with Stephen Cantrell (Warwick).
2024-03-06T00:00:00+01:00
Ryokichi Tanaka
large deviation principle, hyperbolic group, Patterson-Sullivan measure, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-096e0cfbda84b84bbaf1f7e3d619d3dd.jpg
oai:carmin.tv:mathematical-foundation-of-various-mcmc-methods
2024-03-08T11:26:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:mathematical-foundation-of-various-mcmc-methods
https://www.carmin.tv/fr/video/mathematical-foundation-of-various-mcmc-methods
Mathematical Foundation of Various MCMC Methods
video/mp4
IHES
Combinatorial optimization problems are ubiquitous in various fields of practical and theoretical interest. The famous traveling salesman problem is one of them. One approach to tackle those problems is to use an Ising model whose Hamiltonian $H$ takes its minimum at a spin configuration, called a ground state, which corresponds to an optimal solution to the corresponding original problem. Standard MCMC methods, such as the Glauber dynamics and the Metropolis algorithm, have been used for decades to sample the Gibbs distribution, which is proportional to $e^{-H/T}$, hence close to the uniform distribution over the ground states when the temperature $T$ is very small. However, those MCMC methods are based on single-spin flip rules, hence prone to being slow. In this talk, I will explain three other MCMC methods, two among which are based on multi-spin flip rules, hence potentially fast. I will show several mathematical results, as well as numerical results to compare which is better in which context. This talk is based on joint work with Bruno Hideki Fukushima-Kimura and many others involved in the CREST project for the past five years.
2024-03-06T00:00:00+01:00
Akira Sakai
percolation, the Ising model, the φ4 model, self-avoiding walk, lattice trees and lattice animals, oriented percolation and the contact process, random walk with reinforcement, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-6bb1801ec15b7dd04c0159d07c1d9565.jpg
oai:carmin.tv:refined-cauchy-littlewood-identities-and-their-applications-to-kpz-models
2024-03-08T11:28:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:refined-cauchy-littlewood-identities-and-their-applications-to-kpz-models
https://www.carmin.tv/fr/video/refined-cauchy-littlewood-identities-and-their-applications-to-kpz-models
Refined Cauchy/Littlewood Identities and Their Applications to KPZ Models
video/mp4
IHES
The Cauchy identity is a formula about a sum of a product of two Schur functions over partitions and plays an important role in combinatorics, representation theory, and integrable probability. Some generalizations about such as sums of Macdonald polynomials and skew Shur functions are also known.
In this talk, I will report our recent works[1,2] with Matteo Mucciconi (Warwick University) and Tomohiro Sasamoto (Tokyo Institute of Technology) on the identities connecting the sums about the q-Whittaker functions (the case $t=0$ of the Macdonald polynomial) and the skew Schur functions. They can be considered as refinements of the Cauchy/Littlewood identities. We give a proof of them based on algebraic combinatorics: We introduce a deterministic time evolutions called the skew RSK dynamics and show that one can linearize the dynamics by using some techniques of the affine crystal. The combinatorial objects obtained from the linearized one can be seen as building blocks of sum about the q-Whittker functions while those from the skew RSK dynamics itself are associated to the sum about the skew Schur functions.
In the language of the integrable probability, the identities can be regarded as relations between two probability measures, the full space/half space q-Whittaker measures and the periodic/free boundary Schur measures. The former measures are related to various KPZ models while the latter ones are typical models of determinantal/Pfaffian and point processes. From these relations we can immediately get the Fredholm determinant/Pfaffian formulas for distribution functions of certain random variables for KPZ models.
[1] T. Imamura, M. Mucciconi, and T. Sasamoto, Forum of Mathematics, Pi 11(e27) 1-101
[2] T. Imamura, M. Mucciconi, and T. Sasamoto, arXiv:2204.08420
2024-03-06T00:00:00+01:00
Takashi Imamura
integrable probability, Kardar-Parisi-Zhang universality, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-6ee14dc96de1a74f48cf3ec535e3d148.jpg
oai:carmin.tv:fredrickson-andersen-2-spin-facilitated-model-sharp-threshold
2024-03-12T10:39:13+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:fredrickson-andersen-2-spin-facilitated-model-sharp-threshold
https://www.carmin.tv/fr/video/fredrickson-andersen-2-spin-facilitated-model-sharp-threshold
Fredrickson-Andersen $2$-spin Facilitated Model: Sharp Threshold
video/mp4
IHES
The Fredrickson-Andersen $2$-spin facilitated model (FA-$2$f) on $\mathbb Z^d$ is a paradigmatic interacting particle system with kinetic constraints (KCM) featuring cooperative and glassy dynamics. For FA-$2$f vacancies facilitate motion: a particle can be created/killed on a site only if at least $2$ of its nearest neighbors are empty. We will present sharp results for the first time, $\tau$, at which the origin is emptied for the stationary process when the density of empty sites ($q$) is small. In any dimension $d\geq 2$ it holds $$\tau\sim
\exp\left(\frac{d\lambda(d,2)+o(1)}{q^{1/(d-1)}}\right)$$ w.h.p., with $\lambda(d,2)$ the threshold constant for the $2$-neighbour bootstrap percolation on $\mathbb Z^d$.
We will explain the dominant relaxation mechanism leading to this result, give a flavour of the proof techniques, and discuss further results that can be obtained via our technique for more general KCM, including full universality results in two dimensions. Joint work with I.Hartarsky and F.Martinelli.
2024-03-06T00:00:00+01:00
Cristina Toninelli
Poincaré inequality, interacting particle systems, Glauber dynamics, Kinetically constrained models, Sharp threshold, Bootstrap percolation, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-9a855c70d8f82bccc543d5489b510818.jpg
oai:carmin.tv:sharp-interface-limit-for-glauber-kawasaki-process
2024-03-08T11:40:02+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:sharp-interface-limit-for-glauber-kawasaki-process
https://www.carmin.tv/fr/video/sharp-interface-limit-for-glauber-kawasaki-process
Sharp Interface Limit for Glauber-Kawasaki Process
video/mp4
IHES
We discuss scaling limits for Glauber-Kawasaki process. The Glauber-Kawasaki process has been introduced by De Masi, Ferrari and Lebowitz to study a reaction-diffusion equation from a microscopic interacting system. They have derived a reaction-diffusion equation as a limiting equation of the density of particles. This limit is usually called hydrodynamic limit. In this talk, I will focus on several scaling limits related to this hydrodynamic limit. Especially, I will discuss a sharp interface limit for this particle system and its large deviation rate function.
2024-03-06T00:00:00+01:00
Kenkichi Tsunoda
large deviations, reaction-diffusion equation, Sharp interface limit, motion by mean curvature, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-2de62bc6da7caf8e21e6b3a80af83e24.jpg
oai:carmin.tv:cutoff-for-the-transience-time-for-the-ssep-with-traps-and-the-one-dimensional-facilitated-exclusion
2024-03-08T11:44:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:cutoff-for-the-transience-time-for-the-ssep-with-traps-and-the-one-dimensional-facilitated-exclusion
https://www.carmin.tv/fr/video/cutoff-for-the-transience-time-for-the-ssep-with-traps-and-the-one-dimensional-facilitated-exclusion
Cutoff for the Transience Time for the SSEP with Traps and the One-Dimensional Facilitated Exclusion Process (FEP)
video/mp4
IHES
The facilitated exclusion process is a toy model for phase separation, where particles can jump to an empty neighboring site iff their other neighboring site is occupied. Because of this kinetic constraint, at low densities $\rho\leq 1/2$, the FEP ultimately reaches a frozen state where particles are all surrounded by empty sites, whereas at large densities $\rho>1/2$, the FEP reaches an ergodic component where it can be mapped to the classical SSEP. In this talk, I will present a new mapping of the FEP to a process that we call SSEP with traps, that displays the same frozen/ergodic phases. I will then focus on the estimation on the transience time needed to reach either an ergodic or frozen state for this model started from the "worst" possible state, which undergoes a cutoff as the size of the system diverges. I will then explore the consequences of this transience time cutoff on the mixing time on the FEP, and on the mixing time of both processes. Based on JW with Brune Massoulié (Université Paris Dauphine).
2024-03-06T00:00:00+01:00
Clément Erignoux
cutoff phenomenon, Kinetically constrained models, active absorbing transition, interacting lattice gases, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-39efb2b2d8b13680a4114715e394c608.jpg
oai:carmin.tv:a-statistical-physics-approach-to-the-sine-beta-process-and-other-random-point-processes
2024-03-12T10:12:55+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:a-statistical-physics-approach-to-the-sine-beta-process-and-other-random-point-processes
https://www.carmin.tv/fr/video/a-statistical-physics-approach-to-the-sine-beta-process-and-other-random-point-processes
A Statistical Physics Approach to the Sine Beta Process and Other Random Point Processes
video/mp4
IHES
The Sine process (corresponding to inverse temperature beta equal to 2) is an ubiquitous determinantal point process. It appears as the bulk limit of many particle systems in various contexts (random matrix ensembles, zeros of L-functions, growth models etc.) Its universality properties are fascinating. There is also a whole family of Sine beta processes, introduced by Valko and Virag, as the bulk limit of Gaussian beta ensembles, for any positive beta. As soon as beta is different from 2, much less is known. I will explain how tools from classical statistical mechanics such as Dobrushin-Lanford-Ruelle (DLR) can be used to better understand their structure. This will be based on a joint work with David Dereudre, Adrien Hardy (Université de Lille), and Thomas Leblé (Université Paris Cité) but I will also review other - more recent – applications.
2024-03-06T00:00:00+01:00
Mylène Maïda
statistical mechanics, Coulomb gases, random matrices, point processes, number rigidity, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-9dfde6b033b1db2c990d02272f8e360c.jpg
oai:carmin.tv:dominated-representations-intersections-and-large-deviations
2024-03-12T10:41:24+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:dominated-representations-intersections-and-large-deviations
https://www.carmin.tv/fr/video/dominated-representations-intersections-and-large-deviations
Dominated Representations, Intersections and Large Deviations
video/mp4
IHES
We show that mean distortions and growth rates determine rough similarity classes of hyperbolic metrics in groups, and discuss its relation to the rigidity of dominated representations and concentration phenomena for counting measures on large balls. Joint work with Stephen Cantrell (Warwick).
2024-03-06T00:00:00+01:00
Ryokichi Tanaka
large deviation principle, hyperbolic group, Patterson-Sullivan measure, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-3-4
2024-03-05T18:04:01+01:00
videos:institution:ihes
videos:collection:jonathan-pila-point-counting-and-the-zilber-pink-conjecture
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-3-4
https://www.carmin.tv/fr/video/point-counting-and-the-zilber-pink-conjecture-3-4
Point-Counting and the Zilber-Pink Conjecture (3/4)
video/mp4
IHES
The Zilber-Pink conjecture is a diophantine finiteness conjecture. It unifies and gives a far-reaching generalization of the classical Mordell-Lang and Andre-Oort conjectures, and is wide open in general.
Point-counting results for definable sets in o-minimal structures provide a strategy for proving suitable cases which has had some success, in particular in its use in proving the Andre-Oort conjecture.
The course will describe the Zilber-Pink conjecture and the point-counting approach to proving cases of it, eventually concentrating on the case of a curve in a power of the modular curve.
We will describe the model-theoretic contexts of the conjectures and techniques, and the essential arithmetic ingredients.
2024-03-05T00:00:00+01:00
Jonathan Pila
Zilber-Pink conjecture, unlikely intersection, o-minimal structure, Researchers, Graduate Students
en
Jonathan Pila : Point-Counting and the Zilber-Pink Conjecture / 20/02/2024 - 12/03/2024
https://www.carmin.tv/uploads/video/video-72801e43bdf93762dac5c36f5d87fec9.jpg
oai:carmin.tv:a-stable-version-of-gromovs-angle-shrinking-problem-and-its-index-theoretic-applications-part-ii
2024-02-28T21:44:01+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:a-stable-version-of-gromovs-angle-shrinking-problem-and-its-index-theoretic-applications-part-ii
https://www.carmin.tv/fr/video/a-stable-version-of-gromovs-angle-shrinking-problem-and-its-index-theoretic-applications-part-ii
A stable version of Gromov’s angle-shrinking problem and its index theoretic applications (Part II)
video/mp4
IHES
In this talk, I will present a proof of a stable algebraic version of Gromov’s angle shrinking problem, and explain its application to our proof of Gromov’s dihedral rigidity conjecture. In particular, I will explain how it is used in our computation of the Fredholm index of the Dirac type operators on manifolds with polyhedral boundary. This talk is based on joint work with Zhizhang Xie and Guoliang Yu.
2024-02-07T00:00:00+01:00
Jinming Wang
Researchers
en
https://www.carmin.tv/uploads/video/video-52fc4fdb7d6ba9c4bdfdd9ae25269aed.jpg
oai:carmin.tv:a-stable-version-of-gromovs-angle-shrinking-problem-and-its-index-theoretic-applications-part-i
2024-02-28T21:48:01+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:a-stable-version-of-gromovs-angle-shrinking-problem-and-its-index-theoretic-applications-part-i
https://www.carmin.tv/fr/video/a-stable-version-of-gromovs-angle-shrinking-problem-and-its-index-theoretic-applications-part-i
A stable version of Gromov’s angle-shrinking problem and its index theoretic applications (Part I)
video/mp4
IHES
In this talk, we will discuss Gromov’s angle shrinking problem and how it enters into our proof of Gromov’s dihedral extremality/rigidity conjecture. More precisely, we proved Gromov’s dihedral extremality/rigidity conjecture via a new index theorem for manifolds with polyhedral boundary. One of main steps of the proof of this new index theorem is to compute the Fredholm index of a relevant Dirac type operator (with appropriate boundary conditions) on a polyhedral corner. A key ingredient of our proof is a deformation technique that allows us to reduce the computation of the Fredholm index to a model case where the computation becomes more or less straightforward. The deformation technique relies on a version of Gromov’s angle shrinking problem. While the original Gromov’s angle shrinking problem is still open, fortunately our deformation technique only requires a stable and algebraic version of Gromov’s angle shrinking problem, which turns out to be true in general. We will introduce this stable and algebraic version of Gromov’s angle shrinking problem, and explain how it is used in the proof of our index theorem. The talk is based on joint work with Jinmin Wang and Guoliang Yu.
2024-02-07T00:00:00+01:00
Zhizhang Xie
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-411c1a303c035a8e1e2edb8e42396d52.jpg
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-2-4
2024-02-27T22:38:01+01:00
videos:institution:ihes
videos:collection:jonathan-pila-point-counting-and-the-zilber-pink-conjecture
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-2-4
https://www.carmin.tv/fr/video/point-counting-and-the-zilber-pink-conjecture-2-4
Point-Counting and the Zilber-Pink Conjecture (2/4)
video/mp4
IHES
The Zilber-Pink conjecture is a diophantine finiteness conjecture. It unifies and gives a far-reaching generalization of the classical Mordell-Lang and Andre-Oort conjectures, and is wide open in general.
Point-counting results for definable sets in o-minimal structures provide a strategy for proving suitable cases which has had some success, in particular in its use in proving the Andre-Oort conjecture.
The course will describe the Zilber-Pink conjecture and the point-counting approach to proving cases of it, eventually concentrating on the case of a curve in a power of the modular curve.
We will describe the model-theoretic contexts of the conjectures and techniques, and the essential arithmetic ingredients.
2024-02-27T00:00:00+01:00
Jonathan Pila
Zilber-Pink conjecture, unlikely intersection, o-minimal structure, Researchers, Graduate Students
en
Jonathan Pila : Point-Counting and the Zilber-Pink Conjecture / 20/02/2024 - 12/03/2024
https://www.carmin.tv/uploads/video/video-fbf556691fe94eeb8045c65c73494966.jpg
oai:carmin.tv:introduction-to-numerical-relativity-1-2
2024-02-26T13:39:18+01:00
videos:institution:ihes
videos:collection:balzan-lectures
oai:carmin.tv:introduction-to-numerical-relativity-1-2
https://www.carmin.tv/fr/video/introduction-to-numerical-relativity-1-2
Introduction to Numerical Relativity (1/2)
video/mp4
IHES
Numerical General Relativity is the art of solving Einstein’s Field Equations with computational methods. These lectures will review the formalism currently employed for astrophysical simulations in strong-gravity, notably comprising compact binaries, gravitational collapse and gravitational waves. They will cover the following topics: 3+1 formulation of Einstein’s equations, the initial data problem, the evolution problem, the gauge choice and the extraction of gauge-invariant quantities.
A selection of breakthrough results for gravitational-wave astronomy will also be presented.
2024-02-22T00:00:00+01:00
Sebastiano Bernuzzi
Gravitational waves, Numerical Relativity, Neutron Stars, Researchers
en
https://www.carmin.tv/uploads/video/video-e124c87635341a254ce6ae84ed1c8999.jpg
oai:carmin.tv:introduction-to-numerical-relativity-2-2
2024-02-26T13:35:13+01:00
videos:institution:ihes
videos:collection:balzan-lectures
oai:carmin.tv:introduction-to-numerical-relativity-2-2
https://www.carmin.tv/fr/video/introduction-to-numerical-relativity-2-2
Introduction to Numerical Relativity (2/2)
video/mp4
IHES
Numerical General Relativity is the art of solving Einstein’s Field Equations with computational methods. These lectures will review the formalism currently employed for astrophysical simulations in strong-gravity, notably comprising compact binaries, gravitational collapse and gravitational waves. They will cover the following topics: 3+1 formulation of Einstein’s equations, the initial data problem, the evolution problem, the gauge choice and the extraction of gauge-invariant quantities. A selection of breakthrough results for gravitational-wave astronomy will also be presented.
2024-02-22T00:00:00+01:00
Sebastiano Bernuzzi
Gravitational waves, Numerical Relativity, Neutron Stars, Researchers
en
https://www.carmin.tv/uploads/video/video-a197774681fe427926bf9bb4dc11a78c.jpg
oai:carmin.tv:einsteins-path-to-general-relativity
2024-02-26T13:38:01+01:00
videos:institution:ihes
videos:collection:balzan-lectures
oai:carmin.tv:einsteins-path-to-general-relativity
https://www.carmin.tv/fr/video/einsteins-path-to-general-relativity
Einstein's Path to General Relativity
video/mp4
IHES
Einstein's path to the discovery of General Relativity, from 1907 to November 1915, will be described. A particular emphasis will be given to the multi-pronged character of Einstein's strategy.
2024-02-20T00:00:00+01:00
Thibault Damour
general relativity, History and Philosophy of Physics, Researchers
en
https://www.carmin.tv/uploads/video/video-73a6c7a6baf3af44c8f9575cb2af6b0c.jpg
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-1-4
2024-03-12T10:41:42+01:00
videos:institution:ihes
videos:collection:jonathan-pila-point-counting-and-the-zilber-pink-conjecture
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-1-4
https://www.carmin.tv/fr/video/point-counting-and-the-zilber-pink-conjecture-1-4
Point-Counting and the Zilber-Pink Conjecture (1/4)
video/mp4
IHES
The Zilber-Pink conjecture is a diophantine finiteness conjecture. It unifies and gives a far-reaching generalization of the classical Mordell-Lang and Andre-Oort conjectures, and is wide open in general.
Point-counting results for definable sets in o-minimal structures provide a strategy for proving suitable cases which has had some success, in particular in its use in proving the Andre-Oort conjecture.
The course will describe the Zilber-Pink conjecture and the point-counting approach to proving cases of it, eventually concentrating on the case of a curve in a power of the modular curve.
We will describe the model-theoretic contexts of the conjectures and techniques, and the essential arithmetic ingredients.
2024-02-20T00:00:00+01:00
Jonathan Pila
Zilber-Pink conjecture, unlikely intersection, o-minimal structure, Researchers, Graduate Students
en
Jonathan Pila : Point-Counting and the Zilber-Pink Conjecture / 20/02/2024 - 12/03/2024
https://www.carmin.tv/uploads/video/video-e0c078da0107cc2b26db0cf2ae9a548a.jpg
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics-5
2024-02-15T18:54:02+01:00
videos:institution:ihes
videos:collection:hadamard-lectures-2024-maria-colombo-flows-of-irregular-vector-fields-in-fluid-dynamics
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics-5
https://www.carmin.tv/fr/video/flows-of-irregular-vector-fields-in-fluid-dynamics-5
Flows of Irregular Vector Fields in Fluid Dynamics
video/mp4
IHES
Given a vector field in the euclidean space, the classical Cauchy-Lipschitz theorem shows existence and uniqueness of its flow provided the vector field is sufficiently smooth. The theorem looses its validity as soon as the vector field is slightly less regular. However, in 1989, Di Perna and Lions introduced a generalized notion of flow, consisting of a suitable selection among the trajectories of the associated ODE, and they showed existence, uniqueness and stability for this notion of flow for much less regular vector fields.
The course presents a modern view, new results and open problems in the context of flows of irregular vector fields.
We develop, in this framework, recent ideas and techniques such as quantitative regularity estimates on the flow of Sobolev vector fields, nonuniqueness of solutions via convex integration, similarity constructions, mixing, enhanced and anomalous dissipation.
Such ideas have been proved useful to study nonlinear PDEs as well and we apply these results and techniques in the context of the mathematical understanding of phenomena in fluid dynamics, in particular for the Euler and Navier-Stokes equations and in relation to the Kolmogorov theory of turbulence.
2024-02-15T00:00:00+01:00
Maria Colombo
convex integration, Navier-Stokes equation, nonlinear PDEs, Euler equation, Sobolev vector fields, Researchers, Graduate Students
en
Hadamard Lectures 2024 – Maria Colombo – Flows of Irregular Vector Fields in Fluid Dynamics / 30/01/2024 - 15/02/2024
https://www.carmin.tv/uploads/video/video-3b8915a111f6116f9532de5cd80d8060.jpg
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics-4
2024-02-15T12:43:38+01:00
videos:institution:ihes
videos:collection:hadamard-lectures-2024-maria-colombo-flows-of-irregular-vector-fields-in-fluid-dynamics
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics-4
https://www.carmin.tv/fr/video/flows-of-irregular-vector-fields-in-fluid-dynamics-4
Flows of Irregular Vector Fields in Fluid Dynamics
video/mp4
IHES
Given a vector field in the euclidean space, the classical Cauchy-Lipschitz theorem shows existence and uniqueness of its flow provided the vector field is sufficiently smooth. The theorem looses its validity as soon as the vector field is slightly less regular. However, in 1989, Di Perna and Lions introduced a generalized notion of flow, consisting of a suitable selection among the trajectories of the associated ODE, and they showed existence, uniqueness and stability for this notion of flow for much less regular vector fields.
The course presents a modern view, new results and open problems in the context of flows of irregular vector fields.
We develop, in this framework, recent ideas and techniques such as quantitative regularity estimates on the flow of Sobolev vector fields, nonuniqueness of solutions via convex integration, similarity constructions, mixing, enhanced and anomalous dissipation.
Such ideas have been proved useful to study nonlinear PDEs as well and we apply these results and techniques in the context of the mathematical understanding of phenomena in fluid dynamics, in particular for the Euler and Navier-Stokes equations and in relation to the Kolmogorov theory of turbulence.
2024-02-14T00:00:00+01:00
Maria Colombo
convex integration, Navier-Stokes equation, nonlinear PDEs, Euler equation, Sobolev vector fields, Researchers, Graduate Students
en
Hadamard Lectures 2024 – Maria Colombo – Flows of Irregular Vector Fields in Fluid Dynamics / 30/01/2024 - 15/02/2024
https://www.carmin.tv/uploads/video/video-79d9e7c557611e7e418687e261ca4cd1.jpg
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics-3
2024-02-13T18:00:02+01:00
videos:institution:ihes
videos:collection:hadamard-lectures-2024-maria-colombo-flows-of-irregular-vector-fields-in-fluid-dynamics
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics-3
https://www.carmin.tv/fr/video/flows-of-irregular-vector-fields-in-fluid-dynamics-3
Flows of Irregular Vector Fields in Fluid Dynamics
video/mp4
IHES
Given a vector field in the euclidean space, the classical Cauchy-Lipschitz theorem shows existence and uniqueness of its flow provided the vector field is sufficiently smooth. The theorem looses its validity as soon as the vector field is slightly less regular. However, in 1989, Di Perna and Lions introduced a generalized notion of flow, consisting of a suitable selection among the trajectories of the associated ODE, and they showed existence, uniqueness and stability for this notion of flow for much less regular vector fields.
The course presents a modern view, new results and open problems in the context of flows of irregular vector fields.
We develop, in this framework, recent ideas and techniques such as quantitative regularity estimates on the flow of Sobolev vector fields, nonuniqueness of solutions via convex integration, similarity constructions, mixing, enhanced and anomalous dissipation.
Such ideas have been proved useful to study nonlinear PDEs as well and we apply these results and techniques in the context of the mathematical understanding of phenomena in fluid dynamics, in particular for the Euler and Navier-Stokes equations and in relation to the Kolmogorov theory of turbulence.
2024-02-13T00:00:00+01:00
Maria Colombo
convex integration, Navier-Stokes equation, nonlinear PDEs, Euler equation, Sobolev vector fields, Researchers, Graduate Students
en
Hadamard Lectures 2024 – Maria Colombo – Flows of Irregular Vector Fields in Fluid Dynamics / 30/01/2024 - 15/02/2024
https://www.carmin.tv/uploads/video/video-267d597b1e42354962461829fc3512ef.jpg
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics-2
2024-02-12T16:18:01+01:00
videos:institution:ihes
videos:collection:hadamard-lectures-2024-maria-colombo-flows-of-irregular-vector-fields-in-fluid-dynamics
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics-2
https://www.carmin.tv/fr/video/flows-of-irregular-vector-fields-in-fluid-dynamics-2
Flows of Irregular Vector Fields in Fluid Dynamics
video/mp4
IHES
Given a vector field in the euclidean space, the classical Cauchy-Lipschitz theorem shows existence and uniqueness of its flow provided the vector field is sufficiently smooth. The theorem looses its validity as soon as the vector field is slightly less regular. However, in 1989, Di Perna and Lions introduced a generalized notion of flow, consisting of a suitable selection among the trajectories of the associated ODE, and they showed existence, uniqueness and stability for this notion of flow for much less regular vector fields.
The course presents a modern view, new results and open problems in the context of flows of irregular vector fields.
We develop, in this framework, recent ideas and techniques such as quantitative regularity estimates on the flow of Sobolev vector fields, nonuniqueness of solutions via convex integration, similarity constructions, mixing, enhanced and anomalous dissipation.
Such ideas have been proved useful to study nonlinear PDEs as well and we apply these results and techniques in the context of the mathematical understanding of phenomena in fluid dynamics, in particular for the Euler and Navier-Stokes equations and in relation to the Kolmogorov theory of turbulence.
2024-02-12T00:00:00+01:00
Maria Colombo
convex integration, Navier-Stokes equation, nonlinear PDEs, Euler equation, Sobolev vector fields, Researchers, Graduate Students
en
Hadamard Lectures 2024 – Maria Colombo – Flows of Irregular Vector Fields in Fluid Dynamics / 30/01/2024 - 15/02/2024
https://www.carmin.tv/uploads/video/video-e3d1086fef0e5ad055c79d083bd5090a.jpg
oai:carmin.tv:asymptotic-structure-of-gravity-and-bms-group-at-spatial-infinity-1-2
2024-02-08T16:10:01+01:00
videos:institution:ihes
videos:collection:balzan-lectures
oai:carmin.tv:asymptotic-structure-of-gravity-and-bms-group-at-spatial-infinity-1-2
https://www.carmin.tv/fr/video/asymptotic-structure-of-gravity-and-bms-group-at-spatial-infinity-1-2
Asymptotic Structure of Gravity and BMS Group at Spatial Infinity (1/2)
video/mp4
IHES
The asymptotic structure of gravity in the asymptotically flat context will be described at spatial infinity by Hamiltonian methods. The first lecture will provide the main ideas, give the Poisson bracket algebra of the BMS charges and propose a supertranslation-invariant definition of the angular momentum. The second lecture will discuss the connection with null infinity and provide in particular a justification of Strominger's matching conditions of the fields between past null infinity and future null infinity.
2024-02-07T00:00:00+01:00
Marc Henneaux
general relativity, Asymptotic structure, Researchers
en
https://www.carmin.tv/uploads/video/video-e1a5ea3793d0fea6851c0169db430b2b.jpg
oai:carmin.tv:asymptotic-structure-of-gravity-and-bms-group-at-spatial-infinity-2-2
2024-02-08T16:14:02+01:00
videos:institution:ihes
videos:collection:balzan-lectures
oai:carmin.tv:asymptotic-structure-of-gravity-and-bms-group-at-spatial-infinity-2-2
https://www.carmin.tv/fr/video/asymptotic-structure-of-gravity-and-bms-group-at-spatial-infinity-2-2
Asymptotic Structure of Gravity and BMS Group at Spatial Infinity (2/2)
video/mp4
IHES
The asymptotic structure of gravity in the asymptotically flat context will be described at spatial infinity by Hamiltonian methods. The first lecture will provide the main ideas, give the Poisson bracket algebra of the BMS charges and propose a supertranslation-invariant definition of the angular momentum. The second lecture will discuss the connection with null infinity and provide in particular a justification of Strominger's matching conditions of the fields between past null infinity and future null infinity.
2024-02-07T00:00:00+01:00
Marc Henneaux
general relativity, Asymptotic structure, Researchers
en
https://www.carmin.tv/uploads/video/video-743e440098fc4211f07d5adcf5840a39.jpg
oai:carmin.tv:analytic-stacks-27-29
2024-02-06T14:20:20+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-27-29
https://www.carmin.tv/fr/video/analytic-stacks-27-29
Analytic Stacks (27/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2024-02-02T00:00:00+01:00
Peter Scholze
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-92a127efcb13442e4fec4ec7aa03db75.jpg
oai:carmin.tv:generic-regularity-in-obstacle-problems
2024-02-02T11:54:02+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:generic-regularity-in-obstacle-problems
https://www.carmin.tv/fr/video/generic-regularity-in-obstacle-problems
Generic regularity in obstacle problems
video/mp4
IHES
The classical obstacle problem involves determining the equilibrium state of an elastic membrane that is restricted to remain above a predetermined obstacle. By classical results of Caffarelli, the 'free boundary' — the demarcation line where the obstacle and membrane meet — is smooth outside a set of singular points. Also, explicit examples show that the singular set could be, in general, as large as the regular set. This talk aims to introduce this beautiful problem and describe some classical and recent results on the regularity of the free boundary.
2024-01-24T00:00:00+01:00
Alessio Figalli
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-be3ecbcf3fec700708bb461b501e5a94.jpg
oai:carmin.tv:generic-regularity-for-minimizing-hypersurfaces-in-9-and-10-dimensions
2024-02-02T11:54:02+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:generic-regularity-for-minimizing-hypersurfaces-in-9-and-10-dimensions
https://www.carmin.tv/fr/video/generic-regularity-for-minimizing-hypersurfaces-in-9-and-10-dimensions
Generic regularity for minimizing hypersurfaces in 9 and 10 dimensions
video/mp4
IHES
I will describe recent joint work with Christos Mantoulidis and Felix Schulze in which we prove that in 9 and 10 ambient dimensions, area-minimizing hypersurfaces are generically smooth.
2024-01-24T00:00:00+01:00
Otis Chodosh
Researchers
en
https://www.carmin.tv/uploads/video/video-d1368798344fcb5447daa02595d7b3e4.jpg
oai:carmin.tv:analytic-stacks-26-29
2024-02-07T15:49:46+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-26-29
https://www.carmin.tv/fr/video/analytic-stacks-26-29
Analytic Stacks (26/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2024-01-31T00:00:00+01:00
Dustin Clausen
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-eb1e5896cebf05d069ef8ebb24bd1579.jpg
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics-1
2024-02-01T17:07:30+01:00
videos:institution:ihes
videos:collection:hadamard-lectures-2024-maria-colombo-flows-of-irregular-vector-fields-in-fluid-dynamics
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics-1
https://www.carmin.tv/fr/video/flows-of-irregular-vector-fields-in-fluid-dynamics-1
Flows of Irregular Vector Fields in Fluid Dynamics
video/mp4
IHES
Given a vector field in the euclidean space, the classical Cauchy-Lipschitz theorem shows existence and uniqueness of its flow provided the vector field is sufficiently smooth. The theorem looses its validity as soon as the vector field is slightly less regular. However, in 1989, Di Perna and Lions introduced a generalized notion of flow, consisting of a suitable selection among the trajectories of the associated ODE, and they showed existence, uniqueness and stability for this notion of flow for much less regular vector fields.
The course presents a modern view, new results and open problems in the context of flows of irregular vector fields.
We develop, in this framework, recent ideas and techniques such as quantitative regularity estimates on the flow of Sobolev vector fields, nonuniqueness of solutions via convex integration, similarity constructions, mixing, enhanced and anomalous dissipation.
Such ideas have been proved useful to study nonlinear PDEs as well and we apply these results and techniques in the context of the mathematical understanding of phenomena in fluid dynamics, in particular for the Euler and Navier-Stokes equations and in relation to the Kolmogorov theory of turbulence.
2024-01-31T00:00:00+01:00
Maria Colombo
convex integration, Navier-Stokes equation, nonlinear PDEs, Euler equation, Sobolev vector fields, Researchers, Graduate Students
en
Hadamard Lectures 2024 – Maria Colombo – Flows of Irregular Vector Fields in Fluid Dynamics / 30/01/2024 - 15/02/2024
https://www.carmin.tv/uploads/video/video-d30130b2f6d5a3b7c521491ad447d417.jpg
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics
2024-03-12T10:48:42+01:00
videos:institution:ihes
videos:collection:hadamard-lectures-2024-maria-colombo-flows-of-irregular-vector-fields-in-fluid-dynamics
oai:carmin.tv:flows-of-irregular-vector-fields-in-fluid-dynamics
https://www.carmin.tv/fr/video/flows-of-irregular-vector-fields-in-fluid-dynamics
Flows of Irregular Vector Fields in Fluid Dynamics
video/mp4
IHES
Given a vector field in the euclidean space, the classical Cauchy-Lipschitz theorem shows existence and uniqueness of its flow provided the vector field is sufficiently smooth. The theorem looses its validity as soon as the vector field is slightly less regular. However, in 1989, Di Perna and Lions introduced a generalized notion of flow, consisting of a suitable selection among the trajectories of the associated ODE, and they showed existence, uniqueness and stability for this notion of flow for much less regular vector fields.
The course presents a modern view, new results and open problems in the context of flows of irregular vector fields.
We develop, in this framework, recent ideas and techniques such as quantitative regularity estimates on the flow of Sobolev vector fields, nonuniqueness of solutions via convex integration, similarity constructions, mixing, enhanced and anomalous dissipation.
Such ideas have been proved useful to study nonlinear PDEs as well and we apply these results and techniques in the context of the mathematical understanding of phenomena in fluid dynamics, in particular for the Euler and Navier-Stokes equations and in relation to the Kolmogorov theory of turbulence.
2024-01-30T00:00:00+01:00
Maria Colombo
convex integration, Navier-Stokes equation, nonlinear PDEs, Euler equation, Sobolev vector fields, Researchers, Graduate Students
en
Hadamard Lectures 2024 – Maria Colombo – Flows of Irregular Vector Fields in Fluid Dynamics / 30/01/2024 - 15/02/2024
https://www.carmin.tv/uploads/video/video-f5124dcef663c667a79aa6d908c9106a.jpg
oai:carmin.tv:stable-homotopy-group-higher-algebra-and-the-telescope-conjecture
2024-03-04T15:42:32+01:00
videos:institution:ihes
videos:collection:conference-de-lancement-de-la-chaire-jean-pierre-bourguignon
oai:carmin.tv:stable-homotopy-group-higher-algebra-and-the-telescope-conjecture
https://www.carmin.tv/fr/video/stable-homotopy-group-higher-algebra-and-the-telescope-conjecture
Stable Homotopy Group, Higher Algebra and the Telescope Conjecture
video/mp4
IHES
A fundamental motivating problem in homotopy theory is the attempt to the study of stable homotopy groups of spheres. The mathematical object that binds stable homotopy groups together is a spectrum. Spectra are the homotopy theorist abelian groups, they have a fundamental place in algebraic topology but also appear in arithmetic geometry, differential topology, mathematical physics and symplectic geometry. In a similar vein to the way that abelian groups are the bedrock of algebra and algebraic geometry we can take a similar approach of spectra. I will discuss the picture that emerges and how one can use it to learn about the stable homotopy groups of spheres.
2024-01-26T00:00:00+01:00
Tomer Schlank
stable homotopy groups, Homotopy groups of sphere, K theory, Researchers, Graduate Students
en
Conférence de lancement de la Chaire Jean-Pierre Bourguignon / Grâce à un don exceptionnel effectué aux fonds propres de Friends of IHES, l’organisation partenaire de l’Institut aux États-Unis, par Claire-Lise et Philippe Tondeur d’une part, ainsi que Marilyn et Jim Simons de l’autre à travers la Simons Foundation International, l’IHES est fier d’annoncer la création d’une Chaire de professeur permanent au nom de Jean-Pierre Bourguignon, directeur de l’IHES de 1994 à 2013 et désormais professeur honoraire Nicolaas Kuiper à l’Institut. Le premier détenteur de la Chaire Jean-Pierre Bourguignon est Dustin Clausen, qui a rejoint l’Institut en avril 2023.
Pour marquer le lancement de la Chaire Jean-Pierre Bourguignon, une conférence scientifique est organisée par Dustin Clausen vendredi 26 janvier.
Le contenu scientifique de cette journée sera tourné vers la géométrie arithmétique, la géométrie algébrique et la géométrie analytique ainsi que la topologie algébrique. / Dustin Clausen (IHES) / 26/01/2024 - 26/01/2024 / https://indico.math.cnrs.fr/event/11422/
https://www.carmin.tv/uploads/video/video-62efeca51b00b10d6c25bbef245361aa.jpg
oai:carmin.tv:stacks-in-the-p-adic-hodge-theory-of-rigid-analytic-spaces
2024-01-29T20:54:01+01:00
videos:institution:ihes
videos:collection:conference-de-lancement-de-la-chaire-jean-pierre-bourguignon
oai:carmin.tv:stacks-in-the-p-adic-hodge-theory-of-rigid-analytic-spaces
https://www.carmin.tv/fr/video/stacks-in-the-p-adic-hodge-theory-of-rigid-analytic-spaces
Stacks in the p-adic Hodge Theory of Rigid Analytic Spaces
video/mp4
IHES
I would like to explain in this talk how questions in non-abelian p-adic Hodge theory and in the theory of locally analytic representations of p-adic groups lead to consider new geometric objects attached to rigid analytic spaces, which require to go beyond the formalism of diamonds and are naturally defined in the analytic geometry framework developed by Clausen-Scholze. Based on a joint project (very much in progress) with Anschütz, Rodriguez Camargo and Scholze.
2024-01-26T00:00:00+01:00
Arthur-César Le Bras
p-adic Hodge theory, p-adic geometry, Researchers, Graduate Students
Conférence de lancement de la Chaire Jean-Pierre Bourguignon / Grâce à un don exceptionnel effectué aux fonds propres de Friends of IHES, l’organisation partenaire de l’Institut aux États-Unis, par Claire-Lise et Philippe Tondeur d’une part, ainsi que Marilyn et Jim Simons de l’autre à travers la Simons Foundation International, l’IHES est fier d’annoncer la création d’une Chaire de professeur permanent au nom de Jean-Pierre Bourguignon, directeur de l’IHES de 1994 à 2013 et désormais professeur honoraire Nicolaas Kuiper à l’Institut. Le premier détenteur de la Chaire Jean-Pierre Bourguignon est Dustin Clausen, qui a rejoint l’Institut en avril 2023.
Pour marquer le lancement de la Chaire Jean-Pierre Bourguignon, une conférence scientifique est organisée par Dustin Clausen vendredi 26 janvier.
Le contenu scientifique de cette journée sera tourné vers la géométrie arithmétique, la géométrie algébrique et la géométrie analytique ainsi que la topologie algébrique. / Dustin Clausen (IHES) / 26/01/2024 - 26/01/2024 / https://indico.math.cnrs.fr/event/11422/
https://www.carmin.tv/uploads/video/video-3cab5c752e73dbb8f465cc852e7a81d0.jpg
oai:carmin.tv:modularity-of-abelian-surfaces
2024-01-29T20:58:02+01:00
videos:institution:ihes
videos:collection:conference-de-lancement-de-la-chaire-jean-pierre-bourguignon
oai:carmin.tv:modularity-of-abelian-surfaces
https://www.carmin.tv/fr/video/modularity-of-abelian-surfaces
Modularity of Abelian Surfaces
video/mp4
IHES
We prove the modularity of a positive proportion of abelian surfaces over the rationals. This is joint work in progress with G. Boxer, F. Calegari and T. Gee.
2024-01-26T00:00:00+01:00
Vincent Pilloni
abelian surfaces, Siegel modular forms, Researchers, Graduate Students
Conférence de lancement de la Chaire Jean-Pierre Bourguignon / Grâce à un don exceptionnel effectué aux fonds propres de Friends of IHES, l’organisation partenaire de l’Institut aux États-Unis, par Claire-Lise et Philippe Tondeur d’une part, ainsi que Marilyn et Jim Simons de l’autre à travers la Simons Foundation International, l’IHES est fier d’annoncer la création d’une Chaire de professeur permanent au nom de Jean-Pierre Bourguignon, directeur de l’IHES de 1994 à 2013 et désormais professeur honoraire Nicolaas Kuiper à l’Institut. Le premier détenteur de la Chaire Jean-Pierre Bourguignon est Dustin Clausen, qui a rejoint l’Institut en avril 2023.
Pour marquer le lancement de la Chaire Jean-Pierre Bourguignon, une conférence scientifique est organisée par Dustin Clausen vendredi 26 janvier.
Le contenu scientifique de cette journée sera tourné vers la géométrie arithmétique, la géométrie algébrique et la géométrie analytique ainsi que la topologie algébrique. / Dustin Clausen (IHES) / 26/01/2024 - 26/01/2024 / https://indico.math.cnrs.fr/event/11422/
https://www.carmin.tv/uploads/video/video-6dd97a93d751f3027cdbaab60175f1e5.jpg
oai:carmin.tv:motives-and-ring-stacks
2024-01-29T21:02:02+01:00
videos:institution:ihes
videos:collection:conference-de-lancement-de-la-chaire-jean-pierre-bourguignon
oai:carmin.tv:motives-and-ring-stacks
https://www.carmin.tv/fr/video/motives-and-ring-stacks
Motives and Ring Stacks
video/mp4
IHES
Several interesting cohomology theories can be described through (analytic) ring stacks, e.g. de Rham, Hodge, crystalline, prismatic, Betti, and even etale cohomology under some restrictions on the base. In this talk, I will recall that to any 6-functor formalism one can associate a (presentable) symmetric monoidal (\infty,2)-category. Adopting an extreme Tannaka duality-point of view to formulate the result, I will observe that the symmetric monoidal (\infty,2)-category associated to the motivic 6-functor formalism classifies (certain) ring stacks. This picture helps to explain why one has to pass to analytic geometry to find such ring stacks. (For example, the algebraic de Rham stack of A¹ is not a ring stack of the required form, only the analytic de Rham stack is.)
2024-01-26T00:00:00+01:00
Peter Scholze
higher categories, stacks, motives, Researchers, Graduate Students
Conférence de lancement de la Chaire Jean-Pierre Bourguignon / Grâce à un don exceptionnel effectué aux fonds propres de Friends of IHES, l’organisation partenaire de l’Institut aux États-Unis, par Claire-Lise et Philippe Tondeur d’une part, ainsi que Marilyn et Jim Simons de l’autre à travers la Simons Foundation International, l’IHES est fier d’annoncer la création d’une Chaire de professeur permanent au nom de Jean-Pierre Bourguignon, directeur de l’IHES de 1994 à 2013 et désormais professeur honoraire Nicolaas Kuiper à l’Institut. Le premier détenteur de la Chaire Jean-Pierre Bourguignon est Dustin Clausen, qui a rejoint l’Institut en avril 2023.
Pour marquer le lancement de la Chaire Jean-Pierre Bourguignon, une conférence scientifique est organisée par Dustin Clausen vendredi 26 janvier.
Le contenu scientifique de cette journée sera tourné vers la géométrie arithmétique, la géométrie algébrique et la géométrie analytique ainsi que la topologie algébrique. / Dustin Clausen (IHES) / 26/01/2024 - 26/01/2024 / https://indico.math.cnrs.fr/event/11422/
https://www.carmin.tv/uploads/video/video-a9145a501f12ecbf051fc50ecd5a6a7f.jpg
oai:carmin.tv:analytic-stacks-24-29
2024-03-12T10:50:43+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-24-29
https://www.carmin.tv/fr/video/analytic-stacks-24-29
Analytic Stacks (24/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2024-01-24T00:00:00+01:00
Dustin Clausen
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-201e5500fa32e5d2a2b098c9674a3b57.jpg
oai:carmin.tv:analytic-stacks-23-29
2024-01-19T19:20:03+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-23-29
https://www.carmin.tv/fr/video/analytic-stacks-23-29
Analytic Stacks (23/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2024-01-19T00:00:00+01:00
Peter Scholze
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-8264b0d7c384590b1b972cd3a5df2ba7.jpg
oai:carmin.tv:analytic-stacks-22-29
2024-01-17T21:50:02+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-22-29
https://www.carmin.tv/fr/video/analytic-stacks-22-29
Analytic Stacks (22/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2024-01-17T00:00:00+01:00
Dustin Clausen
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-76b89535d6a6ddbbec5d3b3a97107b30.jpg
oai:carmin.tv:analytic-stacks-21-29
2024-01-12T19:40:01+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-21-29
https://www.carmin.tv/fr/video/analytic-stacks-21-29
Analytic Stacks (21/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2024-01-12T00:00:00+01:00
Peter Scholze
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-be47b36a4c8e48b96e997f0e7892f5e8.jpg
oai:carmin.tv:analytic-stacks-20-29
2024-01-10T19:40:01+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-20-29
https://www.carmin.tv/fr/video/analytic-stacks-20-29
Analytic Stacks (20/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2024-01-10T00:00:00+01:00
Dustin Clausen
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-2d806ed16d3f8a6a7ca0b9892d2b17c2.jpg
oai:carmin.tv:analytic-stacks-9-29
2023-12-23T14:02:02+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-9-29
https://www.carmin.tv/fr/video/analytic-stacks-9-29
Analytic Stacks (9/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-11-22T00:00:00+01:00
Dustin Clausen
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/10_Dustin_Clausen-41d5e79a8f97f5b5f2731df912ac8ee0-video--6a07712ad8ced48797070f1a14c328c9.jpg
oai:carmin.tv:analytic-stacks-8-29
2023-12-23T13:54:02+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-8-29
https://www.carmin.tv/fr/video/analytic-stacks-8-29
Analytic Stacks (8/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-11-17T00:00:00+01:00
Peter Scholze
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/09_Peter_Scholze-c5bf251fba17d030d644c57874c7a6e5-video--1cbca0f625bb327a5efa9f94abbbae50.jpg
oai:carmin.tv:analytic-stacks-4-29
2023-12-23T13:54:02+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-4-29
https://www.carmin.tv/fr/video/analytic-stacks-4-29
Analytic Stacks (4/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-10-27T00:00:00+02:00
Peter Scholze
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/04_Peter_Scholze-62bbc61e0db41efc93228a0c41212b8c-video--c6dc38a8752639fcefad14867bea2f92.jpg
oai:carmin.tv:analytic-stacks-17-29
2023-12-22T11:39:37+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-17-29
https://www.carmin.tv/fr/video/analytic-stacks-17-29
Analytic Stacks (17/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-12-20T00:00:00+01:00
Dustin Clausen
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-2f9d019446b2308aa7cfa251cee0d0d8.jpg
oai:carmin.tv:yvonne-choquet-bruhat-a-mathematician-in-einsteins-universe
2023-12-18T17:50:02+01:00
videos:institution:ihes
videos:collection:day-in-honor-of-yvonne-choquet-bruhats-100-th-birthday
oai:carmin.tv:yvonne-choquet-bruhat-a-mathematician-in-einsteins-universe
https://www.carmin.tv/fr/video/yvonne-choquet-bruhat-a-mathematician-in-einsteins-universe
Yvonne Choquet-Bruhat: a Mathematician in Einstein’s Universe
video/mp4
IHES
Yvonne Choquet-Bruhat has made fundamental contributions to both the mathematical and the physical understanding of Einstein's theory of gravitation.
I will briefly summarize some of her achievements including:
1. The first proof of the existence of general (non analytic) solutions of Einstein's theory, including the first rigorous proof that they involve propagation phenomena at the velocity of light, i.e. gravitational waves;
2. Studies of relativistic fluids and of relativistic magneto-hydrodynamics;
3. A study of the exceptional properties of strong high-frequency gravitational waves;
4. Positivity of mass in a neighborhood of Minkowski space;
5. Causality of supergravity and study of Gauss-Bonnet gravity;
6. Existence proofs for classes of cosmological spacetimes; and
6. New formulations of Einstein's equations that proved crucial to the possibility of
numerically simulating the motion and gravitational radiation of coalescing binary black holes.
2023-12-08T00:00:00+01:00
Thibault Damour
general relativity, Einstein equations, Gravitational waves, Researchers, Graduate Students
en
Day in Honor of Yvonne Choquet-Bruhat’s 100 th Birthday / December 2023 marks Yvonne Choquet-Bruhat's 100th birthday. For this special occasion, IHES organizes a day in her honor on December 8, 2023.
Yvonne Choquet-Bruhat's work has had a long-lasting impact on the field of mathematical relativity starting with her seminal 1952 paper on the local well-posedness of Einstein equations. Her numerous contributions, both to constraint equations and to the evolution problem in general relativity, have deeply influenced several generations of researchers. This special day in her honor will be the occasion to present some of the latest developments in the field. / Laure Saint-Raymond, Jérémie Szeftel / 08/12/2023 - 08/12/2023 / https://indico.math.cnrs.fr/event/10606/
https://www.carmin.tv/uploads/video/video-a0223688dc76d2bf4579c26de79e2c9e.jpg
oai:carmin.tv:on-the-canonical-geometric-structure-of-initial-data-for-the-einstein-equations
2023-12-18T17:56:02+01:00
videos:institution:ihes
videos:collection:day-in-honor-of-yvonne-choquet-bruhats-100-th-birthday
oai:carmin.tv:on-the-canonical-geometric-structure-of-initial-data-for-the-einstein-equations
https://www.carmin.tv/fr/video/on-the-canonical-geometric-structure-of-initial-data-for-the-einstein-equations
On the Canonical Geometric Structure of Initial Data for the Einstein Equations
video/mp4
IHES
I will start my talk with an overview of recent results on canonical geometric foliations of asymptotically flat Riemannian manifolds that complete a program initiated by G. Huisken and S.-T. Yau in the early nineties. I will explain how these results are closely tied to what I call effective versions of the positive mass theorem. In the second half of my talk, I will focus on a related conjecture due to R. Schoen on the minimal surface proof of the positive mass theorem, its solution in three space dimensions in my joint work with O. Chodosh, as well as the proof of an important special case of the conjecture and counterexamples to the general conjecture in higher dimensions in joint work with T. Koerber.
2023-12-08T00:00:00+01:00
Michael Eichmair
minimal surfaces, positive mass theorem, constant mean curvature surfaces, isoperimetric surfaces, Researchers, Graduate Students
en
Day in Honor of Yvonne Choquet-Bruhat’s 100 th Birthday / December 2023 marks Yvonne Choquet-Bruhat's 100th birthday. For this special occasion, IHES organizes a day in her honor on December 8, 2023.
Yvonne Choquet-Bruhat's work has had a long-lasting impact on the field of mathematical relativity starting with her seminal 1952 paper on the local well-posedness of Einstein equations. Her numerous contributions, both to constraint equations and to the evolution problem in general relativity, have deeply influenced several generations of researchers. This special day in her honor will be the occasion to present some of the latest developments in the field. / Laure Saint-Raymond, Jérémie Szeftel / 08/12/2023 - 08/12/2023 / https://indico.math.cnrs.fr/event/10606/
https://www.carmin.tv/uploads/video/video-7fa565d5ce0de7ff162d89ff62b54fe0.jpg
oai:carmin.tv:high-frequency-gravitationnal-waves-and-einstein-equations-with-u-1-symmetry
2023-12-18T18:02:02+01:00
videos:institution:ihes
videos:collection:day-in-honor-of-yvonne-choquet-bruhats-100-th-birthday
oai:carmin.tv:high-frequency-gravitationnal-waves-and-einstein-equations-with-u-1-symmetry
https://www.carmin.tv/fr/video/high-frequency-gravitationnal-waves-and-einstein-equations-with-u-1-symmetry
High frequency gravitationnal waves and Einstein equations with U(1) symmetry
video/mp4
IHES
In this talk, I will present two works of Yvonne Choquet-Bruhat. The first one, written in 1969, concerns the behaviour of high-frequency gravitationnal waves, and enlighten the beautiful structure of Einstein equations. She has subsequently generalized this work to Einstein equations coupled with other fields (electromagnetic, fluid...). The second more recent work I will speek about concerns the global existence of cosmological solutions with U(1) symmetry, with the introduction of the elliptic gauge. I will then present a work in collaboration with Jonathan Luk, about high-frequency solutions of Einstein equations with U(1) symmetry, in which the elliptic gauge is a very nice setting to study the superposition of waves.
2023-12-08T00:00:00+01:00
Cécile Huneau
Einstein equations, high frequency gravitationnal waves, Researchers, Graduate Students
en
Day in Honor of Yvonne Choquet-Bruhat’s 100 th Birthday / December 2023 marks Yvonne Choquet-Bruhat's 100th birthday. For this special occasion, IHES organizes a day in her honor on December 8, 2023.
Yvonne Choquet-Bruhat's work has had a long-lasting impact on the field of mathematical relativity starting with her seminal 1952 paper on the local well-posedness of Einstein equations. Her numerous contributions, both to constraint equations and to the evolution problem in general relativity, have deeply influenced several generations of researchers. This special day in her honor will be the occasion to present some of the latest developments in the field. / Laure Saint-Raymond, Jérémie Szeftel / 08/12/2023 - 08/12/2023 / https://indico.math.cnrs.fr/event/10606/
https://www.carmin.tv/uploads/video/video-be2fa25bd5a087536d5fb1852fd79ca1.jpg
oai:carmin.tv:mathematical-gr-seventy-two-years-after-yvonnes-foundational-acta-paper
2023-12-18T18:08:02+01:00
videos:institution:ihes
videos:collection:day-in-honor-of-yvonne-choquet-bruhats-100-th-birthday
oai:carmin.tv:mathematical-gr-seventy-two-years-after-yvonnes-foundational-acta-paper
https://www.carmin.tv/fr/video/mathematical-gr-seventy-two-years-after-yvonnes-foundational-acta-paper
Mathematical GR Seventy Two Years after Yvonne's Foundational Acta Paper
video/mp4
IHES
I will try to review some of the main achievements in mathematical general relativity, field which has its origin in Y.C. Bruhat's foundational Acta paper:
``Théorème d’existence pour certains systèmes d’equations aux dérivées partielles non-linéaires''
2023-12-08T00:00:00+01:00
Sergiu Klainerman
Researchers, Graduate Students
en
Day in Honor of Yvonne Choquet-Bruhat’s 100 th Birthday / December 2023 marks Yvonne Choquet-Bruhat's 100th birthday. For this special occasion, IHES organizes a day in her honor on December 8, 2023.
Yvonne Choquet-Bruhat's work has had a long-lasting impact on the field of mathematical relativity starting with her seminal 1952 paper on the local well-posedness of Einstein equations. Her numerous contributions, both to constraint equations and to the evolution problem in general relativity, have deeply influenced several generations of researchers. This special day in her honor will be the occasion to present some of the latest developments in the field. / Laure Saint-Raymond, Jérémie Szeftel / 08/12/2023 - 08/12/2023 / https://indico.math.cnrs.fr/event/10606/
https://www.carmin.tv/uploads/video/video-2732459bfd1e778cdd51bda24d7e571c.jpg
oai:carmin.tv:analytic-stacks-16-29
2023-12-22T11:39:09+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-16-29
https://www.carmin.tv/fr/video/analytic-stacks-16-29
Analytic Stacks (16/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-12-15T00:00:00+01:00
Peter Scholze
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-c1b5a92887b4211918b7c7af915f7d02.jpg
oai:carmin.tv:stability-of-llarulls-theorem-in-all-dimensions
2023-12-15T15:58:02+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:stability-of-llarulls-theorem-in-all-dimensions
https://www.carmin.tv/fr/video/stability-of-llarulls-theorem-in-all-dimensions
Stability of Llarull’s theorem in all dimensions
video/mp4
IHES
We prove stability of Llarull's theorem in all dimensions using spin geometry. Our results are stated in terms of both intrinsic flat convergence and $C^0$-convergence outside a small set. This is joint work with Yiyue Zhang from UCI.
2023-12-13T00:00:00+01:00
Sven Hirsch
Researchers
en
https://www.carmin.tv/uploads/video/video-5c2e0e453f3e92d6f8feca188a275035.jpg
oai:carmin.tv:some-global-effects-of-positive-scalar-curvature
2023-12-15T15:58:02+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:some-global-effects-of-positive-scalar-curvature
https://www.carmin.tv/fr/video/some-global-effects-of-positive-scalar-curvature
Some global effects of positive scalar curvature
video/mp4
IHES
This is a survey of some of my joint works with my students and postdocs on geometry of scalar curvature that have been done in recent years. In the first part of the talk, I will discuss Gromov’s fill-in problem, which has a deep connection with quasi-local masses in General Relativity. In the second part of the talk, I will discuss Llarull type theorems on complete manifolds with positive scalar curvature.
2023-12-13T00:00:00+01:00
Yuguang Shi
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-bb6f64d94fe673ce3e00044498879e4c.jpg
oai:carmin.tv:spaces-with-ricci-curvature-lower-bounds
2023-12-15T15:54:02+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:spaces-with-ricci-curvature-lower-bounds
https://www.carmin.tv/fr/video/spaces-with-ricci-curvature-lower-bounds
Spaces with Ricci curvature lower bounds
video/mp4
IHES
We will survey some recent results on the geometry and topology of spaces with nonnegative Ricci curvature showing dramatic new features for Ricci curvature lower bound. We will focus on joint work with J. Pan. First, the construction of Ricci limit spaces for which the Hausdorff dimension of the singular set is bigger than the Hausdorff dimension of the regular set, answering a question of Cheeger-Colding in 2000 in negative. This leads to, joint with X. Dai, S. Honda, J. Pan, two surprising types of Weyl’s laws which are fractal-like for some compact Ricci limit spaces. Then I will present, also joint with J. Pan, examples of manifolds with nonnegative Ricci curvature but nonproper Busemann function which were open since the 70's.
2023-11-29T00:00:00+01:00
Guofang Wei
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-b77cf22b6fb942631fb4ce5b3c782e38.jpg
oai:carmin.tv:nonnegative-ricci-curvature-nilpotency-and-hausdorff-dimension
2023-12-15T15:56:01+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:nonnegative-ricci-curvature-nilpotency-and-hausdorff-dimension
https://www.carmin.tv/fr/video/nonnegative-ricci-curvature-nilpotency-and-hausdorff-dimension
Nonnegative Ricci curvature, nilpotency, and Hausdorff dimension
video/mp4
IHES
Continuing Wei's presentation, we will talk about how the universal covers of Nabonnand-type examples came to our attention. One geometric feature in these examples is that the minimal representing loops of $\pi_1(M,p)$ must escape from any bounded sets. This leads to wild limit orbits in the asymptotic cones of $\widetilde{M}$: these orbits are not convex and have large Hausdorff dimension. Then we will discuss the relations in general among the above-mentioned escape phenomenon, orbits in the asymptotic cones, and the virtual abelianness / nilpotency of the fundamental groups.
2023-11-29T00:00:00+01:00
Jiayin Pan
Researchers
en
https://www.carmin.tv/uploads/video/video-fd50892170c4f2e090040d361265ff65.jpg
oai:carmin.tv:analytic-stacks-15-29
2023-12-22T11:38:27+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-15-29
https://www.carmin.tv/fr/video/analytic-stacks-15-29
Analytic Stacks (15/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-12-13T00:00:00+01:00
Dustin Clausen
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-7763793c43924d12fc00e4d188b67c85.jpg
oai:carmin.tv:analytic-stacks-14-29
2023-12-22T11:37:50+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-14-29
https://www.carmin.tv/fr/video/analytic-stacks-14-29
Analytic Stacks (14/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-12-08T00:00:00+01:00
Peter Scholze
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-16ef2859f209ba7cddedd84ab4caf855.jpg
oai:carmin.tv:analytic-stacks-13-29
2023-12-22T11:37:10+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-13-29
https://www.carmin.tv/fr/video/analytic-stacks-13-29
Analytic Stacks (13/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-12-06T00:00:00+01:00
Dustin Clausen
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-48d3309bc27c28357f85d130b76574c2.jpg
oai:carmin.tv:ricci-curvature-fundamental-group-and-the-milnor-conjecture-i
2023-12-05T15:36:01+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:ricci-curvature-fundamental-group-and-the-milnor-conjecture-i
https://www.carmin.tv/fr/video/ricci-curvature-fundamental-group-and-the-milnor-conjecture-i
Ricci curvature, fundamental group and the Milnor conjecture (I)
video/mp4
IHES
It was conjectured by Milnor in 1968 that the fundamental group of a complete manifold with nonnegative Ricci curvature is finitely generated. In this talk we will discuss a counterexample, which provides an example $M^7$ with $\mathrm{Ric}>= 0$ such that $\pi_1(M)=Q/Z$ is infinitely generated. There are several new points behind the result. The first is a new topological construction for building manifolds with infinitely generated fundamental groups, which can be interpreted as a smooth version of the fractal snowflake. The ability to build such a fractal structure will rely on a very twisted gluing mechanism. Thus the other new point is a careful analysis of the mapping class group $\pi_0(\mathrm{Diff}(S^3\times S^3))$ and its relationship to Ricci curvature. In particular, a key point will be to show that the action of $\pi_0(\mathrm{Diff}(S^3\times S^3))$ on the standard metric $g_{S^3\times S^3}$ lives in a path connected component of the space of metrics with $\mathrm{Ric}>0$.
2023-11-15T00:00:00+01:00
Aaron Naber
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-a8b80e9ae91c71117c0e05304d02563f.jpg
oai:carmin.tv:ricci-curvature-fundamental-group-and-the-milnor-conjecture-ii
2023-12-05T15:38:01+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:ricci-curvature-fundamental-group-and-the-milnor-conjecture-ii
https://www.carmin.tv/fr/video/ricci-curvature-fundamental-group-and-the-milnor-conjecture-ii
Ricci curvature, fundamental group and the Milnor conjecture (II)
video/mp4
IHES
The goal of this second talk will be to discuss more in detail some of the main ideas involved in the construction of the counterexamples to the Milnor conjecture. We will review the topological construction and outline the key geometric steps, with particular emphasis on those involving the mapping class group of $S^3\times S^3$. Moreover, we will describe the behavior of the asymptotic cones of the examples, in relationship with the known restrictions.
2023-11-15T00:00:00+01:00
Daniele Semola
Researchers
en
https://www.carmin.tv/uploads/video/video-cb7eefac2ce6e0be3b5ed2f4b478109c.jpg
oai:carmin.tv:analytic-stacks-12-29
2023-12-22T11:36:39+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-12-29
https://www.carmin.tv/fr/video/analytic-stacks-12-29
Analytic Stacks (12/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-12-01T00:00:00+01:00
Peter Scholze
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-60ef5b3f9e9ef36479d09aa4622d1d1f.jpg
oai:carmin.tv:analytic-stacks-11-29
2023-12-22T11:35:59+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-11-29
https://www.carmin.tv/fr/video/analytic-stacks-11-29
Analytic Stacks (11/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-11-29T00:00:00+01:00
Dustin Clausen
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-51820762a974f37fcbf4d763a39fa13c.jpg
oai:carmin.tv:birational-invariants-from-gromov-witten-theory-3-4
2024-03-12T11:02:40+01:00
videos:institution:ihes
videos:collection:maxim-kontsevich-birational-invariants-from-gromov-witten-theory
oai:carmin.tv:birational-invariants-from-gromov-witten-theory-3-4
https://www.carmin.tv/fr/video/birational-invariants-from-gromov-witten-theory-3-4
Birational Invariants from Gromov-Witten Theory (3/4)
video/mp4
IHES
Gromov-Witten invariants of a smooth projective variety give an infinite tower of cohomology classes on powers of the original variety, satisfying a beautiful system of constraints encoded in the notion of quantum connection. Recently Hiroshi Iritani proved a result controlling the quantum connection of the blowup along a smooth center.
The goal of the course is to introduce a new class of birational invariants based on Iritani's theorem.
In particular, one can almost effortlessly prove the non-rationality of a generic cubic 4-fold.
2023-11-21T00:00:00+01:00
Maxim Kontsevich
Researchers, Graduate Students
en
Maxim Kontsevich : Birational Invariants from Gromov-Witten Theory / 06/11/2023 - 27/11/2023
https://www.carmin.tv/uploads/video/03_Maxim_Kontsevich-d581b052f58aff77bfc3c87a3f60d912-video--a216b2181905fb850c0b13174b4ddb7f.jpg
oai:carmin.tv:birational-invariants-from-gromov-witten-theory-4-4
2023-11-28T00:12:02+01:00
videos:institution:ihes
videos:collection:maxim-kontsevich-birational-invariants-from-gromov-witten-theory
oai:carmin.tv:birational-invariants-from-gromov-witten-theory-4-4
https://www.carmin.tv/fr/video/birational-invariants-from-gromov-witten-theory-4-4
Birational Invariants from Gromov-Witten Theory (4/4)
video/mp4
IHES
Gromov-Witten invariants of a smooth projective variety give an infinite tower of cohomology classes on powers of the original variety, satisfying a beautiful system of constraints encoded in the notion of quantum connection.
Recently Hiroshi Iritani proved a result controlling the quantum connection of the blowup along a smooth center.
The goal of the course is to introduce a new class of birational invariants based on Iritani's theorem.
In particular, one can almost effortlessly prove the non-rationality of a generic cubic 4-fold.
2023-11-27T00:00:00+01:00
Maxim Kontsevich
Researchers, Graduate Students
en
Maxim Kontsevich : Birational Invariants from Gromov-Witten Theory / 06/11/2023 - 27/11/2023
https://www.carmin.tv/uploads/video/video-af772c37fe392ef80bc372eb70a21045.jpg
oai:carmin.tv:solving-equations-from-combinatorics-via-computer-algebra-1
2023-11-27T11:04:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-2023
oai:carmin.tv:solving-equations-from-combinatorics-via-computer-algebra-1
https://www.carmin.tv/fr/video/solving-equations-from-combinatorics-via-computer-algebra-1
Solving equations from combinatorics via computer algebra
video/mp4
IHES
Enumerative combinatorics contains a vast landscape of problems that could hardly be solved without the consideration of special functional equations called “Discrete Differential Equations”. Among these problems, the enumeration of walks, planar maps carrying hard particles, etc. These functional equations relate formal power series in n variables with specializations of them to some of the
variables (the specializations being generating functions related to the enumeration of interest). When the involved variables are “nested”, a celebrated result by Popescu (1986) implies algebraicity of the solutions. In 2006, Bousquet-Melou and Jehanne provided an elementary proof of algebraicity of the solutions in the case n = 2. Their proof yields an algorithm, and it has been the state-of-the-art in enumerative combinatorics for solving these equations since then. In this talk, I will present a recent approach, based on the intensive use of effective algebraic geometry, in order to solve more efficiently such equations in the case n=2. Also, I will introduce and discuss recent advances in the case of systems of such equations.
The talk is based on joint works with Alin Bostan, Mohab Safey El Din and Sergey Yurkevich.
2023-11-17T00:00:00+01:00
Hadrien Notarantonio
functional equations, catalytic variable, discrete differential equations, Researchers
en
Combinatorics and Arithmetic for Physics: special days 2023 / The meeting’s focus is about questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics : renormalisation, combinatorial physics, geometry, evolution equations (commutative and noncommutative) or related to its models, but not only. Computations, based on combinatorial structures (graphs,trees, words, automata, semirings, bases) or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. DUCHAMP, Maxim KONTSEVICH, Gleb KOSHEVOY, Sergei NECHAEV and Karol A. PENSON / 15/11/2023 - 17/11/2023 / https://www-lipn.univ-paris13.fr/~duchamp/Conferences/CAP10_2023.html
https://www.carmin.tv/uploads/video/video-cb4f1fbccc40636825cb0a3a2d11dc4e.jpg
oai:carmin.tv:a-twisted-version-of-kitaevs-quantum-double-model-1
2024-03-12T10:51:16+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-2023
oai:carmin.tv:a-twisted-version-of-kitaevs-quantum-double-model-1
https://www.carmin.tv/fr/video/a-twisted-version-of-kitaevs-quantum-double-model-1
A twisted version of Kitaev’s quantum double model
video/mp4
IHES
The quantum double model has been introduced by Kitaev in order to propose a model of quantum computing based on anyonic excitations, thus stable against perturbations. We propose a deformation of this model, induced by an external 3 form. In this model, the role of the quantum double is replaced by its twisted version, a quasi Hopf algebra introduced in orbifold models by Dijkgraaf, Pasquier and Roche.
2023-11-17T00:00:00+01:00
Thomas Krajewski
Researchers
en
Combinatorics and Arithmetic for Physics: special days 2023 / The meeting’s focus is about questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics : renormalisation, combinatorial physics, geometry, evolution equations (commutative and noncommutative) or related to its models, but not only. Computations, based on combinatorial structures (graphs,trees, words, automata, semirings, bases) or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. DUCHAMP, Maxim KONTSEVICH, Gleb KOSHEVOY, Sergei NECHAEV and Karol A. PENSON / 15/11/2023 - 17/11/2023 / https://www-lipn.univ-paris13.fr/~duchamp/Conferences/CAP10_2023.html
https://www.carmin.tv/uploads/video/video-02b15be646c5af563fd250de4b2bef06.jpg
oai:carmin.tv:combinatorial-topological-quantum-field-theories-and-geometrical-constructions-of-integers-in-fini-1
2023-11-27T11:08:02+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-2023
oai:carmin.tv:combinatorial-topological-quantum-field-theories-and-geometrical-constructions-of-integers-in-fini-1
https://www.carmin.tv/fr/video/combinatorial-topological-quantum-field-theories-and-geometrical-constructions-of-integers-in-fini-1
Combinatorial topological quantum field theories and geometrical constructions of integers in finite group representation theory
video/mp4
IHES
Topological quantum field theories (TQFTs) which have a simple physical formulation as lattice gauge theory with finite gauge group G admit elegant expressions for partition functions on closed higher genus Riemann surfaces. There are expressions for the partition functions in terms of the combinatorial counting of flat G-bundles and in terms of dimensions of irreducible representations (irreps). Consideration of the partition functions of these G-Flat-TQFTs across different genuses gives finite algorithms which start from group multiplications and yield the spectrum of dimensions of irreps. The input into the algorithms is formed by identities which generalise the classic formula for the order of a group as a sum of squares of the dimensions of irreps. Considering the partition functions of the G-Flat-TQFTs for surfaces with boundaries leads to the derivation of integrality properties of certain partial sums along columns of the character table of G. Analogous considerations starting from a topological field theory based on the fusion ring of a finite group (denoted G-Fusion-TQFT) allows the proof of analogous integrality properties for partial sums along rows of the character table. These row-column relations between integrality properties of characters can be viewed as a mathematical reflection of a physical row-column duality between the G-flat TQFTs and the G-fusion TQFTs.
2023-11-17T00:00:00+01:00
Sanjaye Ramgoolam
Researchers
en
Combinatorics and Arithmetic for Physics: special days 2023 / The meeting’s focus is about questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics : renormalisation, combinatorial physics, geometry, evolution equations (commutative and noncommutative) or related to its models, but not only. Computations, based on combinatorial structures (graphs,trees, words, automata, semirings, bases) or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. DUCHAMP, Maxim KONTSEVICH, Gleb KOSHEVOY, Sergei NECHAEV and Karol A. PENSON / 15/11/2023 - 17/11/2023 / https://www-lipn.univ-paris13.fr/~duchamp/Conferences/CAP10_2023.html
https://www.carmin.tv/uploads/video/video-68a378f192a81ba61bdbf2aa9af91a7e.jpg
oai:carmin.tv:analytic-stacks-10-29
2024-03-12T10:59:58+01:00
videos:institution:ihes
videos:collection:dustin-clausen-and-peter-scholze-analytic-stacks
oai:carmin.tv:analytic-stacks-10-29
https://www.carmin.tv/fr/video/analytic-stacks-10-29
Analytic Stacks (10/29)
video/mp4
IHES
The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
2023-11-24T00:00:00+01:00
Peter Scholze
analytic geometry, condensed mathematics, Researchers, Graduate Students
en
Dustin Clausen and Peter Scholze : Analytic Stacks / 18/10/2023 - 09/02/2024
https://www.carmin.tv/uploads/video/video-beb67b03dd7d2a89668f01eb81f1827f.jpg
oai:carmin.tv:denombrement-de-cartes-entre-combinatoire-probabilites-et-physique-theorique
2023-11-24T17:28:03+01:00
videos:institution:ihes
videos:collection:11e-seminaire-itzykson-denombrement-de-cartes-entre-combinatoire-probabilites-et-physique-theorique
oai:carmin.tv:denombrement-de-cartes-entre-combinatoire-probabilites-et-physique-theorique
https://www.carmin.tv/fr/video/denombrement-de-cartes-entre-combinatoire-probabilites-et-physique-theorique
Dénombrement de cartes : entre combinatoire, probabilités et physique théorique
video/mp4
IHES
Les cartes – surfaces obtenues par recollement de polygones le long de leurs arêtes –intéressent depuis des décennies différents domaines des mathématiques, de l’informatique et de la physique. On s’attachera principalement dans ce cours à des questions de dénombrement de familles de cartes. Je donnerai d’abord un aperçu des approches, étonnamment variées (et pour certaines déjà vénérables), permettant ce type de dénombrement.
Je tenterai ensuite un petit panorama de questions d’actualité.
2023-11-20T00:00:00+01:00
Mireille Bousquet-Mélou
physique statistique, Processus stochastiques, Dénombrements de cartes, cartes aléatoires, modèles de boucles, Researchers
fr
11e Séminaire Itzykson : Dénombrement de cartes : entre combinatoire, probabilités et physique théorique / Depuis une dizaine d’années l’axe math-physique de la Fondation Mathématique Jacques Hadamard (FMJH) organise un séminaire Itzykson tous les ans à l’IHES. Il s’agit d’une journée consacrée à un thème de physique mathématique, avec un cours en français et deux ou trois exposés spécialisés en français ou en anglais.
Les cartes – surfaces obtenues par recollement de polygones le long de leurs arêtes – intéressent depuis des décennies différents domaines des mathématiques, de l’informatique et de la physique. En particulier, si le recollement est aléatoire, on obtient des cartes aléatoires, qui permettent de décrire des processus stochastiques. Si de plus on décore des cartes aléatoires, on peut décrire des modèles de physique statistique comme le modèle de boucles O(n).
Durant cette journée seront présentés divers aspects des cartes, des problèmes de dénombrement aux applications physiques, des idées fondamentales aux développements récents.
Un cours et deux exposés auront lieu dans la journée, présentés par :
Mireille Bousquet-Mélou, CNRS, LaBRI, Université de Bordeaux
Igor Kortchemski, CNRS, École polytechnique & ETH Zurich
Jérémie Bouttier, IMJ-PRG, Sorbonne Université / Maxim Kontsevich, Sylvain Ribault, Pierre Vanhove / 20/11/2023 - 20/11/2023 / https://indico.math.cnrs.fr/event/10584/
https://www.carmin.tv/uploads/video/video-486a25b8b3962a77261b876009f412bc.jpg
oai:carmin.tv:cartes-aleatoires-entre-croissance-et-fragmentation
2023-11-24T17:30:01+01:00
videos:institution:ihes
videos:collection:11e-seminaire-itzykson-denombrement-de-cartes-entre-combinatoire-probabilites-et-physique-theorique
oai:carmin.tv:cartes-aleatoires-entre-croissance-et-fragmentation
https://www.carmin.tv/fr/video/cartes-aleatoires-entre-croissance-et-fragmentation
Cartes aléatoires : entre croissance et fragmentation
video/mp4
IHES
Les cartes aléatoires sont des surfaces obtenues en assemblant de manière aléatoire des polygones. Les processus de croissance-fragmentation sont des processus stochastiques qui décrivent la dynamique d’un nuage de particules dont la taille peut évoluer et qui peuvent se fragmenter au cours du temps en donnant naissance à de nouvelles particules. Quel est le lien entre ces deux objets ?
2023-11-20T00:00:00+01:00
Igor Kortchemski
physique statistique, Processus stochastiques, Dénombrements de cartes, cartes aléatoires, modèles de boucles, Researchers
fr
11e Séminaire Itzykson : Dénombrement de cartes : entre combinatoire, probabilités et physique théorique / Depuis une dizaine d’années l’axe math-physique de la Fondation Mathématique Jacques Hadamard (FMJH) organise un séminaire Itzykson tous les ans à l’IHES. Il s’agit d’une journée consacrée à un thème de physique mathématique, avec un cours en français et deux ou trois exposés spécialisés en français ou en anglais.
Les cartes – surfaces obtenues par recollement de polygones le long de leurs arêtes – intéressent depuis des décennies différents domaines des mathématiques, de l’informatique et de la physique. En particulier, si le recollement est aléatoire, on obtient des cartes aléatoires, qui permettent de décrire des processus stochastiques. Si de plus on décore des cartes aléatoires, on peut décrire des modèles de physique statistique comme le modèle de boucles O(n).
Durant cette journée seront présentés divers aspects des cartes, des problèmes de dénombrement aux applications physiques, des idées fondamentales aux développements récents.
Un cours et deux exposés auront lieu dans la journée, présentés par :
Mireille Bousquet-Mélou, CNRS, LaBRI, Université de Bordeaux
Igor Kortchemski, CNRS, École polytechnique & ETH Zurich
Jérémie Bouttier, IMJ-PRG, Sorbonne Université / Maxim Kontsevich, Sylvain Ribault, Pierre Vanhove / 20/11/2023 - 20/11/2023 / https://indico.math.cnrs.fr/event/10584/
https://www.carmin.tv/uploads/video/video-7f9c1422d274852906cb0b708d717003.jpg
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