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Videos (7968)
54:22

published on April 27, 2025

Gradient estimates for scalar curvature

By Tobias Colding

IHES

We A gradient estimate is a crucial tool used to control the rate of change of a function on a manifold, paving the way for deeper analysis of geometric properties. A celebrated result of Cheng and Yau gives gradient bounds on manifolds with non-negative Ricci curvature. The Cheng-Yau bound is ...

Appears in collection : Not Only Scalar Curvature Seminar

01:34:22

published on April 25, 2025

Introduction to Teichmüller theory Lecture 1

By Federica Fanoni

CIRM

We will introduce Teichmüller space and its different interpretations. We will discuss its topology and its geometry, and talk about how to construct a boundary. We will concentrate on closed surfaces and give hints at added difficulties when the surface is not closed.

Appears in collection : Geometric structures and discrete group actions / Structures géométriques et actions de groupes discrets

01:32:03

published on April 25, 2025

Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 1

By Barbara Schapira

CIRM

In these lectures, we are interested in the chaotic behaviour of the geodesic flow of hyperbolic surfaces. To understand it from an ergodic point of view, we will build a family of invariant measures called "Gibbs measures", and use their product structure to deduce chaotic properties of the ...

Appears in collection : Geometric structures and discrete group actions / Structures géométriques et actions de groupes discrets

01:25:39

published on April 25, 2025

Introduction to Teichmüller theory Lecture 2

By Federica Fanoni

CIRM

We will introduce Teichmüller space and its different interpretations. We will discuss its topology and its geometry, and talk about how to construct a boundary. We will concentrate on closed surfaces and give hints at added difficulties when the surface is not closed.

Appears in collection : Geometric structures and discrete group actions / Structures géométriques et actions de groupes discrets

01:34:28

published on April 25, 2025

Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 2

By Barbara Schapira

CIRM

In these lectures, we are interested in the chaotic behaviour of the geodesic flow of hyperbolic surfaces. To understand it from an ergodic point of view, we will build a family of invariant measures called "Gibbs measures", and use their product structure to deduce chaotic properties of the ...

Appears in collection : Geometric structures and discrete group actions / Structures géométriques et actions de groupes discrets

01:49:12

published on April 18, 2025

Mathematical Description of Biological Structures (4/4)

By Misha Gromov

IHES

We shall try to assign mathematical meaning to the language used by biologists for describing basic structures and processes in living organisms, from the (sub)cellular level up to evolutionary dynamics of populations. In particular, we shall elucidate the mathematical as well ...

Appears in collection : Misha Gromov : Mathematical Description of Biological Structures

56:53

published on April 18, 2025

Extremal eigenvectors, the spectral action, and the zeta spectral triple

By Alain Connes

CIRM

I will first explain the joint work with Walter van Suijlekom on a new result about th zeros of the Fourier transform of extremal eigenvectors for quadratic forms associated to distributions on a bounded interval and its relation with the spectral action. Then I will explain how these results ...

Appears in collection : Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time / Applications de la Géométrie Non Commutative aux Théories de Jauge, à la Théorie des Champs et aux Espaces-Temps Quantiques

45:04

published on April 18, 2025

Quantum Galilei group as quantum reference frame transformations

By Giulia Gubitosi

CIRM

Recent developments in quantum information led to a generalised notion of reference frames transformations, relevant when reference frames are associated to quantum systems. In this talk, I discuss whether such quantum reference frame transformations could realise a notion of deformed symmetries ...

Appears in collection : Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time / Applications de la Géométrie Non Commutative aux Théories de Jauge, à la Théorie des Champs et aux Espaces-Temps Quantiques
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