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Sums of three squares and Noether-Lefschetz loci

By Olivier Benoist

Also appears in collection : Perspectives in real geometry / Perspectives en géométrie réelle

It is a theorem of Hilbert that a real polynomial in two variables that is nonnegative is a sum of 4 squares of rational functions. Cassels, Ellison and Pfister have shown the existence of such polynomials that are not sums of 3 squares of rational functions. In this talk, we will prove that those polynomials that may be written as sums of 3 squares are dense in the set of nonnegative polynomials. The proof is Hodge-theoretic.

Information about the video

Date of recording 21/09/2017
Date of publication 21/09/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19222303
Cite this video Benoist, Olivier (21/09/2017). Sums of three squares and Noether-Lefschetz loci. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19222303
URL https://dx.doi.org/10.24350/CIRM.V.19222303

Domain(s)

Bibliography

Benoist, O. (2017). Sums of three squares and Noether-Lefschetz loci. <arXiv:1706.02053> - https://arxiv.org/abs/1706.02053

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By Martin Vohralík

35:33

published on August 4, 2016

Optimized Schwarz waveform relaxation methods: theory and applications

By Pascal Omnes

46:12

published on August 3, 2016

Parametrized model order reduction for component-to-system synthesis

By Anthony Patera

01:05:19

published on August 8, 2016

Data-driven wildfire behavior modelling: focus on front level-set data assimilation

By Mélanie Rochoux

44:00

published on August 8, 2016

A discussion about the impact of scalability constraint on the design of futur dynamical kernels of NWP models

By Fabrice Voitus

39:44

published on August 8, 2016

Modeling and data assimilation in cardiac electrophysiology

By Annabelle Collin

57:16

published on August 10, 2016

High performance climate modelling : mimetic finite differences, and beyond?

By Thomas Dubos

57:49

published on August 10, 2016

Direct and inverse biomechanical modeling of the heart

By Dominique Chapelle

54:02

published on September 20, 2016

Crystalline cohomology, period maps, and applications to K3 surfaces

By Christian Liedtke

56:03

published on September 20, 2016

The non-archimedean SYZ fibration and Igusa zeta functions - Part 2

By Johannes Nicaise

53:48

published on September 20, 2016

The non-archimedean SYZ fibration and Igusa zeta functions - Part 3

By Johannes Nicaise

47:11

published on September 22, 2016

The unitary extension principle on LCA groups

By Ole Christensen

50:19

published on September 27, 2016

Some recent insights into computing with positive definite kernels

By Greg Fasshauer

51:15

published on September 22, 2016

Algebraic multigrid and subdivision

By Maria Charina

26:29

published on September 27, 2016

Spherical splines

By Hartmut Prautzsch

54:30

published on October 11, 2016

Forcing theory for transverse trajectories of surface homeomorphisms - Part 1

By Patrice Le Calvez

53:25

published on October 11, 2016

Forcing theory for transverse trajectories of surface homeomorphisms - Part 2

By Patrice Le Calvez

54:00

published on October 11, 2016

Forcing theory for transverse trajectories of surface homeomorphisms - Part 3

By Fabio Tal

48:42

published on October 11, 2016

Forcing theory for transverse trajectories of surface homeomorphisms - Part 4

By Fabio Tal

47:37

published on November 10, 2016

Transferring information across image and shape collections

By Niloy Mitra

43:32

published on November 16, 2016

Quasisemisimple classes

By Jean Michel

01:13:58

published on December 14, 2016

Operators in ergodic theory - Lecture 1: Operators dynamics versus base space dynamics

By Markus Haase

01:01:43

published on December 14, 2016

Operators in ergodic theory - Lecture 2: Dilations and joinings

By Markus Haase

49:47

published on December 14, 2016

Operators in ergodic theory - Lecture 3: Compact semigroups and splitting theorems

By Markus Haase

59:07

published on December 14, 2016

Multiple ergodic theorems: old and new - Lecture 2

By Bryna Kra

01:06:39

published on December 14, 2016

Multiple ergodic theorems: old and new - Lecture 3

By Bryna Kra

01:12:37

published on January 6, 2017

Möbius randomness and dynamics six years later

By Peter Sarnak

01:00:08

published on January 6, 2017

Ergodicity of the Liouville system implies the Chowla conjecture

By Nikos Frantzikinakis

48:04

published on January 6, 2017

The diameter of the symmetric group: ideas and tools

By Harald Helfgott

01:01:12

published on January 6, 2017

Primes with missing digits

By James Maynard

57:14

published on January 6, 2017

The unsolved problems of Halmos

By Benjamin Weiss

50:33

published on March 2, 2017

Generic properties of the geodesic flow in nonpositive curvature

By Yves Coudène

55:54

published on March 3, 2017

Central limit theorems for circle packings

By Mark Pollicott

58:14

published on March 3, 2017

Mixing and rates of mixing for infinite measure flows

By Ian Melbourne

01:01:15

published on March 2, 2017

Fast-Slow partially hyperbolic systems: an example

By Carlangelo Liverani

40:09

published on March 10, 2017

Conditioned determinantal processes are determinantal

By Alexander Shamov

43:02

published on March 8, 2017

A functional limit theorem for the sine-process

By Andrey Dymov

57:46

published on March 23, 2017

Correlation spectrum of Morse-Smale flows

By Gabriel Rivière

59:43

published on April 24, 2017

Skeletons and moduli of Stokes torsors

By Jean-Baptiste Teyssier

01:02:52

published on April 24, 2017

Semi-infinite Hodge structures in noncommutative geometry

By Dmytro Shklyarov

01:25:17

published on April 24, 2017

On the Riemann-Hilbert correspondence for irregular holonomic D-modules

By Andrea D'Agnolo

50:11

published on May 4, 2017

Tilings and non-intersecting paths beyond integrable cases

By Vadim Gorin

01:48:41

published on May 11, 2017

Informatique et physique : quelques interactions

By Gilles Dowek

01:13:28

published on May 11, 2017

La difficile explication du résultat des calculs : des preuves automatiques à l'apprentissage automatique

By Gilles Dowek

02:30:39

published on May 11, 2017

Arithmétique à virgule flottante : plaie ou terrain de jeu ?

By Sylvie Boldo

42:01

published on May 25, 2017

Curvature measures of random sets

By Martina Zähle

45:31

published on May 25, 2017

Random walks on dynamical percolation

By Perla Sousi

42:13

published on June 1, 2017

Angles of Gaussian primes

By Zeév Rudnick

41:55

published on June 1, 2017

Small sumsets in continuous and discrete settings

By Anne de Roton

32:38

published on June 1, 2017

Bounded remainder sets for the discrete and continuous irrational rotation

By Sigrid Grepstad

44:58

published on June 1, 2017

Large character sums

By Youness Lamzouri

43:13

published on August 3, 2017

Splitting algorithm for nested events

By Ludovic Goudenège

53:14

published on August 3, 2017

Projected particle methods for solving McKean Vlasov SDEs

By Denis Belomestny

55:27

published on August 3, 2017

Some asymptotic results about American options and volativity

By Stefano De Marco

47:28

published on August 10, 2017

Mean field type control with congestion

By Mathieu Lauriere

49:24

published on August 28, 2017

Forward and backward simulation of Euler scheme

By Emmanuel Gobet

01:09:54

published on September 8, 2017

Minicourse shape spaces and geometric statistics

By Alain Trouvé , Xavier Pennec

01:31:17

published on September 8, 2017

Geometry of quantum entanglement

By Karol Zyczkowski

54:56

published on September 14, 2017

Coloring graphs with forbidden induced paths

By Maria Chudnovsky

59:25

published on September 14, 2017

Combinatorial and algorithmic properties of Robinsonian matrices

By Monique Laurent

53:47

published on September 14, 2017

Random hyperbolic graphs

By Marcos Kiwi

01:06:10

published on September 14, 2017

Restricted types of matchings

By Dieter Rautenbach

01:03:20

published on September 22, 2017

Real curves and a Klein TQFT

By Penka Georgieva

01:06:05

published on September 21, 2017

Sums of three squares and Noether-Lefschetz loci

By Olivier Benoist

01:04:57

published on September 22, 2017

Complex torus, its good compactifications and the ring of conditions

By Askold Khovanskii

$Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 2$
01:31:10

published on September 28, 2017

Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 2

By François Métayer

01:01:16

published on September 28, 2017

Shuffles of trees

By Eric Hoffbeck

56:01

published on September 28, 2017

Type theories and polynomial monads

By Steve Awodey

$Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 3$
01:22:19

published on September 28, 2017

Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 3

By François Métayer

50:58

published on October 6, 2017

Ill-posedness for Leray solutions of the ipodissipative Navier-Stokes equations

By Camillo de Lellis

56:20

published on October 6, 2017

30 years of $T(b)$ theorems

By Pascal Auscher

55:29

published on October 6, 2017

Localization of eigenfunctions via an effective potential

By David Jerison

59:07

published on October 6, 2017

Parametrizing with Guy

By Tatiana Toro

57:14

published on October 12, 2017

From forcing models to realizability models

By Laura Fontanella

50:22

published on October 12, 2017

The hierarchy of second-order set theories between GBC and KM and beyond

By Joel David Hamkins

$Monochromatic sumsets for colourings of $\mathbb{R}$$
31:42

published on October 12, 2017

Monochromatic sumsets for colourings of $\mathbb{R}$

By Daniel T. Soukup

51:32

published on October 12, 2017

Prikry type forcing and combinatorial properties

By Dima Sinapova

54:45

published on October 26, 2017

Interlacements and the uniform spanning forest

By Tom Hutchcroft

51:45

published on October 26, 2017

Weighted distances in scale free random graphs

By Julia Komjathy

48:31

published on October 26, 2017

Extinction time for the weaker of two competing stochastic SIS logistic epidemics

By Malwina Luczak

19:41

published on November 2, 2017

The quantum Vlasov equation

By Norbert Mauser

37:25

published on November 16, 2017

Viability and arbitrage under Knightian uncertainty

By Matteo Burzoni

36:53

published on November 16, 2017

Market delay and $G$-expectations

By Yan Dolinsky

27:35

published on November 21, 2017

Rough volatility from an affine point of view

By Christa Cuchiero

27:21

published on November 21, 2017

Affine Volterra processes and models for rough volatility

By Martin Larsson

35:36

published on November 16, 2017

Reconstruction by optimal transport: applications in cosmology and finance

By Grégoire Loeper

58:21

published on December 7, 2017

Algebraic sums and products of univoque bases

By Karma Dajani

01:00:42

published on December 7, 2017

A perspective on the The Fibonacci trace map

By David Damanik

55:32

published on December 7, 2017

Yet another characterization of the Pisot conjecture

By Paul Mercat

01:02:42

published on December 11, 2017

Dimension groups and recurrence for tree subshifts

By Valérie Berthé

32:38

published on January 10, 2018

Eigenvalues and variance components

By Iain Johnstone

29:22

published on December 21, 2017

Estimation of functions depending on a parameter observed in Gaussian noise

By Ildar Ibragimov

01:00:53

published on January 10, 2018

Some memories and facts about the work of Oleg Lepski: beyond a 'discourse on method'

By Marc Hoffmann

54:19

published on January 31, 2018

Complex Monge-Ampere equations with prescribed singularities

By Eleonora Di Nezza

50:31

published on January 31, 2018

Kähler-Ricci solitons on crepant resolutions of finite quotients of $C^n$

By Heather Macbeth

49:09

published on January 31, 2018

Extremal Poincaré type metrics and stability of pairs on Hirzebruch surfaces

By Lars Martin Sektnan

01:02:22

published on February 7, 2018

Finite type invariants of knots in homology 3-spheres

By Delphine Moussard

01:06:16

published on February 7, 2018

Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes

By Anton Zorich

01:03:10

published on February 18, 2018

Trisections diagrams and surgery operations on embedded surfaces

By David Gay

01:02:31

published on February 18, 2018

Covering spaces and spanning trees

By David Cimasoni

$Quantum $\mathfrak{sl}_n$ knot cohomology and the slice genus$
50:00

published on February 19, 2018

Quantum $\mathfrak{sl}_n$ knot cohomology and the slice genus

By Andrew Lobb

58:15

published on March 7, 2018

Groups with Bowditch boundary a 2-sphere

By Bena Tshishiku

01:05:09

published on March 7, 2018

The Farrell-Jones conjecture for free-by-cyclic groups

By Mladen Bestvina

57:08

published on March 7, 2018

Homomorphisms to 3-manifold groups and other families

By Daniel Groves

47:35

published on March 14, 2018

Ideals in $L(L_p)$

By William B. Johnson

47:10

published on March 14, 2018

On a difference between two methods of low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces

By Beata Randrianantoanina

44:49

published on March 14, 2018

$L^2$ spectral gap and group actions on Banach spaces

By Mikael de la Salle

47:52

published on March 15, 2018

Finite quotients in coarse geometry

By Anastasia Khukhro

54:04

published on March 28, 2018

The coherent Satake category

By Harold Williams

51:09

published on March 29, 2018

From $Q$-systems to quantum affine algebras and beyond

By Rinat Kedem

51:51

published on March 28, 2018

Newton-Okounkov bodies for Grassmannians

By Lauren Williams

56:25

published on March 28, 2018

Preprojective algebras and Cluster categories

By Osamu Iyama

45:15

published on April 5, 2018

Symmetry and computation: a few of my favourite things

By Hans Z. Munthe-Kaas

51:33

published on April 5, 2018

Hybrid finite element methods preserving local symmetries and conservation laws

By Ari Stern

57:54

published on April 12, 2018

Deformation theory of twistor spaces of K3 surfaces

By Ana-Maria Brecan

53:55

published on April 12, 2018

Improved bounds for the Kobayashi conjecture on generic hyperbolicity

By Jean-Pierre Demailly

50:18

published on April 12, 2018

Nonabelian Hodge correspondences for klt varieties and quasi-etale uniformisation

By Stefan Kebekus

50:08

published on April 12, 2018

Signature morphisms from the Cremona group

By Susanna Zimmermann

$The weak-$A_\infty$ condition for harmonic measure$
58:21

published on April 25, 2018

The weak-$A_\infty$ condition for harmonic measure

By Xavier Tolsa

01:17:43

published on May 10, 2018

Méthodes probabilistes

By Marthe Bonamy

01:16:20

published on May 15, 2018

SMT solving

By David Monniaux

$Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space$
44:58

published on May 22, 2018

Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space

By Martina Hofmanova

49:39

published on May 22, 2018

Bessel-like SPDEs

By Lorenzo Zambotti

55:36

published on May 29, 2018

Recent progress in the classification of torsion subgroups of elliptic curves

By Alvaro Lozano-Robledo

55:55

published on May 30, 2018

A new Northcott property for Faltings height

By Lucia Mocz

01:00:35

published on May 29, 2018

Shimura curves and bounds for the $abc$ conjecture

By Hector Pasten

52:52

published on May 31, 2018

A supercongruence and hypergeometric motives

By Frits Beukers

54:38

published on May 31, 2018

Around Jouanolou-type theorems

By Rahim Moosa

53:45

published on May 31, 2018

Gamma functions, monodromy and Apéry constants

By Masha Vlasenko

58:41

published on June 7, 2018

Geometric recursion

By Jorgen Ellegaard Andersen

56:15

published on June 7, 2018

Exact density matrix for quantum group invariant sector of XXZ

By Fedor Smirnov

54:38

published on June 7, 2018

An introduction to the BV-BFV formalism

By Alberto S. Cattaneo

55:53

published on June 7, 2018

Capelli eigenvalue problem for Lie superalgebras and supersymmetric polynomials

By Vera Serganova

01:00:14

published on June 21, 2018

On the motive of the stack of vector bundles on a curve

By Victoria Hoskins

58:08

published on June 21, 2018

On Hitchin's hyperkähler metric on moduli spaces of Higgs bundles

By Andrew Neitzke

57:39

published on June 21, 2018

The ends of the Hitchin moduli space

By Laura Fredrickson

01:01:23

published on June 21, 2018

The large scale geometry of the Higgs bundle moduli space

By Jan Swoboda

01:23:49

published on June 28, 2018

Establishment in a new habitat under the infinitesimal model

By Alison M. Etheridge , Nicholas H. Barton

01:10:43

published on July 10, 2018

A Jacobian criterion for smoothness of algebraic diamonds

By Laurent Fargues

01:03:48

published on July 12, 2018

Modeling the chemotherapy-induced selection of drug-resistant traits during tumor growth

By Doron Levy

52:47

published on August 1, 2018

Macroscopic limit from a structured population model to the Kirkpatrick-Barton model

By Gaël Raoul

33:21

published on August 3, 2018

Mathematical model of cortical neurogenesis

By Marie Postel

28:04

published on August 3, 2018

Modelling of complex dynamical networks: from agent-based to continuum models

By Diane Peurichard

46:01

published on December 6, 2018

Bayesian capture-recapture in social justice research

By David Corliss

33:03

published on December 6, 2018

Big data for health: a Bayesian spatio-temporal analysis for predicting cardiac risk in Ticino and optimal defibrillators positioning

By Antonietta Mira

49:18

published on April 18, 2019

The partial compactification of the universal centralizer

By Ana Balibanu

01:00:32

published on April 25, 2019

BFN Springer theory

By Joel Kamnitzer

58:38

published on April 18, 2019

$T$-structures from categorical actions

By Clemens Koppensteiner

58:17

published on April 18, 2019

Coulomb branches of quiver gauge theories with symmetrizers

By Hiraku Nakajima

59:44

published on April 18, 2019

Gelfand-Tsetlin theory and Coulomb branches

By Ben Webster

59:16

published on April 18, 2019

Character stacks and $(q-)$geometric representation theory

By Sam Gunningham

52:34

published on April 18, 2019

Schubert calculus and self-dual puzzles

By Iva Halacheva

01:03:31

published on April 18, 2019

Skeins, clusters, and character sheaves

By David Jordan

01:02:09

published on April 18, 2019

Quantum character varieties at roots of unity

By Pavel Safronov

59:48

published on April 19, 2019

Fusion rings from quantum groups and DAHA actions

By Catharina Stroppel

01:00:06

published on April 25, 2019

Partial resolutions/deformations of diagonal invariants and representations of finite reductive groups

By Cédric Bonnafé

58:05

published on April 18, 2019

Symplectic singularities and nilpotent orbits

By Yoshinori Namikawa

01:05:54

published on April 24, 2019

Higher representations of $gl(1|1)^+$

By Raphaël Rouquier

59:52

published on April 21, 2019

Langlands duality and quantum field theory

By Philsang Yoo

01:04:54

published on April 24, 2019

Irreducible equivariant perverse coherent sheaves on affine Grassmannians of type $A$ and dual canonical bases

By Michael Finkelberg

01:03:04

published on April 23, 2019

Mirabolic Satake equivalence

By Victor Ginzburg

01:02:49

published on April 24, 2019

A geometric $R$-matrix for the Hilbert scheme of points on a general surface

By Noah Arbesfeld

56:24

published on April 24, 2019

A sheaf theoretic approach towards calculating simple characters of algebraic groups

By Peter Fiebig

01:05:20

published on April 24, 2019

Affine Springer fibers and G1T modules

By Eric Vasserot

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