Institut Fourier L’Institut Fourier, laboratoire de mathématiques de Grenoble, est une unité mixte de recherche CNRS/Université Grenoble Alpes. Ses activités portent principalement sur les mathématiques fondamentales développées autour de six grands thèmes de recherche : algèbre et géométries, combinatoire et didactique, géométrie et topologie, physique mathématique, probabilités, théorie des nombres. Ses recherches s’ouvrent aussi à d’autres disciplines, telles que la biologie, l’informatique et la physiqu
https://www.canal-u.tv/chaines/ifourier
Wed, 08 Jun 2022 17:08:39 +0100Canal-Ufrhttps://www.canal-u.tv/sites/default/files/styles/carre_1400/public/as/media/images/logo_producteur/logo_fourier.jpg?h=8e341ddd&itok=LuMx09-yInstitut Fourier
https://www.canal-u.tv/chaines/ifourier
Canal-UNoInstitut Fouriercontact@canal-u.tvInauguration de l'exposition - Vanessa Vitse : Nombres de Sophie Germain et codes secrets
https://www.canal-u.tv/146278
Exposé de Vanessa Vitse (Institut Fourier) : Nombres de Sophie Germain et codes secrets
Fri, 15 Sep 2023 14:00:00 +0100https://www.canal-u.tv/146278Inauguration de l'exposition - Clarisse Coulomb : Une scientifique au temps des Lumières
https://www.canal-u.tv/146268
Exposé de Clarisse Coulomb (Historienne, UGA) : Sophie Germain,
une scientifique au temps des Lumières Fri, 15 Sep 2023 13:00:00 +0100https://www.canal-u.tv/146268Exposition - Romain Joly : Figures de Chladni
https://www.canal-u.tv/146273
Démonstration des figures de Chladni. Fri, 15 Sep 2023 13:00:00 +0100https://www.canal-u.tv/146273Inauguration de l'exposition - Séverin Philip : Sophie Germain et le théorème de Fermat
https://www.canal-u.tv/146270
Exposé de Severin Philip (Institut Fourier) : Sophie Germain et
le théorème de Fermat Fri, 15 Sep 2023 13:00:00 +0100https://www.canal-u.tv/146270Inauguration de l'exposition - Hervé Pajot : Présentation
https://www.canal-u.tv/146274
Présentation de l'exposition. Fri, 15 Sep 2023 13:00:00 +0100https://www.canal-u.tv/146274Inauguration de l'exposition - Louis Funar : Mot d'accueil
https://www.canal-u.tv/146272
Accueil par Louis Funar. Fri, 15 Sep 2023 13:00:00 +0100https://www.canal-u.tv/146272Aurel PAGE - Cohomology of arithmetic groups and number theory: geometric, asymptotic and computational aspects 2
https://www.canal-u.tv/134032
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly using Voronoi models and similar complexes (both euclidean and hermitian). We will describe in details the geometric, cohomological and topological tools, as well as Hecke actions on the cohomology of mod Fri, 21 Oct 2022 00:00:00 +0100https://www.canal-u.tv/134032Phong NGUYEN - Recent progress on lattices's computations 2
https://www.canal-u.tv/134034
This is an introduction to the mysterious world of lattice algorithms, which have found many applications in computer science, notably in cryptography. We will explain how lattices are represented by computers. We will present the main hard computational problems on lattices: SVP, CVP and BDD, related to short and close vectors in lattices, and their average version known as SIS and LWE. We will present the celebrated LLL algorithm, Babai’s algorithm and discrete Gaussian sampling. If time allow Fri, 21 Oct 2022 00:00:00 +0100https://www.canal-u.tv/134034Alexander HULPKE - Computational group theory, cohomology of groups and topological methods 4
https://www.canal-u.tv/133997
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computational group theory (mainly focussing on permutation and matrix groups) and then move on to the cohomology used for the construction of perfect groups. Bettina Eick's lectures will again begin with some general com Thu, 20 Oct 2022 00:00:00 +0100https://www.canal-u.tv/133997Alexander HULPKE - Computational group theory, cohomology of groups and topological methods 5
https://www.canal-u.tv/134024
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computational group theory (mainly focussing on permutation and matrix groups) and then move on to the cohomology used for the construction of perfect groups. Bettina Eick's lectures will again begin with some general com Thu, 20 Oct 2022 00:00:00 +0100https://www.canal-u.tv/134024Zachary Himes - On not the rational dualizing module for $\text{Aut}(F_n)$
https://www.canal-u.tv/133998
Bestvina--Feighn proved that $\text{Aut}(F_n)$ is a rational duality group, i.e. there is a $\mathbb{Q}[\text{Aut}(F_n)]$-module, called the rational dualizing module, and a form of Poincar\'e duality relating the rational cohomology of $\text{Aut}(F_n)$ to its homology with coefficients in this module. Bestvina--Feighn's proof does not give an explicit combinatorial description of the rational dualizing module of $\text{Aut}(F_n)$. But, inspired by Borel--Serre's description of the rational dua Thu, 20 Oct 2022 00:00:00 +0100https://www.canal-u.tv/133998Tobias Moede - Coclass theory for nilpotent associative algebras
https://www.canal-u.tv/134026
The coclass of a finite p-group of order p^n and class c is defined as n-c. Using coclass as the primary invariant in the investigation of finite p-groups turned out to be a very fruitful approach. Thu, 20 Oct 2022 00:00:00 +0100https://www.canal-u.tv/134026Oussama Hamza - Hilbert series and mild groups
https://www.canal-u.tv/133999
Let $p$ be an odd prime number and $G$ a finitely generated pro-$p$ group. Define $I(G)$ the augmentation ideal of the group algebra of $G$ over $F_p$ and define the Hilbert series of $G$ by: $G(t):=sum_{n\in \NN} \dim_{\F_p} I^n(G)/I^{n+1}(G)$.The series $G(t)$ gives several information on $G$. First, during the $60$'s, Golod and Shafarevich used Hilbert series to relate the number of generators and relations defining $G$, to the cardinality of $G$. Also, if $G(t)$ satisfies some equalities, w Thu, 20 Oct 2022 00:00:00 +0100https://www.canal-u.tv/133999Gabriele NEBE - Lattices, Perfects lattices, Voronoi reduction theory, modular forms, computations of isometries and automorphisms
https://www.canal-u.tv/134028
The talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and Hermitian). The talk of Nebe will build upon these notions, introduce Boris Venkov's notion of strongly perfect lattices and show that these are perfect and eutactic and hence extreme. We will show how to construct such lattices using representation theory of finite groups and modular forms. Thu, 20 Oct 2022 00:00:00 +0100https://www.canal-u.tv/134028Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, asymptotic and computational aspects 3
https://www.canal-u.tv/133634
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly using Voronoi models and similar complexes (both euclidean and hermitian). We will describe in details the geometric, cohomological and topological tools, as well as Hecke actions on the cohomology of mod Tue, 11 Oct 2022 00:00:00 +0100https://www.canal-u.tv/133634Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, asymptotic and computational aspects 2
https://www.canal-u.tv/133635
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly using Voronoi models and similar complexes (both euclidean and hermitian). We will describe in details the geometric, cohomological and topological tools, as well as Hecke actions on the cohomology of mod Tue, 11 Oct 2022 00:00:00 +0100https://www.canal-u.tv/133635Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, asymptotic and computational aspects 1
https://www.canal-u.tv/133633
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly using Voronoi models and similar complexes (both euclidean and hermitian). We will describe in details the geometric, cohomological and topological tools, as well as Hecke actions on the cohomology of mod Tue, 11 Oct 2022 00:00:00 +0100https://www.canal-u.tv/133633Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, asymptotic and computational aspects 4
https://www.canal-u.tv/133586
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly using Voronoi models and similar complexes (both euclidean and hermitian). We will describe in details the geometric, cohomological and topological tools, as well as Hecke actions on the cohomology of mod Fri, 07 Oct 2022 00:00:00 +0100https://www.canal-u.tv/133586Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, asymptotic and computational aspects 5
https://www.canal-u.tv/133587
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly using Voronoi models and similar complexes (both euclidean and hermitian). We will describe in details the geometric, cohomological and topological tools, as well as Hecke actions on the cohomology of mod Fri, 07 Oct 2022 00:00:00 +0100https://www.canal-u.tv/133587Graham ELLIS - Computational group theory, cohomology of groups and topological methods 3
https://www.canal-u.tv/133584
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computational group theory (mainly focussing on permutation and matrix groups) and then move on to the cohomology used for the construction of perfect groups. Bettina Eick's lectures will again begin with some general com Fri, 07 Oct 2022 00:00:00 +0100https://www.canal-u.tv/133584Graham ELLIS - Computational group theory, cohomology of groups and topological methods 2
https://www.canal-u.tv/133377
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computational group theory (mainly focussing on permutation and matrix groups) and then move on to the cohomology used for the construction of perfect groups. Bettina Eick's lectures will again begin with some general com Fri, 30 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133377Philippe ELBAZ - Cohomology of arithmetic groups and number theory: geometric, asymptotic and computational aspects 4
https://www.canal-u.tv/133365
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly using Voronoi models and similar complexes (both euclidean and hermitian). We will describe in details the geometric, cohomological and topological tools, as well as Hecke actions on the cohomology of modu Fri, 30 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133365Graham ELLIS - Computational group theory, cohomology of groups and topological methods 1
https://www.canal-u.tv/133378
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computational group theory (mainly focussing on permutation and matrix groups) and then move on to the cohomology used for the construction of perfect groups. Bettina Eick's lectures will again begin with some general com Fri, 30 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133378 Philippe ELBAZ - Cohomology of arithmetic groups and number theory: geometric, asymptotic and computational aspects 1
https://www.canal-u.tv/133366
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly using Voronoi models and similar complexes (both euclidean and hermitian). We will describe in details the geometric, cohomological and topological tools, as well as Hecke actions on the cohomology of modu Fri, 30 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133366Bettina EICK - Computational group theory, cohomology of groups and topological methods 4
https://www.canal-u.tv/133325
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computational group theory (mainly focussing on permutation and matrix groups) and then move on to the cohomology used for the construction of perfect groups. Bettina Eick's lectures will again begin with some general com Thu, 29 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133325Bettina EICK - Computational group theory, cohomology of groups and topological methods 3
https://www.canal-u.tv/133326
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computational group theory (mainly focussing on permutation and matrix groups) and then move on to the cohomology used for the construction of perfect groups. Bettina Eick's lectures will again begin with some general com Thu, 29 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133326Renaud COULANGEON - Lattices, Perfects lattices, Voronoi reduction theory, modular forms, ... 2
https://www.canal-u.tv/133128
The talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and Hermitian). The talk of Nebe will build upon these notions, introduce Boris Venkov's notion of strongly perfect lattices and show that these are perfect and eutactic and hence extreme. We will show how to construct such lattices using representation theory of finite groups and modular forms. Tue, 20 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133128Lewis Combes - Computing Selmer groups attached to mod p Galois representations
https://www.canal-u.tv/133132
Selmer groups attached to a p-adic Galois representation have been studied thoroughly, but their mod p cousins have so far received less attention. In this talk we explain the construction of the p-adic Selmer group, how it translates to the mod p setting, and give some progress on understanding the ranks of some Selmer groups over various fields. Tue, 20 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133132Bettina EICK - Computational group theory, cohomology of groups and topological methods 1
https://www.canal-u.tv/133121
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computational group theory (mainly focussing on permutation and matrix groups) and then move on to the cohomology used for the construction of perfect groups. Bettina Eick's lectures will again begin with some general com Tue, 20 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133121Benjamin Brück - High-dimensional rational cohomology ...
https://www.canal-u.tv/133130
By a result of Church-Putman, the rational cohomology of $\operatorname{SL}_n(\mathbb{Z})$ vanishes in "codimension one", i.e. $H^{{n \choose 2} -1}(\operatorname{SL}_n(\mathbb{Z});\mathbb{Q}) = 0$ for $n \geq 3$, where ${n \choose 2}$ is the virtual cohomological dimension of $\operatorname{SL}_n(\mathbb{Z})$. I will talk about work in progress on two generalisations of this result: The first project is joint work with Miller-Patzt-Sroka-Wilson (see https://arxiv.org/abs/2204.11967). We show th Tue, 20 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133130Tobias Braun - Orthogonal Determinants
https://www.canal-u.tv/133118
Basic concepts and notions of orthogonal representations are introduced. If X : G → GL(V ) is a K-representation of a nite group G it may happen that its image X(G) xes a nondegenerate quadratic form q on V . In this case X and its character χ : G → K, g 7 → trace(X(g)) are called orthogonal. If χ is an irreducible orthogonal character of even degree this form is unique up to scalars and there is a unique square class detχ in the character eld Q(χ) = Q(χ(g) | g ∈ G) such that given any eld L Tue, 20 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133118Petru Constantinescu - On the distribution of modular symbols and cohomology classes
https://www.canal-u.tv/133124
Motivated by a series of conjectures of Mazur, Rubin and Stein, the study of the arithmetic statistics of modular symbols has received a lot of attention in recent years. In this talk, I will highlight several results about the distribution of modular symbols, including their Gaussian distribution and the residual equidistribution modulo p. I will also discuss about generalisations to cohomology classes in higher Tue, 20 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133124Kieran Child - Computation of weight 1 modular forms
https://www.canal-u.tv/133131
A major achievement of modern number theory is the proof of a bijection between odd, irreducible, 2-dimensional Artin representations and holomorphic weight 1 Hecke eigenforms. Despite this result, concrete examples have proven difficult to produce owing to weight 1 being non-cohomological, and the contribution to the discrete spectrum from modular forms being inseparable from the contribution from Maass forms. In this talk, I will cover recent work towards an improved method for computing weig Tue, 20 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133131Bettina EICK - Computational group theory, cohomology of groups and topological methods 5
https://www.canal-u.tv/133120
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computational group theory (mainly focussing on permutation and matrix groups) and then move on to the cohomology used for the construction of perfect groups. Bettina Eick's lectures will again begin with some general com Tue, 20 Sep 2022 00:00:00 +0100https://www.canal-u.tv/133120Calista Bernard - Applications of twisted homology operations for E_n-algebras
https://www.canal-u.tv/132788
Applications of twisted homology operations for E_n-algebras Tue, 06 Sep 2022 00:00:00 +0100https://www.canal-u.tv/132788Angelica Babei - A family of $\phi$-congruence subgroups of the modular group
https://www.canal-u.tv/132787
A family of $\phi$-congruence subgroups of the modular group Tue, 06 Sep 2022 00:00:00 +0100https://www.canal-u.tv/132787Exposition : Les audaces de Sophie Germain
https://www.canal-u.tv/132703
À l'occasion de la sortie de la bande-dessinée "Les audaces de Sopjhie Germain" (édition Petit à Petit, 2021), l'institut Fourier a réalisé une exposition du même nom. Fri, 02 Sep 2022 11:01:43 +0100https://www.canal-u.tv/132703Exposition : 250 ans Joseph Fourier
https://www.canal-u.tv/132702
"À la découverte de la vie de Joseph Fourier" est une exposition proposée par l'institut Fourier à l'occasion du 250ème anniversaire de la naissance de Joseph Fourier. Elle est été présentée du 21 novembre au 20 décembre 2018 dans les locaux du laboratoire. Fri, 02 Sep 2022 10:48:34 +0100https://www.canal-u.tv/13270250 ans du bâtiment 2016
https://www.canal-u.tv/132701
À l'occasion du 50ème anniversaire de la construction du bâtiment de l'institut Fourier, le laboratoire a réaliser un film pour retracer l'histoire du lieu et organiser un événement scientifique honorer toute la recherche scientifique qui s'y est tenue depuis toutes ces années. Fri, 02 Sep 2022 10:31:27 +0100https://www.canal-u.tv/132701M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem
https://www.canal-u.tv/107573
The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in particular the idea to use surfaces of prescribed mean curvature (as opposed to minimal surfaces). Having the classic positive mass theorem of Schoen-Yau in mind, we describe a new positive mass theorem for manifolds that allows for possibly non asymptotically flat ends, points of incompleteness, Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/107573P. Burkhardt - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow
https://www.canal-u.tv/84851
We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from C0 initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from C0 initial data. Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/84851R. Perales - Recent Intrinsic Flat Convergence Theorems
https://www.canal-u.tv/107563
Théorèmes récents de convergence plane intrinsèque Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/107563J. Fine - Knots, minimal surfaces and J-holomorphic curves
https://www.canal-u.tv/107583
I will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space which have ideal boundary equal to L, and in this way obtain a knot invariant. In other words the number of minimal surfaces doesn’t depend on the isotopy class of the link. These counts of minimal surfaces can be organised into a two-variable polynomial which is perhaps a known polynomial inv Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/107583D. Semola - Boundary regularity and stability under lower Ricci bounds
https://www.canal-u.tv/107569
The theory of non smooth spaces with lower Ricci Curvature bounds has undergone huge developments in the last thirty years. On the one hand the impetus came from Gromov’s precompactness theorem and the Cheeger-Colding theory of Ricci limit spaces. On the other hand “synthetic” theories of lower Ricci bounds have been developed, based on semigroup tools (the Bakry-Émery theory) and on Optimal Transport (the Lott-Sturm-Villani theory). The Cheeger-Colding theory did not consider m Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/107569Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wings
https://www.canal-u.tv/84839
We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at infinity. The 3d flying wings are collapsed. For dimension n ≥ 4, we find a family of Z2 × O(n − 1)-symmetric but non-rotationally symmetric n-dimensional steady gradient solitons with positive curvature operator. We show that these solitons are non-collapsed. Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/84839D. Stern - Harmonic map methods in spectral geometry
https://www.canal-u.tv/107575
Over the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to connections to the study of sphere-valued harmonic maps and minimal immersions. In this talk, I'll describe a series of results which shed new light on this problem by relating it to the variational theory of the Dirichlet energy on sphere-valued maps. Recent applications include new (H^{-1}-) Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/107575R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions
https://www.canal-u.tv/107565
We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural non-collapsing condition, this limiting flow is smooth on the complement of a singular set of parabolic codimension at least 4. We furthermore obtain a stratification of the singular set with optimal dimensional bounds depending on the symmetries of the tangent flows. Our metho Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/107565C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
https://www.canal-u.tv/107571
In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC manifold of dimension 4 (resp. 5) has vanishing π2 (resp. vanishing π2 and π3), then a finite cover of it is homotopy equivalent to Snor connected sums of Sn-1 x S1. This extends a previous theorem on the non-existence of Riemannian metrics of positive scalar curvature on aspherical manifolds Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/107571J. Wang - Topological rigidity and positive scalar curvature
https://www.canal-u.tv/84845
In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with positive scalar curvature is homeomorphic to the Euclidean 3-space. We will furthermore explain the interplay between, minimal surfaces, scalar curvature and the topology at infinity. Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/84845T. Ozuch - Noncollapsed degeneration and desingularization of Einstein 4-manifolds
https://www.canal-u.tv/107561
We study the noncollapsed singularity formation of Einstein 4-manifolds. We prove that any smooth Einstein 4-manifold close to a singular one in a mere Gromov-Hausdorff (GH) sense is the result of a gluing-perturbation procedure that we develop. This sheds light on the structure of the moduli space of Einstein 4-manifolds near its boundary and lets us show that spherical and hyperbolic orbifolds (which are synthetic Einstein spaces) cannot be GH-approximated by smooth Einstein metr Mon, 30 Aug 2021 12:00:00 +0100https://www.canal-u.tv/107561