### Operators in ergodic theory - Lecture 2: Dilations and joinings

Markus Haase
The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems

### Counter - EzPaarse

Thomas Porquet & Dominique Lechaudel
COUNTER est un code de bonnes pratiques qui définit la façon dont les rapports d'usage des revues, bases de données, e-books, et contenus multimédia doivent être formatés et mis à disposition des établissements par les fournisseurs. Il permet leur récupération automatisée et leur mise en commun, sur un portail commun comme MESURE. EzPAARSE est un logiciel libre et gratuit développé en partenariat par Couperin.org, l'Inist-CNRS et l'université de Lorraine qui fournit des données d'usage détaillée...

### The Onsager Theorem

Camillo De Lellis
In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is. Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics. Our remark sparked a series of discoveries and...

### Mean-field analysis of an excitatory neuronal network: application to systemic risk modeling?

François Delarue
Inspired by modeling in neurosciences, we here discuss the well-posedness of a networked integrate-and-fire model describing an infinite population of companies which interact with one another through their common statistical distribution. The interaction is of the self-excitatory type as, at any time, the debt of a company increases when some of the others default: precisely, the loss it receives is proportional to the instantaneous proportion of companies that default at the same time. From a...

### Hodge-GUE Correspondence

Di Yang
An explicit relationship between certain cubic Hodge integrals on the Deligne–Mumford moduli space of stable algebraic curves and connected GUE correlators of even valencies, called the Hodge–GUE correspondence, was recently discovered. In this talk, we prove this correspondence by using the Virasoro constraints and by deriving the Dubrovin–Zhang loop equation. The talk is based on a series of joint work with Boris Dubrovin, Si-Qi Liu and Youjin Zhang.

### Table ronde: qu'est-ce qui peut contribuer à rendre les mathématiques plus vivantes dans les classes ?

Pierre Arnoux, Francis Loret, Valérie Théric, Farida Méjani, Olivier Brébant & Thomas Garcia
Comment enrichir son enseignement pour des mathématiques qui transportent ? Cinq professeurs de mathématiques feront part de leurs pratiques et réflexions.

### Signature morphisms from the Cremona group

Susanna Zimmermann
The plane Cremona group is the group of birational transformations of the projective plane. I would like to discuss why over algebraically closed fields there are no homomorphisms from the plane Cremona group to a finite group, but for certain non-closed fields there are (in fact there are many). This is joint work with Stéphane Lamy.

### Prédire aussi bien que les meilleurs (et en plus en faisant des maths !)

Pierre Alquier
​L'intérêt pour l'intelligence artificielle (IA) s'est considérablement accru ces dernières années et l'IA a été appliquée avec succès à des problèmes de société. Le Big Data, le recueil et l’analyse des données, la statistique se penchent sur l’amélioration de la société de demain. Big Data en santé publique, dans le domaine de la justice pénale, de la sécurité aéroportuaire, des changements climatiques, de la protection des espèces en voie de disparition, etc. ​ ​C'est sur...

### Character sums for primitive root densities

Peter Stevenhagen
We study the entanglement of radical extensions over the rational numbers, and describe their Galois groups as subgroups of the full automorphism group of the multiplicative groups involved. A character sum argument then yields the densities (under GRH) for a wide class of primitive root problems in terms of simple ‘local’ computations.

### ​Diffusion limit for a slow-fast standard map

Jacopo De Simoi
​Consider the map $(x, z) \mapsto (x + \epsilon^{-\alpha} \sin (2\pi x) + \epsilon^{-(1+\alpha)}z, z + \epsilon \sin(2\pi x))$, which is conjugate to the Chirikov standard map with a large parameter. For suitable $\alpha$, we obtain a central limit theorem for the slow variable $z$ for a (Lebesgue) random initial condition. The result is proved by conjugating to the Chirikov standard map and utilizing the formalism of standard pairs. Our techniques also yield for the...

### The Daugavet equation for Lipschitz operators

Dirk Werner
We study the Daugavet equation $\parallel Id+T\parallel$ $=1$ $+$ $\parallel T\parallel$ for Lipschitz operators on a Banach space. For this we introduce a substitute for the concept of slice for the case of non-linear Lipschitz functionals and transfer some results about the Daugavet and the alternative Daugavet equations previously known only for linear operators to the non-linear case. numerical radius - numerical index - Daugavet equation - Daugavet property - SCD space - Lipschitz operator

### Topics on $K3$ surfaces - Lecture 4: Nèron-Severi group and automorphisms

Alessandra Sarti
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space. The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire. The topics of the lecture are the following:...

### Dynamics of bounded solutions of parabolic equations on the real line - Part 1

Peter Polacik
We consider parabolic equations of the form $u_t = u_{xx} + f (u)$ on the real line. Unlike their counterparts on bounded intervals, these equations admit bounded solutions whose large-time dynamics is not governed by steady states. Even with respect to the locally uniform convergence, the solutions may not be quasiconvergent, that is, their omega-limit sets may contain nonstationary solutions. We will start this lecture series by exhibiting several examples of non-quasiconvergent solutions, discussing also...

### Multi-norms and Banach lattices

H. Garth Dales
I shall discuss the theory of multi-norms. This has connections with norms on tensor products and with absolutely summing operators. There are many examples, some of which will be mentioned. In particular we shall describe multi-norms based on Banach lattices, define multi-bounded operators, and explain their connections with regular operators on lattices. We have new results on the equivalences of multi-norms. The theory of decompositions of Banach lattices with respect to the canonical 'Banach-lattice multi-norm'...

### Calabi-Yau manifolds, mirror symmetry, and $F$-theory - part I

David R. Morrison
There are five superstring theories, all formulated in 9+1 spacetime dimensions; lower-dimensional theories are studied by taking some of the spatial dimensions to be compact (and small). One of the remarkable features of this setup is that the same lower-dimensional theory can often be realized by pairing different superstring theories with different geometries. The focus of these lectures will be on the mathematical implications of some of these physical “dualities.” Our main focus from the...

### Approximating clutters with matroids

Anna De Mier
There are several clutters (antichains of sets) that can be associated with a matroid, as the clutter of circuits, the clutter of bases or the clutter of hyperplanes. We study the following question: given an arbitrary clutter $\Lambda$, which are the matroidal clutters that are closest to $\Lambda$? To answer it we first decide on the meaning of closest, and select one of the different matroidal clutters. We show that for almost all reasonable choices...

### A microlocal toolbox for hyperbolic dynamics

Semyon Dyatlov
I will discuss recent applications of microlocal analysis to the study of hyperbolic flows, including geodesic flows on negatively curved manifolds. The key idea is to view the equation $(X + \lambda)u = f$ , where $X$ is the generator of the flow, as a scattering problem. The role of spatial infinity is taken by the infinity in the frequency space. We will concentrate on the case of noncompact manifolds, featuring a delicate interplay between...

### Interactions of analytic number theory and geometry - lecture 3

Damaris Schindler
A general introduction to the state of the art in counting of rational and integral points on varieties, using various analytic methods with the Brauer–Manin obstruction.

### Interactions of analytic number theory and geometry - lecture 4

Damaris Schindler
A general introduction to the state of the art in counting of rational and integral points on varieties, using various analytic methods with the Brauer–Manin obstruction.

### Cohomological obstructions to local-global principles - lecture 4

Cyril Demarche
Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these cohomological tools.

### Interactions of analytic number theory and geometry - lecture 2

Damaris Schindler
A general introduction to the state of the art in counting of rational and integral points on varieties, using various analytic methods with the Brauer–Manin obstruction.

### Cohomological obstructions to local-global principles - lecture 3

Cyril Demarche
Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these cohomological tools.

### Cohomological obstructions to local-global principles - lecture 2

Cyril Demarche
Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these cohomological tools.

### Cohomological obstructions to local-global principles - lecture 1

Cyril Demarche
Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these cohomological tools.

### Interactions of analytic number theory and geometry - lecture 1

Damaris Schindler
A general introduction to the state of the art in counting of rational and integral points on varieties, using various analytic methods with the Brauer–Manin obstruction.

• 2017
948
• 2018
192
• 2019
142

• Audiovisual
1,282