### 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.

### High frequency back reaction for the Einstein equations

Cécile Huneau
It has been observed by physicists (Isaacson, Burnett, Green-Wald) that metric perturbations of a background solution, which are small amplitude but with high frequency, yield at the limit to a non trivial contribution which corresponds to the presence of an energy impulsion tensor in the equation for the background metric. This non trivial contribution is of due to the nonlinearities in Einstein equations, which involve products of derivatives of the metric. It has been conjectured...

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

Martina Hofmanova
I will present some recent results on global solutions to singular SPDEs on $\mathbb{R}^d$ with cubic nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensions $d=4,5$ and in the parabolic setting for $d=2,3$. A motivation for considering these equations is the construction of scalar interacting Euclidean quantum field theories. The parabolic equations are related to the $\Phi^4_d$ Euclidean quantum field theory via Parisi-Wu stochastic quantization, while the elliptic equations are linked...

### Pathwise or quasi-sure towards dynamic robust framework for pricing and hedging

Jan Obloj
I discuss some recent developments related to the robust framework for pricing and hedging in discrete time. I introduce pointwise approach based on pathspace restrictions and compare it with the quasi-sure setting of Bouchard and Nutz (2015), and show that their versions of the Fundamental Theorem of Asset Pricing and the Pricing-Hedging duality may be deduced one from the other via a construction of a suitable set of paths which represents a given set of...

### Systèmes de stockage distribués pour la gestion de grands volumes de données

Jérôme Pansanel
Les solutions logicielles pouvant être mises en place pour assurer une disponibilité optimale et une rapidité d'accès adéquate aux fichiers n'ont jamais été aussi nombreuses, en particulier lorsque nous parlons de systèmes de fichiers distribués. Quand vient l'heure du choix, quelle(s) solution(s) choisir ? Après un panorama des systèmes de fichiers distribués (CEPH, BeeGFS, DPM, OpenIO, iRODS, ...). les critères de choix seront détaillés. Enfin, des exemples de déploiements seront présentés en perspective des besoins...

### Quantum character varieties at roots of unity

Pavel Safronov
Character varieties of closed surfaces have a natural Poisson structure whose quantization may be constructed in terms of the corresponding quantum group. When the quantum parameter is a root of unity, this quantization carries a central subalgebra isomorphic to the algebra of functions on the classical character variety. In this talk I will describe a procedure which allows one to obtain Azumaya algebras via quantum Hamiltonian reduction. As an application, I will show that quantizations...

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