### The ordered differential field of transseries

Lou Van Den Dries
The field of Laurent series (with real coefficients, say) has a natural derivation but is too small to be closed under integration and other natural operations such as taking logarithms of positive elements. The field has a natural extension to a field of generalized series, the ordered differential field of transseries, where these defects are remedied in a radical way. I will sketch this field of transseries. Recently it was established (Aschenbrenner, Van der Hoeven,...

Guy Henniart

Alexandre Ern

### Panorama des services numériques de la Pateforme en Ligne pour les Mathématiques

Damien Ferney
Un panorama des Services Numériques disponibles sur la Plateforme en Ligne pour les Mathématiques (PLM). Nous ferons un inventaire des services numériques accessibles à travers le Portail des Mathématiques et décrirons leur utilité dans un cadre collaboratif ou nomade et nous aborderons brièvement leur utilisation et leur configuration.

### The H-Principle and Turbulence

László Székelyhidi
It is well known since the pioneering work of Scheffer and Shnirelman that weak solutions of the incompressible Euler equations exhibit a wild behaviour, which is very different from that of classical solutions. Nevertheless, weak solutions in three space dimensions have been studied in connection with a long-standing conjecture of Lars Onsager from 1949 concerning anomalous dissipation and, more generally, because of their possible relevance to the K41 theory of turbulence. In recent joint work...

### Boundary calculus on conformally compact manifolds, and a boundary Yamabe problem

A. Rod Gover
On conformally compact manifolds of arbitrary signature I will describe a natural boundary calculus for computing the asymptotics of a class of natural boundary problems. This is applied to the non-linear problem of finding, conformally, a conformally compact constant scalar curvature metric on the interior of a manifold with boundary. This problem was studied from a different point of view by Andersson, Chrusciel, Friedrich (ACF) in 1992. They identified a conformal submanifold invariant that obstructs...

### Nearby Lagrangians are simply homotopic

Mohammed Abouzaid
I will describe joint work with Thomas Kragh proving that closed exact Lagrangians in cotangent bundles are simply homotopy equivalent to the base. The main two ideas are (i) a Floer theoretic model for the Whitehead torsion of the projection from the Lagrangian to the base, and (ii) a large scale deformation of the Lagrangian which allows a computation of this torsion.

### Structures de données complexes et traitement de données massives

Christian Lenne
Proposition d'une démarche pour le traitement de données complexes et/ou massives à des fins d'exploration interactive. Basée sur la mise en œuvre effective dans un contexte de données de santé, cette démarche propose d'explorer des notions connues mais peu utilisées qui émergent comme les bases graphes pour modéliser un lac de données et l'exploiter. Nous balayons quelques environnements système (Hadoop, bases NoSQL, ETL) et effleurons les contraintes de sécurité d'accès.

### Trisections diagrams and surgery operations on embedded surfaces​

David Gay
Various surgery operations on dimension four begin with a 4–manifold $X$ and an embedded surface $S$, then remove a neighborhood of $S$ and replace it with something else to produce an interesting new 4–manifold. In a few standard surgery constructions, especially the Gluck twist operation, I will show how, given a trisection diagram of $X$ with decorations that describe the embedded surface $S$, to produce a trisection diagram for the new 4–manifold. This is joint...

### Counting and equidistribution of integral representations by quadratic norm forms in positive characteristic?

Frédéric Paulin
In this talk, we will prove the projective equidistribution of integral representations by quadratic norm forms in positive characteristic, with error terms, and deduce asymptotic counting results of these representations. We use the ergodic theory of lattice actions on Bruhat-Tits trees, and in particular the exponential decay of correlation of the geodesic flow on trees for Hölder variables coming from symbolic dynamics techniques.

### On real algebraic knots and links

Stepan Orevkov
I will present the following results on real algebraic spatial curves: (1) (joint with Mikhalkin) Classification of smooth irreducible spatial real algebraic curves of genus 0 or 1 up to degree 6 up to rigid isotopy. (2) (joint with Mikhalkin) Classification of smooth irreducible spatial real algebraic curves with maximal encomplexed writhe up to (not rigid yet) isotopy. (3) Classification of smooth spatial real algebraic curves of genus 0 with two irreducible components up to...

### Exemples de modélisation mathématiques en médecine - partie 1

Dominique Barbolosi
Il sera exposé divers exemples de modélisation en médecine (biologie du cancer, pharmacologie, imagerie fonctionnelle) pouvant donner lieu à des activités pédagogiques reposant de manières essentielles sur l'utilisation de l'informatique.

### Spherical splines

Hartmut Prautzsch
The Bézier representation of homogenous polynomials has little and not the usual geometric meaning if we consider the graph of these polynomials over the sphere. However the graph can be seen as a rational surface and has an ordinary rational Bézier representation. As I will show, both Bézier representations are closely related. Further I consider rational spline constructions for spherical surfaces and other closed manifolds with a projective or hyperbolic structure.

### Rank 3 rigid representations of projective fundamental groups

Carlos Simpson
This is joint with Adrian Langer. Let $X$ be a smooth complex projective variety. We show that every rigid integral irreducible representation $\pi_1(X,x) \to SL(3,\mathbb{C})$ is of geometric origin, i.e. it comes from a family of smooth projective varieties. The underlying theorem is a classification of VHS of type $(1,1,1)$ using some ideas from birational geometry.

### Simultaneous rational approximations to several functions of a real variable

Victor Beresnevich
As is well known, simultaneous rational approximations to the values of smooth functions of real variables involve counting and/or understanding the distribution of rational points lying near the manifold parameterised by these functions. I will discuss recent results in this area regarding lower bounds for the Hausdorff dimension of $\tau$-approximable values, where $\tau\geq \geq 1/n$ is the exponent of approximations. In particular, I will describe a very recent development for non-degenerate maps as well as...

### Programming with numerical uncertainties

Eva Darulova
Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. Finite-precision arithmetic, such as fixed-point or floating-point, is a common and efficient choice, but introduces an uncertainty on the computed result that is often very hard to quantify. We need adequate tools to estimate the errors introduced in order to choose suitable approximations which satisfy the accuracy requirements. I will present a...

### Multiple ergodic theorems: old and new - Lecture 3

Bryna Kra
The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of these advances and the different techniques that have been used, focusing on convergence results and what can be said about the limits.

### Interview at CIRM: Mark Pollicott

Mark Pollicott
Mark Pollicott (born 24 September 1959) is a British mathematician known for his contributions to ergodic theory and dynamical systems. He has a particular interest in applications to other areas of mathematics, including geometry, number theory and analysis. Pollicott attended High Pavement College in Nottingham, where his teachers included the Booker prize winning author Stanley Middleton. He gained a BSc in Mathematics and Physics in 1981 and a PhD in Mathematics in 1984 both at...

### The weak KPZ universality conjecture. Lecture 3

Milton Jara
The aim of this series of lectures is to explain what the weak KPZ universality conjecture is, and to present a proof of it in the stationary case. Lecture 1: The KPZ equation, the KPZ universality class and the weak and strong KPZ universality conjectures. Lecture 2: The martingale approach and energy solutions of the KPZ equation. Lecture 3: A proof of the weak KPZ universality conjecture in the stationary case.

### Chemins du plan évitant un quadrant

Mireille Bousquet-Mélou
Les chemins du plan confinés dans un quadrant, ou plus généralement dans un cône convexe, ont été beaucoup étudiés ces dernières années, et ont donné lieu à de jolis résultats. Le plus remarquable dit que, pour les chemins à petits pas, la série génératrice est différentiellement finie si et seulement si un certain groupe de transformations rationnelles, construit à partir des pas autorisés, est fini. Les méthodes employées, allant de l’algèbre élémentaire sur les séries...

### On sum sets of sets having small product set

Sergei V. Konyagin
We improve a result of Solymosi on sum-products in $\mathbb{R}$, namely, we prove that max $(|A+A|,|AA|\gg |A|^{4/3+c}$, where $c>0$ is an absolute constant. New lower bounds for sums of sets with small product set are found. Previous results are improved effectively for sets $A\subset \mathbb{R}$ with $|AA| \le |A|^{4/3}$. Joint work with I. D. Schkredov.

### Inference for spatio-temporal changes of arctic sea ice

Noel A. C. Cressie
Arctic sea-ice extent has been of considerable interest to scientists in recent years, mainly due to its decreasing trend over the past 20 years. In this talk, I propose a hierarchical spatio-temporal generalized linear model (GLM) for binary Arctic-sea-ice data, where data dependencies are introduced through a latent, dynamic, spatio-temporal mixed-effects model. By using a fixed number of spatial basis functions, the resulting model achieves both dimension reduction and non-stationarity for spatial fields at different...

### Modèles Bayésiens non paramétriques pour l'analyse de données

Guillaume Kon Kam King
​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...

### From Vlasov-Poisson to Euler in the gyrokinetic limit

Evelyne Miot
We investigate the gyrokinetic limit for the two-dimensional Vlasov-Poisson system in a regime studied by F. Golse and L. Saint-Raymond [1, 3]. First we establish the convergence towards the Euler equation under several assumptions on the energy and on the norms of the initial data. Then we analyze the asymptotics for a Vlasov-Poisson system describing the interaction of a bounded density of particles with a moving point charge, characterized by a Dirac mass in the...

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

Johannes Nicaise
The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint work with Mircea Mustata and Chenyang Xu.

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