Using ultraproducts, I will describe the spectrum of the profinite completion of the integers and of the finite adeles over the rationals.The final aim is to describe the structure sheaf of these structures.Joint work with Margarita Otero and Angus Macintyre.
Nous présenterons une preuve de la Propriété (T) de Kazhdan pour les groupes d'automorphismes de structures métriques aleph_0-catégoriques. Ceci généralise des résultats précédents de Bekka (pour le groupe unitaire) et de Evans et Tsankov (pour les groupes pro-oligomorphes), sans besoin de faire appel à des résultats de classification de représentations unitaires. En effet, l'argument est purement modèle-théorique et basé sur des principes de la stabilité locale.
In the first part of this talk, we introduce the notion of viscosity solutions for nonlocal elliptic equations and revisit the two main tools used in the analysis of such problems, that is comparison principle and regularity. In the second part, we describe the use of these concepts in the study of periodic homogenization for nonlocal equations.
14.00-14.45 Joshua Frisch (Caltech) Proximal actions, Strong amenability, and Infinite conjugacy class groups15.00-15.45 Andy Zucker (Paris VII) Bernoulli Disjointness15.45-16.15 coffee break16.15-17.00 Christophe Garban (Université Lyon 1) Inverted orbits of exclusion processes, diffuse-extensive-amenability and (non-?)amenability of the interval exchanges
The Zilber-Pink conjecture predicts that an algebraic curve in A_2 has only finitely many intersections with the special curves, unless it is contained in a proper special subvariety.Under a large Galois orbits hypothesis, we prove the finiteness of the intersection with the special curves parametrising abelian surfaces isogenous to the product of two elliptic curves, at least one of which has complex multiplication. Furthermore, we show that this large Galois orbits hypothesis holds for curves satisfying a condition on their intersection with the boundary of the Baily--Borel compactification of A_2.More […]
I will explain how tame topology seems the natural setting for variational Hodge theory. As an instance I will sketch a new proof of the algebraicity of the components of the Hodge locus, a celebrated result of Cattani-Deligne-Kaplan (joint work with Bakker and Tsimerman).
Let k be an algebraically closed complete rank 1 non-trivially valued field. Let X be an algebraic curve over k and let X^an be its analytification in the sense of Berkovich. We functorially associate to X^an a definable set X^S in a natural language. As a corollary, we obtain an alternative proof of a result of Hrushovski-Loeser about the iso-definability of curves. Our association being explicit allows us to provide a concrete description of the definable subsets of X^S: they correspond to radial sets. This is a joint work with […]
There is a well-known analogy between the arithmetic of rational numbers and the theory of meromorphic functions over a normed field. It is a classical result of Julia Robinson that the first order theory of the field of rational numbers is undecidable, and one would expect such a result in the meromorphic setting. In this talk I'll give an outline of the proof of undecidability for rigid meromorphic functions in positive characteristic
Dans cet exposé je discuterai de la conjecture de cristallisation, qui consiste à prouver que des points se mettent automatiquement sur un réseau périodique, dans certaines situations. Je parlerai principalement du cas particulier des gaz de Riesz et de Coulomb qui sont omniprésents dans de nombreuses branches des mathématiques. Ils décrivent par exemple la répartition des zéros de solutions d'équations aux dérivées partielles, la statistique des valeurs propres des matrices aléatoires, le placement optimal de points de discrétisation sur des surfaces, et sont reliés à la fonction Zeta de Epstein.
A continuous theory T of bounded metric structures is said to be kappa-categorical if T has a unique model of density kappa. Work of Ben Yaacov and Shelah+Usvyatsov shows that Morley's Theorem holds in this context: if T has a countable signature and is kappa-categorical for some uncountable kappa, then T is kappa-categorical for all uncountable kappa. In classical (discrete) model theory, there are several characterizations of uncountable categoricity. For example, there is a structure theorem for uncountably categorical theories T, due to Baldwin+Lachlan: there is a strongly minimal set […]
