Géométrie et Théorie des Modèles

Zoé Chatzidakis, co-organiser and co-founder (together with François Loeser, in 2006) of the GTM seminar, passed away on the 22nd of January 2025 in Paris. Zoé had been for years the life and soul of the scientific life in model theory, in Paris and abroad; this was an immense loss for the mathematical community and for her many friends.

Fondateurs : Zoé Chatzidakis (vous trouverez ici un lien vers le prix de thèse décerné à sa mémoire) et François Loeser.

Organisateurs : Raf Cluckers, Georges Comte, Antoine Ducros, Tamara Servi.

Vous pourrez également trouver les informations relatives au GTM sur sa page dédiée du site des évènements co-organisés par l'IMJ-PRG.

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Les vidéos des exposés passés sont accessibles ici.

PROCHAINE SÉANCE

Vendredi 27 mars 2026 (salle Yvette Cauchois, bâtiment Perrin, IHP)

11h00. Pierre Schapira (SU). Subanalytic sheaves and exponential D-modules.
En voici le résumé.

14h00. Tomas Ibarlucia (UPC). Affine logic and the geometry of simplices of invariant measures.

A Choquet simplex is a compact convex set in which every point is the barycenter of a unique boundary measure. Infinite-dimensional simplices are quite diverse, e.g., any Polish space can be obtained as the set of extreme points of a metrizable Choquet simplex. However, those that arise naturally in functional analysis and ergodic theory tend to be either Bauer (i.e., the extreme points form a compact set) or the Poulsen simplex (the unique metrizable simplex whose extreme points are dense). A famous result of Glasner and Weiss captures a precise instance of this dichotomy: for any countable group G, the simplex Pr_G(2^G) of invariant probability measures of the topological Bernoulli shift is either Bauer or the Poulsen simplex. Moreover, it is Bauer if and only if G has Property (T). I will discuss a generalization of the Glasner--Weiss Theorem to a larger class of simplices arising from permutation groups. This addresses questions of Austin motivated by the theory of exchangeable random variables. The proof is based on continuous model theory, and more precisely on recent developments in affine logic.

15h30. Sylvy Anscombe (UPC). Geometric formulations of existential Ax-Kochen-Ershov-statements.

In joint work with Dittmann and Fehm (2023) we showed that decidability of the existential theory of (Fq((t)),t) follows from a property we called (R4), studied before by Kuhlmann in connection with problems of local uniformization. The property (R4) is: every large field k is existentially closed in every extension that admits a k-rational k-place. he result from 2023 was an improvement on a result of Denef and Schoutens (2003), who showed that Resolution of Singularities implies the same decidability problem, and related to a previous result from other work of Fehm and I (2016). Recently Dittmann has proved a general statement, also dependent on (R4), that extends the known results for existential theories of henselian valuation rings in a range of settings. More recently, with Fehm (2026), we studied weakenings of (R4) to deal only with existential closedness (again of large k in extensions with k-rational k-places) restricted to existential formulas with at most a certain number of quantifiers. In turn this yields the decidability of the corresponding fragments of the existential theory of k((t)), relative to the corresponding fragment of the existential theory of k. In this talk I will explain this newer work (previous GTM talks having already addressed the other results), and explore further potential extensions of this fragmented approach which seem to be related to Kuhlmann's work on valuation regular function fields over defectless fields, from the theory of tame valued fields.

SÉANCES ULTÉRIEURES

Il y aura une séance le 17 avril 2025 à l'IHP. Orateurs confirmés : Konstantinos Kartas, Adrien Deloro, Sam Mattheus.

Il y aura une séance le 29 mai (à Jussieu, exceptionnellement) et une le 26 juin (à l'IHP).

Programme des séances passées : 2006-07, 2007-08, 2008-09, 2009-10, 2010-11, 2011-12, 2012-13, 2013-14, 2014-15, 2015-16, 2016-17, 2017-18, 2018-19, 2019-20, 2020-21, 2021-22, 2022-23, 2023-24, 2024-25.

Ce séminaire est subventionné par : l'IMJ-PRG, UPCité (APPR), le GDR EFI, et la bourse KU Leuven Grant IF C16/23/010.