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.

Pour s'abonner à la liste de diffusion de nos messages, consultez https://listes-lm.math.univ-paris-diderot.fr/sympa/help/user-subscribe.html.

Les vidéos des exposés passés sont accessibles ici.

PROCHAINE SÉANCE

Vendredi 6 novembre 2026 (salle Pierre Grisvard, IHP, 3ème étage du bâtiment Borel).

11h00. Michaël Maex (École polytechnique). Weight functions on the Berkovich affine line over any non-Archimedean field

The theory of weight functions by Mustaţă-Nicaise on Berkovich spaces hints at an intrinsic approach to studying skeleta without the limitations of the usual tools from algebraic geometry, i.e., semistable reduction or resolution of singularities. In this talk we discuss how Mustaţă-Nicaise's construction can be generalised to define weight functions intrinsically on any quasi-smooth Berkovich space as a sort of normalised log-discrepancy of a canonical form. Next, we turn our attention to computing weight functions on the Berkovich affine line over any non-Archimedean field K. This question reduces to the entirely value-theoretic problem of describing the integral log differentials L/K for a simple extension of real valued fields L/K , which we describe using the data in MacLane-Vaquié chains. We find that on the affine line, weight functions are completely determined by the integral piecewise linear (Z-PL) structure the affine line and vice versa, yielding new insight into the Z-PL structure. Finally, we discuss how this can be used to define and compute the essential skeleton of certain Berkovich spaces.

14h15. Antoine Commaret (INRIA, Sophia Antipolis). Persistent Homology and the Geometry of Definable Sets.

This talk investigates the normal cycle (also known as the characteristic cycle in the subanalytic semialgebraic settings), an object in geometric measure theory that encodes the extrinsic curvature of singular sets in Euclidean spaces. Using persistent homology, we establish the continuity of the map associating a compact set with its normal cycle under small homotopy-controlled perturbations. Combined with Kurdyka–Łojasiewicz inequalities, this continuity yields a construction of normal cycles for compact definable sets in arbitrary o-minimal structures, extending previous results in the subanalytic setting. Furthermore, we establish a definable version of Hadwiger's theorem: in Euclidean spaces, every isometry-invariant valuation on definable compact sets that is continuous with respect to normal cycles is a linear combination of intrinsic volumes (also called quermassintegrals or Lipschitz-Killing curvatures).

16h00. Sebastian Eterovic (Vienne). Modular Zilber-Pink for generic varieties .

The modular Zilber-Pink conjecture governs the behavior of unlikely intersections in powers of the modular curve. In this talk, I will present joint work with V. Aslanyan and G. Fowler where we prove that the conjecture holds for "generic varieties". This result is in the same spirit as (but does not follow from) other "generic Zilber-Pink" results, like those found in the works of Barroero-Dill and Klingler-Tayou. Our methods differ from the ones used in these works, by building upon the work of Pila-Scanlon, which relies on the model theory of differential fields, and combining this with an arithmetic input in the form of the Modular Mordell-Lang theorem of Habegger-Pila.

SÉANCES ULTÉRIEURES

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, 2025-26.

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