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 2 octobre 2026 (salle Pierre Grisvard, IHP, 3ème étage du bâtiment Borel).

11h00. François Loeser (SU). Nash structure of curves over a valued field and tame henselian rationality.

In joint work with Antoine Ducros we provide a new proof, model-theoretic and geometric in nature, of the tame henselian rationality theorem of Kuhlmann. The proof takes place within the framework of stable completions of algebraic varieties over a valued field. It relies on two main results of independent interest: a Nash structure theorem for the stable completion of an algebraic curve and a tame descent theorem for abstract open polydiscs.

14h15. Antonio Lerario (Trieste). Sard’s theorem in infinite dimension: from real algebraic geometry to sub-Riemannian geometry.


Sard’s theorem asserts that the set of critical values of a smooth map between finite-dimensional manifolds has measure zero. Smale extended this result to maps between infinite-dimensional Banach manifolds with Fredholm differential. When the domain is infinite dimensional and the target is finite dimensional, however, the differential cannot be Fredholm, and the Sard property may fail even for maps that are polynomial on every finite-dimensional subspace. (Kupka constructed an example of a cubic polynomial on a Hilbert space with a full interval of critical values.) At the finite-dimensional core of the problem lies a question in quantitative real algebraic geometry: how does the size of the almost-critical values of a polynomial map from R^n to R^m depend on n, and which estimates remain meaningful as n tends to infinity? I will explain how approximate definable choices and Vitushkin variations provide bounds with an explicit dependence on the ambient dimension. The construction replaces exact semialgebraic selections, whose complexity can grow rapidly with n, by controlled Hausdorff approximations of low dimension. These estimates can then be combined with quantitative finite-dimensional approximation of subsets of a Hilbert space. The resulting Sard criteria are governed by a competition between the growth of semialgebraic complexity and the decay of the approximation error, measured by Kolmogorov n-widths. In this way, algebraic information carried by finite-dimensional sections continues to control the critical values of a genuinely infinite-dimensional map. Finally, I will explain how Kupka’s classical infinite-dimensional counterexample can be realized inside the endpoint map of a smooth bracket-generating distribution. The resulting endpoint map has no regular values, disproving the sub-Riemannian Sard conjecture in the smooth category. Together, these results describe what can survive, and what can fail, when finite-dimensional algebraic estimates are pushed to an infinite-dimensional limit.
This is based on joint works with Luca Rizzi and Daniele Tiberio.

16h00. Isaac Goldring (UC Irvine). On the undecidability of the QWEP for C*-algebras.

In his landmark 1993 paper, Kirchberg introduced a property of C*-algebras called the QWEP, which stands for “quotient of the weak expectation property”. As the name suggests, the property is defined by the fact that the algebra is a quotient of a C*-algebra with the weak expectation property, which was a property introduced by Lance years earlier in connection with the theory of tensor products of C*-algebras. While at first glance this seems to be a strange property, Kirchberg showed that whether or not every C*-algebra has the QWEP is equivalent to the famous Connes Embedding Problem (CEP) from von Neumann algebra theory. The CEP remained open for nearly 50 years until its recent refutation in 2020 via a result in quantum complexity theory (as well as the equivalence with Kirchberg’s QWEP conjecture). Several years ago, I showed that the QWEP is an axiomatizable property of C*-algebras. In this talk, I will present joint work with Aruseelan and Hart where we show that the QWEP does not have an effective axiomatization and, in fact, there can be no effectively axiomatizable satisfiable theory of C*-algebras all of whose models have the QWEP (modulo some nontrivially conditions). The proofs uses the connection with the quantum complexity results mentioned above as well as other techniques from C*-algebra theory. No prior knowledge of continuous logic, operator algebras, or quantum complexity will be assumed.

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.