FRANCQUI Chair |2025–2026 |

Professor François Loeser

Institut de Mathématiques de Jussieu-Paris Rive Gauche

A Francqui Chair has been awarded by the FRANCQUI Foundation to Professor François Loeser;
He will visit Belgium during -the month of March and at the beginning of April. He will deliver a series of lectures that may be attended independently of one another. Each reading will kick off with an introductory part about the topic of the day. The theme will revolve around non-Archimedean methods and valued fields.

 

The Inaugural Lecture will take place on Thursday, 12th March 2026, at UMONS, Building BSM, Auditorium. Hermann, Campus of the Plaine de Nimy, Maistriau Avenue, Mons

15:45 Welcome Introduction

16:00 F. Loeser : On the unexpected ubiquity of non-archimedean methods in mathematics

17:15 Reception

Registration for the inaugural lecture is required. Due to space restrictions, the number of attendants will be limited to 60 people . Please use the following link Registration

 

All the lectures will take place at UMONS, Building BSM, Auditorium. Hermann, Campus of the Plaine de Nimy, Maistriau Avenue, Mons

Schedule

• Thursday 19/03/2026 16:00-18:15 :Ax-Kochen-Ershov Theorems, old and new

Abstract: The classical Ax-Kochen-Ershov Theorem asserts that p-adic fields and fields of power series over finite fields have the same limit theory. We shall explain how it follows from a cell decomposition theorem due to Denef and Pas. This theorem allows to transfer statements from local non-archimedean fields of characteristic zero to characteristic p and vice-versa. We shall explain how such transfer results can be extended to definable sets (work with J. Denef) and to integrals (work with R. Cluckers). We shall end with some explicit examples.

• Friday 20/03/2026 16:00-18:15 : Non-archimedean integrals as limits of complex integrals

Abstract: The asymptotic behavior of complex analytic objects is often described in terms of non-archimedean geometry. In this talk we shall explain how non-Archimedean integrals considered by Chambert-Loir and Ducros naturally arise in asymptotics of families of complex integrals. To perform this analysis, we work over a nonstandard model of the field of complex numbers, which is endowed at the same time with an Archimedean and a non-Archimedean norm. Such fields were introduced long ago by Abraham Robinson with the explicit hope that they would be useful for asymptotic analysis. This is joint work with A. Ducros and E. Hrushovski.

• Tuesday 31/03/2026 16:00-18:15 : Arcs and Monodromy

Abstract: Somewhat unexpectedly, formal arcs play an important role in the study of singularities of complex hypersurfaces, in particular in relation with the Milnor fiber and its monodromy. After reviewing these results we shall explain how that connexion can be understood in terms of non-archimedean geometry and how it leeds to a surprising parallelism with symplectic geometry. 

• Wednesday 01/04/2026 16:00-18:15 : Tame geometry over valued fields

Abstract: Over the reals, o-minimal structures provide a general framework to develop tame geometry. We will start by presenting a general overview of this theory, focusing on applications to number geometry, before presenting some of the non-archimedean analogues obtained in recent years.

François Loeser is also the holder of the second edition of the Jacques Tits Chair, awarded by the Belgian Mathematical Society.

More information : christian.michaux@umons.ac.be