Marianne_Le_Vexier-Geometrie_integrale

Integral Geometry Day in Paris

Organizers: Andreas Bernig (Goethe University Frankfurt/Main) and Vadim Lebovici (Sorbonne University)


>> Registration is free but mandatory: form


Where:
Institut de Mathématiques Jussieu - Paris Rive Gauche,
4 Place Jussieu, 75005 Paris

When:
2nd, October 2026

Abstract
The Integral Geometry Day in Paris wishes to gather the integral geometers from France and neighbors to strengthen the connections between the various poles of this field: geometric probabilities, geometry of singularities and algebraic geometry.

Speakers
Hermine Biermé (Université de Tours)
Antoine Commaret (Inria Centre at Université Côte d'Azur)
Agnès Desolneux (ENS Paris-Saclay)
Antonio Lerario (SISSA)
Francesca Pistolato (ENS Paris-Saclay)

Travel support
Limited travel support will be available for young researchers. You can apply by sending [CV + travel details + estimated budget] at the following address: lebovici@imj-prg.fr
Deadline: 10th, September 2026

Schedule

--------------------
09h15--09h30       Welcome

--------------------
09h30--10h30       Talk: Antonio Lerario

Abstract: ?

--------------------
10h30-11h00       Break

--------------------
11h00-12h00       Talk: Antoine Commaret - Continuity of the normal cycle with respect to C0 convergence

Abstract: The normal cycle NX of a (possibly singular) subset X of Rd is essentially the integral current associated with the unit normal bundle of X. It allows one to recover second order information such as the curvature measures of X or their tensorial variantes. It is a crucial object in integral geometry, especially in the theory of smooth valuations developed by Alesker, where it is used to define smooth, isometry-invariant valuations. Fu's uniqueness result on normal cycles may be seen as definition of the broadest possible class of subsets of Rd for which a normal cycle can be defined; yet the extent of this class remains to be understood.
In this talk I will introduce two distinct topologies on compact subsets of Rd, coming from the homotopy distance and the acyclic convergence. We show that normal cycles are continuous with respect to these topologies on sets with smooth boundaries, which may come as a surprise since these convergence do not a priori provide any control on the convergence of tangent spaces. As a corollary, we show that every compact set definable in an o-minimal structure admits a normal cycle.

--------------------
12h00-13h30       Lunch
--------------------

--------------------
13h30-14h30       Talk: Hermine Biermé - The anisotropy of Gaussian random fields through their Lipschitz-Killing curvature densities

Abstract: I will present a joint work with Agnès Desolneux on the geometry of excursion sets of smooth stationary Gaussian fields. In this work, we focus on the effect of anisotropy on their Lipschitz-Killing curvature densities (close from area, perimeter and Euler characteristics of excursion sets for 2D fields) and propose new geometrical spectral moments. Using isoperimetric inequalities, they allow to define a new geometrical index of anisotropy.

--------------------
14h30-15h00       Break

--------------------
15h00-16h00       Talk: Francesca Pistolato

Abstract: ?

--------------------
16h00-16h30       Break

--------------------
16h30-17h30       Talk Agnès Desolneux

Abstract: ?
--------------------



Image credits: Marianne Le Vexier