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 (University of Luxembourg)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
--------------------09h00--09h30 Welcome
--------------------09h30--10h30 Talk: Antonio Lerario
Abstract: ?--------------------10h30-11h00 Break
--------------------11h00-12h00 Talk: Hermine Biermé
Abstract: ?--------------------12h00-13h30 Lunch--------------------
--------------------13h30-14h30 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 present a new result obtained with David Cohen-Steiner on the behavior of the map X ↦ NX. We 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 suprise 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 X definable in an o-minimal structure admits a normal cycle, which can be obtained as the limits of the normal cycles of the r-offsets Xr = { x : dX(x) <= r } when r tends to zero. As another corollary, we obtain a new proof of the fact that sublevel sets of differences of convex functions at weakly regular values (so-called WDC sets) admit a normal cycle. Our proof answers a question raised by Fu on the normal cycles of sublevel sets of differences of convex functions.
--------------------14h30-15h00 Break
--------------------15h00-16h00 Talk: Francesca Pistolato
Abstract: ?--------------------16h00-16h30 Break
--------------------16h30-17h30 Talk Agnès Desolneux
Abstract: ? --------------------Image credits: Marianne Le Vexier