Singularities and Applications - Research School
Université de Lille
June 19-23, 2023

Program                            Room:  "Salle des Réunions", M2 building

Monday, June 19		Thuesday, June 20		Wednesday, June 21		Thursday, June 22		Friday, June 23
9h10-10h00	C2	9h00-9h50	C1	9h00-9h50	C1	9h00-9h50	C3	9h00-9h50	C3
10h00-10h50	C2	10h00-10h50	C1	10h00-10h50	C1	10h00-10h50	C3	10h00-10h50	C3
*	coffee break	*	coffee break	*	coffee break	*	coffee break	*	coffee break
11h15-12h15	TBA	11h15-12h15	C2	11h15-12h15	C2	11h15-12h15	T3	11h15-12h15	T4
***	lunch break	***	lunch break	***	lunch	***	lunch break	***	lunch break
14h30-15:20	T1	14h30-15:20	T2	**	**	14h30-15:20	T3	14h30-15:20	T4
*	coffee break	*	coffee break	*	**	*	coffee break	*	coffee break
15h50-16h40	T1	15h50-16h40	T2	*	*	15h50-16h40	C1	15h50-16h40	TBA
17h00-17h50	C1	17h00-17h50	TBA	*	*	17h00-17h50	TBA	17h00-17h50	TBA

List of registered participants

Aline Bartel (Oldenburg) Adam Bialozyt (Krakow) Nero Budur ** Cezar Joita

Anne Frühbis-Krüger Laurentiu Maxim ** Laurentiu Paunescu **

** Dirk Siersma Alexander Suciu Mihai Tibar Matthias Zach

 

Courses

C1: Anne Frühbis-Krüger and Matthias Zach                 Computational Aspects of Singularities
Abstract

C2: Cezar Joita, Dirk Siersma, and Mihai Tibar           Invariants of hypersurfaces. Fibrations.
Details
Abstract The talks include:
(1). New (and old) results on Milnor numbers, Morse numbers, polar degree, Betti numbers.
(2). Bifurcation of affine maps, and polynomial optimisation.

C3: Laurentiu Maxim                 Applications of singularity theory to optimisation
Program
Abstract I will discuss several applications of singularity theory to concrete optimizations problems in algebraic statistics and applied algebra. In particular, I will discuss the notion of algebraic degree of an optimization problem, and derive topological formulae for such invariants relevant to the nearest point problem and the maximum likelihood estimation. (Based on joint work with J. Rodriguez, M. Tibar, B. Wang and L. Wu.)

Invited Talks

Nero Budur                 Jets, arcs, and singularities

Abstract  Contact loci are sets of arcs or jets on a variety with prescribed contact order along a fixed hypersurface. They can be regarded as the building blocks of motivic integration. I give an overview of recent results about the relations between the topology of the contact loci, singularity theory, and symplectic geometry.

Laurentiu Paunescu                 Lipschitz geometry of singularities : bi-Lipschitz invariants of holomorphic function germs of 2 and 3 variables.
Program
Abstract Combining analytic and geometric viewpoints on the concentration of the curvature of the Milnor fibre, we show that Lipschitz homeomorphisms preserve the zones of multi-scale curvature concentration as well as the gradient canyon structure of holomorphic functions of two variables. In particular, we obtain the first new Lipschitz invariants after those discovered by Henry and Parusinski in 2003.


Alex Suciu                 Topology of hyperplane arrangements

Abstract Much of the fascination with arrangements of complex hyperplanes comes from the rich interplay between the combinatorics of the intersection lattice, the algebraic topology of the complement and its Milnor fibration. A key bridge between these objects is provided by the geometry of two sets of algebraic varieties associated to the complement: the resonance varieties of the cohomology ring and the characteristic varieties of the fundamental group. I will discuss some recent advances in our understanding of these topics, illustrating with concrete examples aided by computer computations.