February 12, 2025

PROGRAM

13h30 - Jean-Bernard LASSERRE & Victor MAGRON (LAAS CNRS)

Modern trends in polynomial optimization

In the first part of the talk, given by Victor Magron, the basics of polynomial optimization will be introduced. This problem is known to be NP-hard in general, therefore we will explain how to approximate it as closely as desired with a converging hierarchy of moment/sum-of-square relaxations. Some applications of these hierarchies to power systems and quantum information theory will be sketched.

In the second part of the talk, given by Jean-Bernard Lasserre, Christoffel-Darboux kernels will be introduced and related to the moment/sum-of-square hierarchies. We will then show how to leverage this tool for several applications in data analysis, including outlier detection and trajectory reconstruction.

15h00 - Yohann GENZMER

The Poincaré and inverse Poincaré problems

In this talk, we will focus on a question adressed by Poincaré at the end of the 19th century: namely, can we decide whether or not a given dynamical system is integrable ? In the particular context of complex continuous dynamical systems on the complex plane, we will describe a famous counterexample due to A. Lins Neto. In this interpretation, the initial problem presents a mirror version, known as the inverse Poincaré problem, some aspects of which we will discuss.

16h00 - Coffee Break

https://indico.math.cnrs.fr/event/13741/