Seminaire des Master 4

La fédération OcciMath s’associe aux masterclasses de l’EUR MINT pour un séminaire régional présentant aux étudiants de Master les domaines de recherche en mathématiques étudiés dans la région occitanie. La quatrième  session des ces séminaires mensuels a lieu le 12 Février 2025 selon le programme suivant:

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

Title : Modern trends in polynomial optimization

Abstract: 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.

15h : Yohann GENZMER (IMT)

Title : The Poincaré and inverse Poincaré problems

Abstract : 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.