【报告摘要】Even though the Christoffel function (CF) is well-known in approximation theory and orthogonal polynomials, it is only recently that some of its remarkable properties have been shown to be useful in some other applications, like data analysis and mining (e.g. for outlier detection and support inference), and approximation of possibly discontinuous functions with no Gibbs phenomenon. So in this talk we will briefly introduce the CF and describe how some of its main features can be exploited in some applications. Moreover we will also describe connections of the CF with seemingly unrelated fields, like positive polynomials, Pell’s equation and equilibrium measure of compact sets. If time permits we will also describe some variants with interesting additional properties.

【报告人简介】Professor Jean-Bernard Lasserre obtained his PhD (1978) and Doctorat d’État (1984) degrees from Paul Sabatier University in Toulouse, France, and has been at LAAS-CNRS in Toulouse since 1980, where he is currently the Directeur de Recherche émérite. He is also a member of the Institute of Mathematics of Toulouse. His research interests include optimization, probability theory, real algebraic geometry, and operations research. His most notable contributions include developing the theory of polynomial optimization and establishing the moment-SOS hierarchy, which is also known as the Lasserre hierarchy.

Professor Lasserre received the John von Neumann Theory Prize and the Khachiyan Prize (both in 2015), and the Lagrange Prize (2009). He is a SIAM Fellow (2014) and was an invited speaker at the International Congress of Mathematicians (ICM) in 2018.