Time: 14:00-15:00, Thursday, August 7 2024
Venue: E4-233, Yungu Campus
Host: Thierry De Pauw, ITS
Speaker: Laurent Moonens, Université Paris-Saclay
Biography: Laurent Moonens completed his PhD in Mathematics at the University of Louvain-la-Neuve (Belgium) under the supervision of Th. De Pauw in 2008. After post-docs in Orsay (France), Ann Arbor and Urbana-Champaign (USA) and Louvain-la-Neuve (Belgium), he was appointed Maître de Conférences (Associate Professor) at the Université Paris-Saclay in 2012, where he obtained the Habilitation (Habilitation à Diriger des Recherches) in 2023. His main interests are Real and Harmonic Analysis, Geometric Measure Theory and Non-absolute Integration theories.
Title: Removable sets for linear PDEs: a survey
Abstract: In this colloquium talk, we will introduce the notion of a removable set for a linear partial differential equation with respect to a space of functions as a set having the property that every function in the above mentioned space satisfying the equation (in the sense of distributions) outside of it, actually satisfies it in the whole Euclidean space. We will then survey several important cases (case of the Laplace equation, of the divergence equation, of linear equations associated to elliptic and canceling operators) and explain how geometric measure theoretic notions of ``smallness’’ can imply removability in those contexts.
