Vorträge in der Woche 16.12.2024 bis 22.12.2024

Montag, 16.12.2024: Matrix coefficients and the pre-trace formula

Giacomo Gavelli

Mittwoch, 18.12.2024: Hilbert schemes of points of singular curves and their combinatorics

Javier Sendra (CUNEF Madrid)

The Hilbert scheme of points parametrizes sets of points a the variety counted with multiplicity. In the case of smooth curves their structure is well understood, whereas for singular curves their geometry becomes quite complicated. I will report on a joint work with Ángel David Rios Órtiz about a class of singular curves for which we describe the irreducible components of their Hilbert schemes of points and a particularly nice combinatorial description emerging from them.

Donnerstag, 19.12.2024: Prescribing the Lorentzian mean curvature of a spacelike hypersurface, and the Born-Infeld model

Prof. Dr. Luciano Mari (Universität Mailand)

The talk aims to introduce the reader to the existence and regularity problem for spacelike hypersurfaces in Lorentz-Minkowski space whose mean curvature is a prescribed measure. The class includes, for instance, maximal surfaces with point singularities. Motivation comes from General Relativity and from the electrostatic Born-Infeld theory, according to which the graph function represents the electric potential and its mean curvature the given charge distribution. Various open problems will be discussed. The talk is based on joint works with J. Byeon, N. Ikoma, A. Malchiodi and L. Maniscalco.