Ομιλητής : Prof. Gerard Freixas i Montplet (École Polytechnique) https://perso.pages.math.cnrs.fr/users/gerard.freixas/
Ημερομηνία, ώρα : Τετάρτη 4 Δεκεμβρίου 2024, 13:150
Τοποθεσία : Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.
Τίτλος : “Detecting singular hypersurfaces with spectra of Laplacians”.
Περίληψη : “In this talk, we will be concerned with hypersurfaces defined by the zeros of holomorphic functions in several variables. The study of the singularities of such spaces is classically approached by a beautiful blend of topology, complex analysis and algebraic geometry.
For instance, one may develop cohomological tools from which one can extract numerical invariants capturing some features of the singularities. I will explain how some of these invariants mysteriously appear when one considers the holomorphic analytic torsion of hypersurfaces in projective space. This is another numerical invariant of a very different nature: it is constructed from the spectrum of the Laplacians acting on differential forms. I will also explain the relationship with a conjecture in singularity theory from the 70’s, due to Durfee, and how this leads to new results on determinants of Laplacians.“.