Date/heure
17 septembre 2026
14:15 - 15:15
Oratrice ou orateur
Nigel Higson (Penn State University)
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
Jean-Michel Bismut’s hypoelliptic Laplacian is a one-parameter family of linear differential operators that interpolates between the Laplacian on a Riemannian manifold and the generator of the geodesic flow on its tangent bundle. Bismut has analyzed the hypoelliptic Laplacian in a variety of contexts, but in this lecture I shall concentrate on Lie groups and symmetric spaces. In this context, the heat supertraces associated to the operators in the hypoelliptic Laplacian family remain constant throughout the interpolation. By studying the limits at both ends of the family, remarkable formulas are obtained, including for example the Selberg trace formula. I shall explain a few of the basic ideas underlying Bismut’s method, as re-worked by Shiqi Liu, Ed McDonald, Fedor Sukochev, Dima Zanin and myself in ongoing work.