Noncommutative Geometry Seminar

Date: January 25, 2023

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Shiqi Liu, Penn State

Title: Analysis of the hypoelliptic Laplacian

Abstract: Invented by Jean-Michel Bismut, the hypoelliptic Laplacian is the centerpiece of a new type of index theory. It leads to a remarkable trace formula and reveals completely new insights into geometry and representation theory. However, the subject relies on analysis that is made difficult by the non-ellipticity of the hypoelliptic Laplacian operator. Recently, with techniques from noncommutative geometry, we have shown that the hypoelliptic Laplacian is actually elliptic under a new calculus. This will significantly reduce the complexity of the analysis. This is joint work with N. Higson, E. MacDonald, F. Sukochev, and D. Zanin.