Events for 09/20/2023 from all calendars

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Shiqi Liu, TAMU

Title: Introduction to the hypoelliptic Laplacian and Bismut’s formula.

Abstract: Invented by Jean-Michel Bismut, the hypoelliptic Laplacian is the centerpiece of a new type of index theory. It provides a remarkable trace formula (Bismut’s formula). In the circle case, it is an application of Possion summation formula. In the compact Lie group case, it becomes Frenkel’s formula. In the symmetric space case, it provides an explicit calculation of Selberg trace formula. In this talk, I will give an overview of the hypoelliptic Laplacian, and briefly explain the analytical proof of Bismut’s formula. Recently, using noncommutative geometry, we developed a series of new techniques in analysis to reduce the difficulty of the proof. This is joint work with N. Higson, E. MacDonald, F. Sukochev, and D. Zanin.

Numerical Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Johnny Guzman, Brown University

Title: Discrete elasticity complexes

Abstract: Mixed finite element methods for elasticity have several advantages including being robust in the nearly incompressible limit. Since the 2002 paper by Arnold and Winther there have been several inf-sup stable elasticity finite elements (a space for the stress and displacement) developed in two and three dimensions. However, finding an entire elasticity complex remained challenging in three dimensions. In the last few years, a few discrete elasticity complexes have been constructed. I will discuss our construction that uses macro-triangulations. This is joint work with Snorre Christiansen, Kaibo Hu, Sining Gong, Jay Gopalakrishnan, Michael Neilan.