Events for 03/03/2015 from all calendars

Working Seminar in Geometry

Time: 1:00PM - 2:00PM

Location: BLOC 220

Speaker: Colleen Robles, TAMU

Title: Hypergeometric Functions 7

Abstract: Continue with Chapter 4 of Yoshida.

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Vu Hoang, Rice University

Title: Nonlinear PDEs seminar

Abstract:

Title: Singularities for a nonlocal version of Burgers' equation

Abstract:
I consider a non-local, nonlinear transport equation in one space dimension (without dissipation). Here, the velocity field is given by a integral operator with weakly singular kernel. The goal is to prove the existence of blowup in finite time, starting from, say, continuously differentiable initial data. Previous, known blowup proofs rely on studying a Lyapunov functional and on the use of clever identities and/or clever inequalities. A drawback of this approach is that it gives little information on the nature of the singularity. In this talk, I present ongoing work whose chief goal is to gain a deeper understanding of the singularity formation for these equations, and maybe providing a more systematic approach. We construct blowup solutions such that the gradient of blows up at one point only, the solution otherwise retaining its initial regularity. (joint work with A. Kiselev, M. Radosz and X. Xu)

Noncommutative Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Weiping Zhang, Chern Institute of Mathematics

Title: An introduction to analytic torsion (Colloquium)

Abstract: Ray and Singer introduced analytic torsion in 1971 as an analytic analogue of the Reidemeister torsion, a classical topological invariant, and conjectured that the analytic torsion equals to the Reidemeister torsion. This conjecture was proved independently by Cheeger and Mueller around 1978. In this talk we will summarize developments surrounding this important analytic invariant, including a recent joint work with Jean-Michel Bismut and Xiaonan Ma on the asymptotics of the analytic torsion.