Un of Tenn | Math Department

Seminars and Colloquiums
for the week of January 23, 2012

Speaker:

Professor Xia Chen, Monday
Algebra Seminar, Monday
Juraj Foldes, Vanderbilt University, Tuesday
Mr. Shuaibing Luo, Wednesday
Professor Zhou Gang, Institute for Theoretical Physics, Switzerland, Thursday

If you are interested in giving or arranging a talk for one of our seminars or colloquiums,
please review our calendar.

If you have questions, or a date you would like to confirm, please contact Dr. Judy Day.

Monday, January 23

PROBABILITY SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 122
SPEAKER: Professor Xia Chen
TITLE: Quenched asymptotics for Brownian motion in generalized Gaussian potential

ALGEBRA SEMINAR
TIME: 3:35.
ROOM: Ayres B004
Organizational meeting.

Tuesday, January 24

COLLOQUIUM
TIME: 3:35 - 4:25 p.m.
ROOM: Ayres 405
SPEAKER: Juraj Foldes, Vanderbilt University
TITLE: Positive solutions of elliptic and parabolic problems on symmetric domains
ABSTRACT: In this talk we will focus on qualitative properties of positive solutions of very general elliptic and parabolic partial differential equations. Such equations naturally arise as models of phenomena in various sciences such as physics, biology, or economy. In the first part we will discuss how the shape of the domain influences the asymptotic properties of solutions of parabolic equations, that is, their behavior for large times. We show that regardless of the initial conditions, the domain is determining the shape of the limit profiles. Also, the shape of the domain simplifies the dynamics of solutions and it enables us to prove nontrivial convergence results, such as convergence of a solution to an equilibrium. In the second part of the talk we will discuss positivity of non-negative solutions to elliptic problems on symmetric domains. These solutions naturally arise as possible limit profiles of solutions of parabolic problems. Again, the symmetry of the domain plays a crucial role in our results.

Refreshments available at 3:00.

Wednesday, January 25

ANALYSIS SEMINAR
TIME: 3:35 - 4:25 p.m.
ROOM: Ayres 112
SPEAKER: Shuaibing Luo, UTK
TITLE: Trace estimate of commutators of multiplication operators on function spaces (continued)
ABSTRACT: I will present the Arveson's conjecture on the Drury-Arveson space, and some analogous results on Bergman space and Hardy space over the d-dimensional complex unit ball (d>2). I will then talk about the Schatten p class, and the estimate of Schatten 2p norm of commutators on Bergman and Hardy spaces.

Thursday, January 26

COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 405
SPEAKER: Professor Zhou Gang, Institute for Theoretical Physics, Switzerland
TITLE: On Singularity Formation Under Mean Curvature Flow
ABSTRACT: In this talk I present our recent works, jointly with D. Knopf and I.M. Sigal, on singularity formation under mean curvature flow. By methods borrowed from dispersive equations and mathematical physics we present a very different way of studying it, and moreover obtain asymptotic of singularity formation on asymmetric surfaces for the first time. After reviewing known results I will compare our approaches to the old ones. Some key elements will be discussed. A few problems, which might be tackled by our techniques, will be formulated.

Refreshments will be available at 3:00 p.m.

Past notices:

winter break