**Seminars and Colloquiums**

for the week of January 16, 2018

for the week of January 16, 2018

*SPEAKERS*

*Tuesday*

Ryan Unger, UTK

*Wednesday*

Dr. Stefan Richter, University of Tennessee

*Friday*

Dr. Sandra Cerrai, University of Maryland, College Park

*TEA TIME -
3:00 pm – 3:30 pm
Tuesday and Wednesday: Ayres 401
Hosted by: Jimmy Scott and Alan Cherne
*

**Tuesday, January 16th**

**GEOMETRIC ANALYSIS**

Title: What is the mass of spacetime?

Speaker: Ryan Unger, UTK

Time: 5:05 PM-6:05 PM

Room: Ayres 113

The Riemannian positive mass theorem is a powerful tool for solving the Yamabe problem and the Brendle-Marques-Schoen stability problem, but the statement is rather strange at first. The complete proof was given by Lohkamp in 2016 using skin structures, and by Schoen and Yau in 2017 using minimal i-slicings. Its statement can be traced back to a special case of the positive mass theorem for spacetimes in general relativity. Here we discuss the physical motivation for the ADM 4-momentum, and how the physics is related to Riemannian geometry.

**Wednesday, January 17th**

**ANALYSIS SEMINAR**

Title: Pick kernels and radially weighted Besov spaces

Speaker: Dr. Stefan Richter, University of Tennessee

Time: 2:30 PM-3:20 PM

Room: Ayres 113

Let m be a radial measure on the unit ball of C^d, let Rf denote the radial derivative of the analytic function f. For a positive integer N the N-th order weighted Besov space consists of all analytic functions f such that R^N f is square-integrable with respect to m.

We prove a number of results about multipliers and invariant subspaces of such weighted Besov spaces. Some of the results are new even in the case where m is Lebesgue measure.

**COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR**

Time: 3:35 PM-4:35 PM

Room: Ayres 112

This will be an organizational meeting.

**Friday, January 19th**

**COLLOQUIUM**

Title: New Frontiers in Probability and Applications Lecture: Small noise asymptotics for some non-linear SPDEs with vanishing noise correlation

Speaker: Dr. Sandra Cerrai, University of Maryland, College Park

Time: 3:30 PM-4:30 PM

Room: Ayres 405

I will present a series of recent results about the validity of a large deviation principle for some nonlinear PDEs, perturbed by a Gaussian random forcing. I will focus my analysis on the study of the regime where both the strength of the noise and its spatial correlation are vanishing, on a length scale $\epsilon$ and $\delta$, respectively, with $0<\epsilon, \delta<<1$. Depending on the relationship between $\epsolin$ and $\delta$, I will prove the validity of the large deviation principle in different functional spaces. I will illustrate my method by considering the two-dimensional stochastic Navier-Stokes equation and a class of stochastic reaction-diffusion equations, defined in any space dimension, including the dynamical $\Phi^{2n}_d$ model.

Sandra Cerrai got her Ph.D. in 1998, at the Scuola Normale Superiore of Pisa, under the supervision of Giuseppe Da Prato. She has been working at the University of Florence (Italy) until 2008, when she moved to the University of Maryland. In the more recent years, she has been working on the analysis of different asymptotic problems for SPDEs in presence of multiple scales, from large deviations to averaging, singular perturbation results and long-time behavior. She is particularly interested in understanding the interplay among all these different asymptotic features of the analyzed systems.

*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 colloquium AT math DOT utk DOT edu *

**Past notices:**