Mon, Mar 10

Algebra Seminar
Mohammad Javad Latifi Jebelli, Dartmouth College
Algebra of functions on a Hilbert space and QFT 
4:00PM, Mathematics Building room 250

We consider a space of square-integrable functions \(L^2(H)\) on an infinite-dimensional background space, a central mathematical notion in quantum field theory and stochastic processes. We then examine certain Banach algebras of functions within \(L^2(H)\) that are closed under pointwise multiplication. We describe the character spectrum of these algebras, followed by a discussion on induced CCR relations.

Wed, Apr 2

Analysis Seminar
Yusheng Luo, Cornell University
Uniformization of gasket Julia set
4:00PM, 250 Math Building

The quasiconformal uniformization problem for fractal sets is a classical question that has seen significant recent progress. In the 1970s, Ahlfors provided a geometric characterization of when a Jordan curve can be quasiconformally uniformized to a round circle. A closely related question--when a Sierpinski carpet can be quasiconformally mapped to a round carpet--has been extensively studied in both geometric and dynamical settings, with key contributions from McMullen, Bonk, and Bonk-Lyubich-Merenkov.   
In contrast, the problem of determining when a gasket can be quasiconformally mapped to a circle packing is more subtle. In this talk, I will discuss recent joint work with D.Ntalampekos that provides a characterization of when a gasket Julia set is quasiconformally equivalent to a circle packing. The proof builds on new results from some joint work with Y.Zhang on renormalization theory for circle packings.

Fri, Apr 4

Applied Math Seminar
Chunmei Wang, University of Florida
TBD
3:00PM, Math 250

TBD

Fri, Apr 18

Applied Math Seminar
Abner Salgado (University of Tennessee, Knoxville)
Energy, pointwise, and free boundary approximation of the obstacle problem for nonlocal operators

3:00PM, Math 250

We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order 0<s<1. We derive regularity results in weighted Sobolev spaces, where the weight is a power of the distance to the boundary. These are then used to obtain optimal error estimates in the energy norm. 

Next, we develop a monotone, two-scale discretization of the operator, and apply it to develop numerical schemes. We derive pointwise convergence rates for linear and obstacle problems governed by such operators. As applications of the monotonicity, we provide error estimates for free boundaries and a convergent numerical scheme for a concave fully nonlinear, nonlocal, problem.

This presentation is based on several works in collaboration with: A. Bonito, J.P. Borthagaray, W. Lei, R.H. Nochetto, and C. Torres.

Fri, Apr 25

Applied Math Seminar
Sathyanarayanan Chandramouli (University of Massachusetts Amherst)
TBD
3:00PM, Math 250

TBD