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.

Apr 21

Algebra Seminar
Michael R. Montgomery, Dartmouth College
Colored planar algebras and applications to Hadamard matrix quantum groups 
UB Mathematics building room 250

In this talk we define a colored planar algebra associated to a non-degenerate commuting square and identify the biunitary of the square as an element of the planar algebra. We use the biunitary to construct representations of annular algebras and quantum groups from the commuting square. When the corresponding quantum group is amenable we can compute elements in the spectrum of the adjacency matrix for a generating core presentation. This leads to two criteria which imply non-flatness of the biunitary and infinite dimension of the corresponding quantum group. Computations with these criteria are performed with a continuous family of biunitaries on the 3311 principal graph, Petrescu’s continuous family of complex Hadamard matrices, and type-II Paley Hadamard matrices. We conclude that all of Petrescu’s complex Hadamard matrices and all type-II Paley Hadamard matrices yield infinite-dimensional compact matrix quantum groups.

Wed, Apr 23

Analysis Seminar
Xiaoqing Li, SUNY at Buffalo
Lower bounds of the Riemann zeta function on the line 1 and GL(3)
4:00PM, 250 Math Building

In this talk, we will present a soft method deriving effective lower bounds for the Riemann zeta function on Re(s)=1, using the theory of GL(3) Eisenstein series.

Fri, Apr 25

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

TBD

Mon, May 5

Algebra Seminar
Claudiu Raicu, University of Notre Dame
Polynomial functors and stable cohomology
4:00PM, 250 Math Building

The theory of polynomial representations of the general linear group goes back to the thesis of Issai Schur at the turn of the 20th century. Such representations include the tensor, symmetric, and exterior powers of a vector space, and have been completely classified in the work of Schur when the underlying field is the complex numbers. While there has been significant progress since the work of Schur, the story over a field of positive characteristic remains largely unknown. In my talk I will describe some novel stabilization results for sheaf cohomology, and explain their connection to the study of polynomial representations / functors. This is based on joint work with Keller VandeBogert.