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 L2(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 L2(H) that are closed under pointwise multiplication. We describe the character spectrum of these algebras, followed by a discussion on induced CCR relations.
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