Senior Thesis Presentation: A Cohomological Perspective to Nonlocal Operators
Title: A Cohomological Perspective to Nonlocal Operators
Speaker: Nick White
Advisors: Mikil Foss (Mathematics) and Adam Larios (Mathematics)
Date: Tuesday, March 19th at 12:00-1:00 pm
Location: 351 Avery Hall
Abstract:
Nonlocal models have experienced a large period of growth in recent years. In particular, nonlocal models centered around a finite horizon have been the subject of many novel results. In this work we consider three nonlocal operators defined via a finite horizon: a weighted averaging operator in one dimension, an averaging differential operator on R^n, and the truncated Riesz fractional gradient. We primarily explore the kernel of each of these operators when we restrict to open sets in R^n. We discuss how the topological structure of the domain can give insight into the behavior of these operators, and more specifically the structure of their kernels. In particular, we define a nonlocal analogue to the 0th de Rham cohomology group and compare its structure to the classical case.
Please consider attending to support Nick and his efforts concerning a senior thesis.