Title: Nonlocal methods for fractional operators in homogeneous groups

Abstract: We discuss methods for producing nonlocal estimates for solutions to integro-differential equations arising from the fractional Laplacian and it's generalizations.  Such operators and settings arise naturally arise in various areas, most notably in non-local problems in quantum mechanics (i.e. in problems involving quantum entanglement).   We begin with motivation for the definition of the operators via the Fourier transform.  Next, we introduce Homogeneous Groups and the tail function and provide some basic non-local estimates in that setting.  Lastly, if time permits, we visit a non-local Harnack inequality in R^n.

This seminar will also function as Galen's Comprehensive Exam.  The talk will be held on Teams.  Here is the link:

https://teams.microsoft.com/l/meetup-join/19%3a2caee950bba8404799e499500...