Title: Fundamentals of Potential Theory With Applications to Polynomial and Rational Approximations

Abstract: Potential Theory is a subject that exists at the intersection of Complex Analysis and Measure Theory.  In this talk, we will discuss the major results of Classical Potential Theory, including Frostman's Theorem and the FFS Theorem.  In particular, we will show how Potential Theory can be used to solve problems in polynomial and rational approximations, such as generalized Chebyshev norms.  We will present some recent results from UNM and discuss possible paths for further exploration.

This seminar also serves as the speaker's comprehensive exam.