Complex analysis and the exit time of planar Brownian motion (joint with pure mathematics)

Abstract: 

The time it takes Brownian motion to leave a planar domain provides a method of measuring the size and shape of the domain. There a number of connections between this quantity and complex analysis, as I will describe. Included will be probabilistic proofs of several results from analysis, including Euler's Basel sum and a general form of the Phragmen-Lindelof principle for analytic functions.