Thomas Carroll

Research interests: Complex Analysis, Potential Theory, links with Probability Theory, especially Brownian motion.

My main research area is Complex Analysis, in particular the interplay between analytic quantities associated with a planar domain (such as the first Dirichlet eigenvalue of the Laplacian, the torsion function, the hyperbolic metric, lifetime of Brownian motion) and geometric quantities associated with the domain (such as its area, its inradius). Generalised isoperimetric problems in this area often have counterparts in higher dimensions, where potential theoretic techniques apply, or for special classes of planar regions, for example convex regions. Such problems are of interest within pure and applied mathematics. A wide variety of techniques from conformal mapping and geometric function theory, complex analysis in general, potential theory and probability theory are used.  

My main teaching interests are in the area of Analysis, including calculus, complex analysis, real analysis, and measure theory. That said, in the past I have taught various courses on, for example, number theory, linear algebra, financial mathematics. Modules taught: 2014-2015 MA1059 Calculus (5 credits) MA2051 Mathematical Analysis 1 (5 credits) MF2052 Derivatives, Securities and Option Pricing (5 credits) MA1060 Introduction to Analysis (5 credits)