I have been at Trinity University since the fall of 2006. Prior to that I worked as a post-doc for two years at Dartmouth College in Hanover, New Hampshire. Although I grew up in Las Vegas, Nevada, I studied mathematics for nine years in Southern California, earning my undergraduate degree from the University of Redlands in 1999 and completing my graduate work at UCLA in 2004. My primary research interests are in analytic and algebraic number theory.
Ph.D. in Mathematics, University of California, Los Angeles
B.S. in Mathematics (summa cum laude), University of Redland
On the primitivity of Dirichlet characters, preprint.
Extremal class numbers of non-abelian number fields, UCLA Ph.D. thesis (2004).
My primary research interests are in the broad fields of algebraic and analytic number theory. In particular, I am interested in how zero-density estimates for families of L-functions can be used as substitutes for the Generalized Riemann Hypothesis in the solution of certain number theoretic problems. In this regard I have spent a good deal of time thinking about the extremal nature of class numbers of number fields. Through Trinity's REU I have also dabbled somewhat in combinatorial number theory, considering certain divisibility properties of integers related to their representations in various bases, as well as the asymptotic behavior of the repeated iteration of certain arithmetic functions.