Number Theory Research Group

Number theory is the study of all mathematics arising from the arithmetic of the ordinary integers. It is at once one of the most ancient disciplines, with integral Pythagorean triples appearing on ancient cuneiform tablets which are thousands of years old, and at the same time one of the most active and modern areas of study including the most famous problems of mathematics such as Fermat's Last Theorem, the Twin Primes Conjecture, the Riemann Hypothesis, and the grand system of conjectures known as the Langlands Program. Modern number theory is now also involved in vital applications through out society including digital communications and security systems.

Faculty

Mahdi Asgari

Ph.D., Purdue, 2000.

Number Theory, Automorphic Forms, and L-functions.
John Doyle

B.S./M.A./Ph.D. University of Georgia, 2014.

Dr. Doyle's main research interests are in the field of arithmetic dynamics, which is the study of dynamical systems from an algebraic perspective. His research involves techniques from number theory and algebraic geometry, and much of his work deals with moduli spaces which classify dynamical systems with prescribed dynamical behaviors.
Melissa Emory

Ph.D. University of Missouri, 2018.

Dr. Emory's research interests are automorphic forms and representations, number theory, and representation theory.
Paul Fili

A.B., Harvard University; Ph.D., University of Texas at Austin, 2010.

Dr. Fili's research interests are in number theory and analysis, primarily focusing on topics relating to the distribution of algebraic numbers and points of small height in arithmetic dynamics. Dr. Fili's work uses techniques from potential theory in both archimedean and non-archimedean settings in order to prove number theoretic results about heights and dynamical systems.
Maria Fox

Ph.D., Boston College, 2019; B.S., University of Texas, 2014.

Dr. Fox's research interests are in the field of number theory, specifically arithmetic geometry. She is interested in topics related to the geometry of Shimura varieties in characteristic p.
Amit Ghosh

B.Sc., Imperial College of London; Ph.D., Nottingham, 1981.

Analytic number theory, L-functions.
Anthony Kable

B.Sc. (Hon), Australian National University, 1986; M.Sc., Oxford University, 1989; Ph.D., Oklahoma State, 1997.

Representation Theory, Number Theory, and Invariant Theory.
Igor Pritsker

B.A., M.S. Donetsk State University, USSR, 1990, Ph.D. University of South Florida, Tampa, FL, 1995.

Complex Analysis, Approximation Theory, Potential Theory, Analytic Number Theory and Numerical Analysis.
David Wright

A.B., Cornell U., 1977; Part III, Cambridge U., 1978; A.M./Ph.D., Harvard, 1982.

His primary interest is the study of the properties of algebraic number fields, in particular, those properties (discriminants, class-numbers, regulators) that can be studied with tools from the theory of algebraic matrix groups. This theory dates back to the work of Gauss on the theory of equivalence of binary integral quadratic forms. He also studies the theory of Riemann surfaces and Kleinian groups, a subfield of complex analysis. Surprisingly, many concepts in algebraic number theory have very precise analogues in the theory of surfaces. He is particularly interested in the properties of limit sets of Kleinian groups and in the shape of Teichmuller space, which is a kind of parameter space for Riemann surfaces. SeeIndra's Pearls, (Mumford, Series, Wright).