Number Theory


  • Jeff Lagarias:   Algebraic and analytic number theory, Diophantine approximation
  • Hugh Montgomery:   Analytic number theory, distribution of prime numbers, Fourier analysis, analytic inequalities, probability
  • Kartik Prasanna:   Arithmetic of automorphic forms and periods, special values of L-functions, Iwasawa theory
  • Michael Zieve:   Algebraic number theory and arithmetic geometry, especially Galois theory, Diophantine equations, and arithmetic dynamics

Faculty in related areas: Mitya Boyarchenko and Stephen DeBacker (representation theory);  William Fulton, Mircea Mustaţă, and Karen Smith (algebraic geometry);  Harm Derksen and Gopal Prasad (algebraic groups).

Visiting faculty: In 2013–2014, Bob Vaughan is a Gehring Visiting Professor.

Postdocs: Burcu Baran, Daniel Fiorilli, Ben Linowitz, and Danny Neftin.

Graduate students (advisor): Adam Kaye (Prasanna), Sijun Liu (Zieve), Hieu Ngo (Lagarias), Suchandan Pal (Prasanna), and Ari Shnidman (Prasanna).

Former faculty: Brian Conrad (2000-2008),  Chris Skinner (2000-2007),  Kannan Soundararajan (2000-2007),  Trevor Wooley (1991-2007),  David Masser (1983-1992),  James Milne (1969-1999),  Donald J. Lewis (1957-1996),  William J. LeVeque (1949-1971).

Electronic resources: Go here for links to e-journals and other electronic resources for number theorists. These links should work both from on-campus and off-campus.

Courses: The following full-year graduate courses are offered in alternating years:

  • analytic number theory (Math 675/775)   and
  • algebraic number theory and class field theory (Math 676/776)

We also offer a range of courses on advanced topics in number theory. Previous year's topics include: elliptic curves, complex multiplication, Diophantine problems, Diophantine approximation, arithmetic of dynamical systems, Iwasawa theory, Hida theory, transcendence theory, spectral theory of modular forms, Galois representations and modular forms, and automorphic forms on algebraic groups.

Group, Lie and Number Theory
Student Arithmetic

Previous graduates

Recent postdocs

This page maintained by Michael Zieve. Please send comments or questions to numbertheory [at]