Number Theory at the University of Michigan

Faculty:

  • 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 and arithmetic dynamics.

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

Postdocs: Burcu Baran, Ruochuan Liu, Chris Lyons, and Danny Neftin.

Graduate students (advisor): Hunter Brooks (Prasanna), Sijun Liu (Zieve), Andrey Mishchenko (Lagarias), Alex Mueller (Zieve), Julian Rosen (Lagarias), Zach Scherr (Zieve), 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).

Conferences: In May 2011, we hosted a workshop on L-functions, Galois representations, and Iwasawa theory. In November 2010, we hosted the Midwest Number Theory Day and the Midwest Number Theory Conference for Graduate Students.

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)  (to be taught in Fall 2011 by Jeff Lagarias),  and
  • algebraic number theory and class field theory (Math 676/776)  

We also offer a range of courses on advanced topics in number theory. In 2011–2012, Kartik Prasanna will teach a course on elliptic curves, complex multiplication, and modular forms. Previous year's topics include: elliptic curves, 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.

Seminars:
  • Group Theory/Lie Theory/Number Theory: Weekly research seminar with speakers from around the world on topics in number theory and related areas.
  • Michigan Lectures in Number Theory: Annual event in which a distinguished visitor gives three talks on a current research topic in number theory. In Winter 2010, Matt Baker lectured on applications of potential theory on the Berkovich projective line to problems in arithmetic dynamics.
  • Learning seminar: Weekly student lectures on a common theme under guidance of faculty for the duration of the year. Past topics include Gross-Zagier formula, Shimura varieties, torsion in elliptic curves, complex multiplication in abelian varieties, and Serre's conjecture.
  • Working seminar: Weekly sessions in which students and faculty work their way through a paper, topic, or problem. This differs from the Learning seminar in that the talks are less formal and more interactive, and the emphasis is on audience understanding rather than quantity of material covered.
  • Student Arithmetic Seminar: Student organized; lectures by graduate students.

Previous graduates

Recent postdocs


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