# Number Theory

** 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

- Andrew Snowden: Arithmetic geometry and algebraic number 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.

**Seminars**

Group, Lie and Number Theory

Student Arithmetic

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