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Number Theory

The Department of Mathematics at the University of Illinois at Urbana-Champaign has long been known for the strength of its program in number theory. The department has a large and distinguished faculty noted for their work in this area, and the graduate program in number theory attracts students from throughout the world. At present over twenty students are writing dissertations in number theory. Each semester upper level graduate courses are offered in a variety of topics in analytic, algebraic, combinatorial, and elementary number theory.

Weekly Seminars

One or two regularly scheduled seminars are held each week, with lectures being given by faculty, graduate students, and visiting scholars. The lectures may be elementary introductions, surveys, or expositions of current research.

Number Theory Conferences

Illinois has hosted a long running series of number theory conferences, the most recent being

In addition, every two of three years Illinois hosts the Midwest Graduate Number Theory conference for Graduate Students and recent PhDs, a unique type of conference organized almost entirely by graduate students.

Number Theory faculty and their research interests

Scott Ahlgren [Homepage] — Modular forms and number theory

Bruce Berndt [Homepage] — Ramanujan's notebooks, elliptic functions, theta-functions, q-series, continued fractions, character sums, classical analysis

Florin Boca [Homepage] — Diophantine approximation, spacing statistics

Iwan Duursma [Homepage] — Cryptography, algebraic coding theory, algebraic curves

Kevin Ford [Homepage] — Arithmetic functions, probabilistic number theory, Weyl sums, comparative prime number theory, sieve theory, Riemann zeta function

Martin Luu [Homepage] — Various aspects of the Langlands program. This includes compatibility results between local and global Langlands correspondences, applications of the modularity lifting results introduced by Wiles, the role of p-adic deformations of the various notions appearing in the Langlands program, and also relations to mathematical physics in particular dualities of quantum field theories.

Bruce Reznick [Homepage] — Sums of squares of polynomials, combinatorial number theory

Alexandru Zaharescu [Homepage] — Number theory

Faculty in related areas

Jayadev Athreya — Ergodic theory and dynamics of group actions on parameter spaces of geometric objects.

József Balogh — graph theory, extremal combinatorics, additive combinatorics

Nathan Dunfield — 3-dimensional geometry and topology, hyperbolic geometry, geometric group theory, experimental mathematics, connections to number theory.

Postdoctoral Faculty in Number Theory

Armin Straub (Doob Postdoc) [Homepage] — q-series, modular forms, hypergeometric functions, symbolic computation

Francesco Cellarosi (Doob Postdoc) — Statistical properties of dynamical systems: applications to number theory, quantum mechanics, and random processes. Probabilistic and multiplicative number theory.

Detchat Samart (Doob Postdoc) — Mahler measures, Modular forms, L-functions, Arithmetic of algebraic varieties.

Emeritus Faculty in Number Theory

Harold G. Diamond [Homepage] — Prime number theory, sieves, connections with analysis

A.J. Hildebrand [Homepage] — Analytic and probabilistic number theory, asymptotic analysis

Leon McCulloh — Algebraic number theory, relative Galois module structure of rings of integers, class groups of integral group rings, Stickelberger relations

Ken Stolarsky [Homepage] — Diophantine approximation, special functions, geometry of zeros of polynomials

Stephen Ullom [Homepage] — Galois modules, class groups

Courses

Each year, the following one semester courses are offered:

In addition, at least four topics courses are also offered each year, with student input helping to determine the choice of the topics courses. In recent years, enrollment in these courses has been excellent, typically ranging from 10 to 25. We list below some of the topics courses taught between 2005 and 2013:

Graduate Awards

The Bateman Prize and the Bateman Fellowship are given annually for outstanding research in number theory. They are named for former Professor Paul T. Bateman, who was on the faculty from 1950 to 1989 and continued being active in the group's activities until shortly before his death in 2012. Bateman served as Department Head for the years 1965-1980.

Recipients of the Bateman Prize in Number Theory

Recipients of the Bateman Fellowship in Number Theory

Recent former postdocs in number theory

Xiannan Li (Postdoc, 2011-2013)

Jimmy Tseng (Postdoc, 2011-2012)

Youness Lamzouri (Postdoc, 2010-2012)

Paul Pollack (NSF Postdoc, 2008-2011)

Mathew Rogers (NSF Postdoc, 2008-2011)

Andrew Schultz (Postdoc, 2007-2010)

Jeremy Rouse (Postdoc, 2007-2010)

Sung-Geun Lim (Postdoc 2007-2009)

Maria Sabitova (Postdoc, 2006-2009)

Nayandeep Deka Baruah (Postdoc 2006-2007)

Emre Alkan (Postdoc, 2003-2006)

Matt Boylan (Postdoc, 2002-2005)

Ae Ja Yee (Postdoc, 2000-2003)