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. At least three 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. Almost every year, our number theorists hold one or two conferences.
The research interests of the number theorists here include prime number theory, probabilistic number theory, elliptic curves, Galois module structure, deformations of Galois representations, Iwasawa theory, Wiles' proof of Fermat's Last Theorem, Ramanujan's Notebooks, modular forms, partition theory, special functions, elliptic functions, geometry of numbers, Diophantine approximation, arithmetic functions, sieves, transcendence and irrationality, continued fractions, q-series, and coding theory. A description of many of the areas of number theory studied at the university can be found at Areas of Study.