University of Oulu

Infotech Oulu Graduate School

Lectures on modular forms

Lecturer: Professor Wadim Zudilin, Moscow State University, Russia

Date, time & room

Monday, November 19, 2007, 10-12, M 201
Tuesday,  November 20, 16-18, M 201
Thursday,  November 22, 12-14, M 242
Friday, November 23, 10-12, M201
Monday, November 26, 10-12, M 201
Wednesday, November 28, 12-14, M 201
Thursday, November 29, 12-14, M 242

The main idea of "Lectures on modular forms" is to not only to briefly review the classical knowledge on the interrelationship between hypergeometric series, modular functions and elliptic curves, but also to indicate some striking applications of modular forms in diophantine and computational number theory. I plan to sketch the standard course in hypergeometric series/modular forms/elliptic curves (providing all necessary references to an accessible literature). The applications are related to many open problems in the subject, and they are of an essential interest in contemporary number theory. All mathematical (and around) students and researchers can find something curious for their future research.

1. Configuration space of four points on the projective line. Isomorphism classes of elliptic curves. (4 hours)
2. Hypergeometric function. (2 hours)
3. Modular group. Modular forms and modular functions. (3 hours)
4. Modular invariant. Differential equations for modular forms (after Ramanujan). (3 hours)
5. Ramanujan's formulae for 1/(pii) and their generalizations. (2 hours)

More information: Keijo Väänänen