UNIVERSITY OF PENNSYLVANIA

Department of Mathematics

Fall 2003 - Hans Rademacher Lectures in Mathematics

Richard E. Borcherds

Mathematics Department, University of California, Berkeley

will deliver four lectures on

Modular forms, Lie algebras & infinite products

Modular forms
Monday....September 22, 2003....4:30pm

Abstract: What are modular forms and why are they so important?

The Hardy-Ramanujan-Rademacher series
Tuesday....September 23, 2003....4:30pm Abstract: In a notoriously difficult paper, Hardy and Ramanujan gave a non-convergent but asymptotic series for the partition function. While preparing notes on their work, Rademacher found a simpler series that converged exactly.

Modular forms and infinite products
Wednesday....September 24, 2003....4:30pm Abstract: Some modular forms can be written as infinite products; a classical example is Euler's infinite product for the generating function of partitions. The zeros of these modular forms correspond to the terms of the Hardy-Ramanujan-Rademacher series.

Lie algebras and infinite products
Thursday....September 25, 2003....3:30pm
Abstract: The representations of semisimple Lie algebras are described by the Weyl character formula, whose denominator is given as a product. There is an analogue for some infinite dimensional Lie algebras, where the denominator turns out to be a sort of modular form given as an infinite product. In particular the root multiplicities of these Lie algebras can be calculated using the Hardy-Ramanujan-Rademacher series.

Lectures on Monday, Tuesday and Wednesday will be held in room A-6 of the David Rittenhouse Laboratory,
Thursday's lecture will be held in A-5 of the David Rittenhouse Laboratory
corner of 33rd and Walnut Streets, Philadelphia, PA.

Tea: 4E17 David Rittenhouse Laboratory, preceding the lectures at 4:00pm.

For further information, please call the Department of Mathematics at the University of Pennsylvania - 215-898-8627.

Previous Rademacher Lecturers