Partition Problems: Old and New
by
George Andrews
Penn State University

We propose to examine several problems in partitions. We shall begin with older problems that might be amenable to new methods. First we look at Rademacher's long standing conjecture that proposes to reconcile the 19th century Cayley-Sylvester work with the Hardy- Ramanujan-Rademacher achievements. Next we consider some ideas of E.M. Wright and the possibilities for finding asymptotic expansions of partition generating functions near the unit circle; modular forms and mock theta functions form the prototypes, and we hope to look beyond them. Third we examine the currently explosive state of partition identities. Finally we call attention to positivity questions for partitions.

Date received: March 20, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caew-42.