Thursday, September 22
Time: 4:00 p.m.
Location: 114 McAllister Building
Name: Krishnaswami Alladi
Affiliation: University of Florida
Title: A theorem of Gollnitz and its place in the theory of partitions
Abstract: One of the deepest results in the theory of partitions is a theorem of Gollnitz connecting partitions into parts satisfying certain difference conditions with partitions into parts satisfying certain congruence conditions. We begin by presenting a far reaching three parameter generalization of this from which a variety of new identities, as well as new relationships among known partition functions emerge. These include Schur's celebrated theorem as a special case, congruences modulo powers of 2, new combinatorial proofs of Jacobi's fundamental triple product identity in the theory of theta functions, and new weighted identities involving Rogers-Ramanujan partitions. Toward the end a glimpse of what lies beyond Gollnitz's theorem will be given. The talk will include joint work of the speaker with George Andrews, Basil Gordon, and Alexander Berkovich.