George Andrews and the Gollnitz theorem

Meeting Details

For more information about this meeting, contact Nigel Higson, Stephanie Geyer.

Speaker: Krishnaswami Alladi, University of Florida

Abstract: A Rogers-Ramanujan (R-R) type partition theorem is one that equates partitions whose parts satisfy difference conditions with partitions whose parts satisfy congruence conditions. One of the deepest R-R type partition theorems is a 1967 identity due to Gollnitz. His proof of this identity is very difficult. Andrews is one of the very few to have understood Gollnitz' proof. Andrews subsequently simplified the proof, and in his famous CBMS Lecture Notes asks for an approach to Gollnitz' theorem that would clearly explain the underlying structure. Such an approach was provided by Alladi-Andrews-Gordon in 1995 who viewed a generalization and refinement of Gollnitz theorem as emerging from a remarkable key identity in three free parameters. Andrews' proof of this key identity is a classic achievement. Subsequently, Andrews proved two other key identities for Gollnitz' theorem discovered by Alladi using combinatorial reformulations. And most recently, Andrews found an intriguing new companion to Gollnitz' theorem which was shown by Alladi to also emerge from the 1995 key identity. In this talk the role of Andrews over the years in the exploration of the many facets of Gollnitz' theorem will be described, and in that process, links with a number of fundamental and classical theorems on partitions and q-hypergeometric series will be discussed. The talk will be accessible to non-experts.

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Room Reservation Information

Room Number: 114 McAllister

Date: 11/14/2013

Time: 3:35pm - 4:25pm