Moduli spaces and combinatorics (06w5087)


(University of British Columbia)

Richard Kenyon (Yale University)

Andrei Okounkov (Columbia University)

Rahul Pandharipande (Princeton University)


Mathematicians from North America and Europe will gather this week at the BIRS workshop, "Moduli spaces and combinatorics" July 22-27, to discuss recent developments in the theory of moduli spaces. A moduli space is a fancy name for the set of shapes which an object can take: imagine for example the set of configurations of a robot arm which is composed of several linkages, or the set of configurations of a complicated molecule such as a polymer whose individual atoms can be folded in many different ways. The other word in the title, combinatorics, refers to counting. Techniques for counting configurations of discrete subsets of spaces of configurations often play a fundamental role in the understanding of a moduli space. Recent research by some of the participants has shown sophisticated connections between moduli spaces and string theory, with classical combinatorial theorems linking previously unconnected concepts.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is administered by the Pacific Institute for the Mathematical Sciences, in collaboration with the Mathematics of Information Technology and Complex Systems Network (MITACS), the Berkeley-based Mathematical Science Research Institute (MSRI) and the Instituto de Matematicas at the Universidad Nacional Autonoma de Mexico (UNAM).