Matrix Factorizations in Physics and Mathematics (08w5080)


Ragnar-Olaf Buchweitz (University of Toronto Scarborough)

Kentaro Hori (University of Toronto)

Anton Kapustin (Simons Center for Geometry and Physics)

Wolfgang Lerche (CERN, European Organization for Nuclear Research)

Duco van Straten (Johannes Gutenberg-Universitie)


Let W be a polynomial in several variables. A matrix factorization of W is just a pair of square matrices F and G of the same size and with polynomial entries, such that the products FG is W times the identity matrix. The concept was introduced in 1980 by D.Eisenbud, and its algebrac as well as geometric aspects were studied during the entire 1980's. In early 2000's, two new waves came and totally changed the perspective --- String theory and knot theory. In String theory, matrix factorizations are important tools to find out what kind of particles exist and how they interact, in the context of braneworld scenario. In knot theory, matrix factorizations are used to define `invariants', quantities that are invariant under deformations of knots. The workshop to take place at the Banff International Research Station, May 11 - 16, 2008, brings together physicists and mathematicians from different backgrounds --- algebra, topology, geometry and String theory --- who have common interest centered around matrix factorizations. They will present their new results, exchange ideas, and discuss new directions of research.

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 supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).