Hodge theory and string duality (11w5090)


(University of Missouri - St. Louis)

(University of Alberta)

(Washington University in St. Louis)

Johannes Walcher (McGill University)


The Banff International Research Station will host the "Hodge theory and string duality (HALF)" workshop from December 4th to December 9th, 2011.

The mathematical theory that describes how integrals and differential equations control the shape of algebraic spaces in various dimensions is known as Hodge theory. One of the million-dollar prize Clay Millenium Problems, the most important conjecture in algebraic geometry -- the Hodge Conjecture -- can be thought of as "a metaphor for transforming transcendental computations into algebraic ones." The physical theory able to describe the universe at both micro- (quantum mechanics) and macro- (general relativity) scales, and at the same time thought to be a suitable candidate for unifying all known forces of nature, is string theory. There are several variants of this "theory of everything," linked by dualities which can radically alter mathematical formulations while preserving physical predictions. String dualities thus imply conjectures: seemingly unrelated pieces of mathematics must be related since they offer different descriptions of the same physical world.

Although a role for Hodge theory in string theory has been hinted at for some time, only very recently has the depth and precision of this relationship begun to emerge. Cutting edge results suggest that a mathematical "grand unification" relating arithmetic geometry and symplectic geometry is taking shape. This workshop brings together at BIRS experts in both the mathematics of Hodge theory and the physics of string dualities. Their goal in Banff: to find the common key linking the abstract machinery of Hodge theory with uncharted sectors of string theory.

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 U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).