New Recursion Formulae and Integrablity for Calabi-Yau Spaces (11w5114)

The Banff International Research Station will host the "New Recursion Formulae and Integrablity for Calabi-Yau Spaces" workshop from October 16th to October 21st, 2011.

Calabi-Yau spaces play a fundamental role in string theory. One of the fundamental problems in theoretical physics today is to find a set of laws which can describe both the behaviour of very large objects (such as planets and stars) and the behaviour of very small objects (such as atoms and subatomic particles) at the same time. String theory is a leading candidate for such a unified theory. It makes a number of surprising predictions, among them that the Universe that we live in may have to be ten-dimensional. We are familiar with four of these dimensions (three space dimensions and one time dimension); string theorists propose that the other six dimensions are curled up into an extremely small shape called a Calabi-Yau space. It turns out that by studying the physics of string theory, we can extract many new and unexpected mathematical properties of Calabi-Yau spaces.

Calabi-Yau spaces are also of great interest to mathematicians, who have studied their geometrical properties for many years. A recent breakthrough inspired by string theory, led by the mathematical physicists Eynard and Orantin, has profound implications for the mathematics of Calabi-Yau spaces. As well as uniting several different areas of mathematics (matrix models, algebraic geometry, and the theory of integrable systems) in a very elegant way, the theory of Eynard and Orantin suggests that there should be a totally unexpected structure, called Virasoro constraints, in the geometry of Calabi-Yau spaces. This workshop brings together many mathematicians --- both leading experts and young researchers --- from around the world to investigate the consequences of the Eynard-Orantin theory. The aim is to identify these new non-trivial Virasoro constraints for Calabi-Yau spaces and find an associated integrable structure. This joint effort will open the way to solving several long-standing problems in both pure mathematics and string theory, and to a better understanding of how the world works at very small scales.

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).