(0,2) Mirror Symmetry and Heterotic Gromov-Witten Invariants (10w5047)


(University of Texas)

(University of Pennsylvania)

Ilarion Melnikov (Max Planck Institute for Gravitational Physics (Albert Einstein Institute))

(University of Chicago)

Eric Sharpe (Virginia Tech)


The Banff International Research Station will host the "(0,2) Mirror Symmetry and Heterotic Gromov-Witten Invariants" workshop from March 7th to March 12th, 2010.

String theory has served as a remarkable bridge builder between theoretical physics and mathematics.
The former lends to the latter new, physically motivated perspectives on difficult mathematical problems,
as well as suggests interesting new directions of research. The latter is invaluable to the former by helping
to precisely formulate and often solve problems that could not be tackled without new mathematical tools.

One of the best known of these bridges is the study of Mirror Symmetry. The origin of this subject lies
in attempts to build a four-dimensional physical world out of the ten-dimensional string theory. One way to
achieve this goal is to wrap six of the dimensions in a very small space, leaving four dimensions to span
something that resembles our universe. Many properties of the resulting four-dimensional physics are then
encoded in the geometric properties of the internal space chosen. Mirror symmetry is a remarkable property
that there exist pairs of topolgically distinct internal spaces M and W that lead to exactly the same four-dimensional
physics. Under this equivalence, difficult questions about the geometric properties of M wind up being equivalent
to much simpler questions about the properties of W.

This property, and details of such "mirror pairs" have received great scrutiny from mathematicians and physicists, to
the considerable advantage to both mathematics and physics. There are indications in current research that this property
may be significantly extended, leading to new developments in mathematics, as well as an improved understanding of
physical theories that resemble more closely the four-dimensional world we inhabit. The aim of this workshop is to
bring together mathematicians and physicists to attempt to formulate this extension.

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).