Refined invariants in geometry, topology and string theory (13w5134)

Arriving in Banff, Alberta Sunday, June 2 and departing Friday June 7, 2013

Organizers

(University of British Columbia)

Duiliu Emanuel Diaconescu (University of Alberta)

(EPF Lausanne)

(Oxford University)

Description

The Banff International Research Station will host the "Refined invariants in geometry, topology and string theory" workshop from June 2nd to June 7th, 2013.

In the physics of string theory, the universe is a ten dimensional
space. While four of the dimensions comprise the usual notions of
space and time, the remaining six are curled up into tiny complicated
geometric spaces called Calabi-Yau threefolds. Understanding the
geometry of Calabi-Yau threefolds is central to both algebraic
geometry and physics. Fundamental invariants of these spaces can be
obtained in seemingly very different ways. In physics, we can
count the number of a certain kind of particle in the associated
string theory; in mathematics, we can count the number of ways a
surface can sit in the space, or the number of bundles (twisted families
of linear spaces like the M\"obius band) on the space. Amazingly, these
counts all turn out to be equivalent in subtle and deep ways. This
surprising link between the
mathematics and physics has led to a flurry of recent advances in both
fields. This workshop brings together both mathematicians and
physicists to explore an even more recent discovery: that the
correspondence between the mathematical and physical counts can be
''refined'' to even subtler counts on both the geometric and physical
sides. These refinements have led to several amazing conjectures in a
variety of fields, ranging from the topology of knots to integrable systems.

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).