Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4 (13w5037)


Denis Auroux (University of California, Berkeley)

Hans Boden (McMaster University)

Olivier Collin (Université du Quebec à Montréal)

(Georgia Institute of Technology)


The Banff International Research Station will host the "Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4" workshop from March 24th to March 29th, 2013.

This workshop will highlight new results in low-dimensional topology coming
from a wide range of geometric methods. Low-dimensional topology studies
the global properties of geometric spaces in
dimensions 3 and 4, such as 3-dimensional space and 4-dimensional space-time.
Surprisingly, the study of spaces in dimensions 3 and 4 is more
challenging than in higher dimensions: for instance, the famous Poincar'e
conjecture, which gives an intrinsic topological characterization of the
sphere, was solved recently by Perelman in dimension 3, and has not yet
been completely settled in dimension 4, while its higher dimensional
generalizations were previously known. In fact, studying 3- and
4-dimensional spaces requires combining a
variety of different approaches, many of which are geometric in nature and
have their roots in theoretical physics. Much of the recent progress in
this extremely active area of mathematics makes use of the interplay between
sophisticated mathematical invariants (quantities that can be used to
distinguish one space from another) coming from gauge theory and from
contact and symplectic geometry, and clever new cut-and-paste constructions
that modify known spaces in surprising ways. The workshop will feature new
discoveries on the shape of space and knotted objects inside space,
and will host leading experts from around the world.
This event is organized by Professors Denis Auroux of University of
California Berkeley, Hans Boden of McMaster University, Olivier Collin
of Universit'e du Qu'ebec `a Montr'eal, and John Etnyre of Georgia
Institute of Technology.

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).