Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4 (22w5164)

The Banff International Research Station will host the "Interactions of Gauge Theory with Contact and Symplectic Topology in Dimensions 3 and 4" workshop in Banff from March 6 to March 11, 2022.

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 Poincaré 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.

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).