The Analysis of Gauge-Theoretic Moduli Spaces (17w5149)

The Banff International Research Station will host the "The Analysis of Gauge-Theoretic Moduli Spaces" workshop from August 27th to September 1st, 2017.

The introduction of gauge theories in theoretical physics goes back to the 1950’s, while the mathematical analysis of these theories traces back to the 1970’s. These mathematical developments turned out to have numerous far-reaching consequences in low-dimensional topology, and this area of mathematical study provides a beautiful set of interactions between geometric analysis, topology and mathematical physics. There remain many deep questions about the geometry and analysis of these moduli spaces, and this is the subject of intense current research both in the mathematics and the physics communities.

This workshop will address an intricate web of questions about these gauge-theoretic moduli spaces, including their metric structure, L^2 cohomology and the analysis of the natural differential operators on them. Participants will explore the conjectured equivalences of different constructions of these moduli spaces. For the more recently introduced gauge theory equations, the fundamental questions about the basic properties of the associated moduli spaces will be discussed. The subject presents an extraordinarily fertile ground where mathematicians and physicists are able to exchange ideas. This workshop is aimed at fostering serious interactions between the two groups and producing important new results of interest to a large community of geometers, analysts and mathematical physicists.

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 disc
iplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineeri
ng 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).