The Geometry, Algebra, and Physics of Higgs Bundles (23w5082)



(ENS Paris and IPhT Saclay)

Steven Rayan (quanTA / University of Saskatchewan)

(Virginia Tech)


The Banff International Research Station will host the "The Geometry, Algebra, and Physics of Higgs Bundles" workshop at the UBC Okanagan campus in Kelowna, B.C., from May 28 to June 2, 2023.


Higgs bundles have received much attention in mathematics for over 30 years now. They are solutions to certain differential equations that originate in mathematical physics -- specifically, the self-dual Yang-Mills equations reduced by two dimensions -- but have become staples in geometry (algebraic, differential, and symplectic), representation theory, and even number theory. In a spectacular way, Higgs bundles were used to prove the Fundamental Lemma, a Fields Medal-worthy result. Coming full circle, Higgs bundles have a renewed importance in high-energy physics through applications to string theory and mirror symmetry.

The workshop will tackle four of the main directions in which Higgs bundles have recently taken a leading role within the mathematics and physics communities, following the breakthroughs of the last years. Bringing together leaders in the area both in mathematics and physics, as well as young researchers in the subfields of the workshop, the meeting will present the ideal setting for novel discoveries and understanding of the uses that Higgs bundles and Hitchin systems may have.

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. BIRS 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).