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Analytic and Geometric Aspects of Gauge Theory August 22, 2022 to December 21, 2022
Organizers Laura Fredrickson (University of Oregon), Rafe Mazzeo (Stanford University), Tomasz Mrowka (Massachusetts Institute of Technology), Laura Schaposnik (University of Illinois at Chicago), LEAD Thomas Walpuski (Humboldt-Universität)
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The mathematics and physics around gauge theory have, since their first interaction in the mid 1970’s, prompted tremendous developments in both mathematics and physics.  Deep and fundamental tools in partial differential equations have been developed to provide rigorous foundations for the mathematical study of gauge theories.  This led to ongoing revolutions in the understanding of manifolds of dimensions 3 and 4 and presaged the development of symplectic topology.  Ideas from quantum field theory have provided deep insights into new directions and conjectures on the structure of gauge theories and suggested many potential applications.  The focus of this program will be those parts of gauge theory which hold promise for new applications to geometry and topology and require development of new analytic tools for their study.
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