I will discuss some ongoing work on three-dimensional supersymmetric gauge theories and their relationship to (equivariant) quantum K-theory. I will emphasise the interplay between the physical and mathematical motivations and approaches, and attempt to build a dictionary between the two. As an interesting example, I will discuss the quantum K-theory of flag manifolds. The QK ring will be related to the vacuum structure of a gauge theory with Chern-Simons interactions, and the (genus-0) K-theoretic invariants will be computed in terms of explicit residue formulas that can be derived from the relevant supersymmetric path integrals.
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- Geometry and Analysis Seminar