Abstract:
Homological mirror symmetry predicts an equivalence between the derived category of equivariant coherent sheaves on the additive Coulomb branch X and a version of the wrapped Fukaya category on multiplicative Coulomb branch Y with superpotential W. If one decategorifies both sides by taking K-theory, the construction still gives an interesting identification between well-known objects in the equivariant K-theory of X and cycles with coefficients in local systems on Y. The talk will show how it works for the fixed point basis and the stable envelopes. Work in progress with Andrey Smirnov, with many insights from the joint project with Mina Aganagic, Peng Zhou and Yixuan Li.