String-Math Seminar: A Sheaf-Theoretic model for \(SL(2,\mathbb C)\) Floer homology

Seminar | March 18 | 2-3 p.m. | 402 LeConte Hall

 Mohammed Abouzaid, Columbia University

 Department of Mathematics

I will describe joint work with Ciprian Manolescu on constructing an analogue of instanton Floer homology replacing the group \(SU(2)\) by \(SL(2,\mathbb C)\). Having failed to do so using the standard Floer theoretic tools of gauge theory and symplectic topology, we turned to sheaf theory to produce an invariant. After describing our approach, I will discuss some features of this theory that are expected to be visible from a Floer-theoretic point of view, but that we cannot currently access.