Shaoyun Bai: Orbifold bordism and equivariant transversality

Speaker
Shaoyun Baiisten, MIT

Abstract
Due to the presence of symmetries, the moduli spaces of pseudo-holomorphic maps are not manifolds in general due to the failure of equivariant transversality. Nevertheless, they can be presented asA derived orbifolds with complex orientations, which serve as the universal receptacle from which more traditional invariants can be obtained. I will discuss what we know about the bordism group of such derived orbifolds from the geometric perspective, highlighting how to use algebraic geometry to go from derived orbifolds to manifolds, thereby producing complex-bordism-valued Gromov-Witten invariants. This is based on joint work with Abouzaid, also inspired by earlier work with Xu.