Topic: Orbifolds in symplectic topology
Organizers: Ceyhun Elmacioglu and Frank Zheng
Description: The moduli space of pseudoholomorphic curves \(\overline{\mathcal{M}}(X, J)\) in a symplectic manifold \(X\) is known to be a highly singular object. That being said, it naturally carries the structure of being a derived orbifold. Moreover, as we vary the almost complex structure \(J\), the derived orbifold bordism type of \(\overline{\mathcal{M}}(X, J)\) is well-defined. Thus, in some sense the bordism class of \(\overline{\mathcal{M}}(X, J)\) can be thought of as a universal enumerative invariant for the symplectic manifold \(X\). In this seminar, we will study the bordism theory of orbifolds and how this theory can be used to define symplectic invariants.
Date | Speaker | Topic | References |
---|---|---|---|
Feb. 12 | Frank | Lie groupoids, I | [Ler09], notes |
Feb. 19 | Frank | Lie groupoids, II | [Ler09], notes |
Feb. 26 | Frank | Stacks | [Ler09], notes |
Mar. 5 | Shuhao | Spectra and generalized cohomology theories | notes |
Mar. 12 | Shuhao | Unoriented bordism and the Steenrod problem | notes |
Apr. 2 | Ceyhun | Complex bordism I | |
Apr. 9 | Ceyhun | Complex bordism II | |
Apr. 16 | Frank | AMS '21 | |
Apr. 23 | Frank | Alexander and Atiyah duality | |
May 7 | Ceyhun | More on Morava K-theory |