Symplectic Topology Student Seminar (Spring 2025)

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.

Schedule

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

References

[Ler09]
E. Lerman. Orbifolds as stacks? Preprint. (2009). arXiv:0806.4160.