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.

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