Speaker:  Zihong Chen (MIT)

Abstract: The (small) quantum connection is one of the simplest objects built out of Gromov-Witten theory, yet it gives rise to a repertoire of rich and important questions such as the Gamma conjectures and the Dubrovin conjectures. There is a very basic question one can ask about this connection: what is its formal singularity type? People's (e.g. Kontsevich-Katzarkov-Pantev, Iritani) expectation for this is packaged into the so-called exponential type conjecture, and the goal of this talk is to discuss a proof in the case of closed monotone symplectic manifolds. My approach uses a reduction mod p argument, and I will start by introducing some basic ordinary differential equations (in particular in characteristic p) and Katz's local monodromy theorem. Then I will demonstrate the key idea of proof pretending we were working in a B-side mirror situation---matrix factorizations, where it is particularly simple. Finally, I will explain how to adapt the proof to the case of quantum connections using certain equivariant operations on quantum cohomology.