The Exponential Type Conjecture for Quantum Connection

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 expectation for this is packaged into the so-called exponential type conjecture, and I will discuss a proof in the case of closed monotone symplectic manifolds. My approach follows a reduction mod p argument, by combining Katz's classical result on differential equations and the more recent quantum Steenrod operations.