Speaker: Zihong Chen (MIT)

Title: Singularity and decomposition of the quantum connection

Abstract: The (small) quantum connection is one of the simplest objects built out of Gromov-Witten invariants, yet it gives rise to a repertoire of rich and important questions. This connection has a simple pole (well-behaved) at infinity and a quadratic pole at 0. Despite its simple form, very little is understood about the latter. In this talk, I will discuss my result that for all Fano symplectic manifolds, this quadratic singularity is of unramified exponential type—-meaning it has a spectral decomposition where each piece is as simple as possible. Surprisingly, the proof follows a reduction mod p argument, and uses Katz's classical monodromy theorem and the more recent quantum Steenrod operations in symplectic Gromov-Witten theory. If time permits, I will discuss other recent developments in the field regarding (p-adic) analytic decompositions of the quantum connection.