Frobenius Structures on Quantum Connections of Calabi--Yau 3-Folds

The quantum connection is a flat connection arising from genus 0 Gromov--Witten theory. They can be defined integrally for sufficiently positive symplectic manifolds, allowing one to consider their characteristic p or p-adic versions which bear similarity to Gauss--Manin connections in arithmetic geometry. We focus on the case of Calabi--Yau 3-folds and explain the arithmetic aspects of the quantum connection, emphasizing the role of quantum power operations. This talk is based on joint work with Shaoyun Bai and Daniel Pomerleano.