Quantum Field Theory and Physical Mathematics Seminar

Speaker: Shaoyun Bai (MIT)

Title: On the p-curvature of quantum connections of CY threefolds

Abstract: The small quantum connection of Calabi-Yau varieties has integral coefficients, thus admits reduction mod a prime number p. A fundamental invariant associated with flat connections over characteristic p is the p-curvature, which lies at the heart of study of algebraic differential equations. I will explain how to identify the p-curvature of quantum connection of any compact Calabi-Yau threefold with the quantum Steenrod operation, thereby providing a modular description of the p-curvature in this setting. I will also discuss the role of BPS invariants and the mirror symmetry context. This is based on joint work with Jae Hee Lee.