Frobenius structures on quantum connections of Calabi--Yau 3-folds
Frobenius structures on quantum connections of Calabi--Yau 3-folds
-
Jae Hee Lee, Stanford University
IAS - Simonyi Hall 101
TheÌýquantumÌýconnectionÌýis a flatÌýconnectionÌýarising 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--ManinÌýconnectionsÌýin arithmetic geometry. We focus on the case of Calabi--Yau 3-folds and explain the arithmetic aspects of the quantum connection,Ìýemphasizing the role of quantum power operations. This talk is based on joint work with Shaoyun Bai and Daniel Pomerleano.