K-Theoretic Gromov-Witten Invariants and q-Difference equations

par Xiaohan Yan (Université de Toulouse)

jeudi 15 janv. 2026, 10:30 → 11:30 Europe/Paris

The Gromov-Witten theory gives deformation invariants of a complex variety by counting curves. The generating function of these invariants satisfies naturally some differential equations. These equations are related to the derived category of coherent sheaves by the Dubrovin conjecture when the variety is Fano, and to period integrals of a mirror variety by the 2D mirror symmetry when the variety is Calabi-Yau. 

In this talk, I discuss a K-theoretic version, where the invariants are still defined by counting curves but the generating functions satisfy naturally q-difference equations instead. I discuss my work on the generating function of the K-theoretic Gromov-WItten invariants of type-A flag varieties, and predictions on the q-difference equations by the 3D mirror symmetry.