Andrey Smirnov - Frobenius structures for quantum differential and q-difference equations (Lec 1)
Автор: M-Seminar, Kansas State University
Загружено: 2025-12-02
Просмотров: 88
Andrey Smirnov (University of North Carolina); December 2, 2025
There is a known connection between the Kloosterman sum in number theory and the Bessel differential equation. This connection was explained by B. Dwork in 1974 through his discovery of Frobenius structures in the p-adic theory of the Bessel equation. In this talk, I will speculate that this connection extends to the quantum differential equations appearing in the quantum cohomology of Nakajima varieties. As an example, I will present an explicit conjectural description of the corresponding Frobenius structures. The traces of these Frobenius structures serve as natural finite-field analogs of the integral solutions to quantum differential equations known from mirror symmetry. Some of these results also extend to the setting of q-difference equations, where a similar picture emerges when q is close to a root of unity in the p-adic norm. I will review these developments and discuss their connections to other recent advances, including quantum Steenrod operations, Habiro cohomology, and related topics.
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