1. M. Ivlev, Novosibirsk State University
On commuting differential operators of rank 2 corresponding to trigonal spectral curves of genus 3.
Аннотация
Construction of ordinary commuting differential operators is a classical problem of differential equations and integrable systems, which has applications to soliton theory. Operators of rank 1 in the case of smooth spectral curves were found by Krichever. The problem of constructing operators of rank $l > 1$ has not been solved in the general case. In all known examples of such operators, the spectral curves are hyperelliptic. In this report, the first examples of operators of rank 2 corresponding to trigonal spectral curves of genus 3 will be described.
2. Yuze Sun, Peking University, Beijing
Functoriality of coherent-constructible correspondence.
Аннотация
The talk will be streamed through "Tencent": https://meeting.tencent.com/dm/UqFOv8ai0tSh
Meeting code: 486-939-892
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In the context of homological mirror symmetry, the coherent-constructible correspondence (CCC) establishes a dictionary between the derived category of a toric variety and constructible sheaves, thus is a dictionary between algebraic and microlocal (reads as: symplectic geometry on a cotangent bundle) geometry.
We explore how algebraic geometric operations translate into microlocal ones. The talk will start from the basics of categorical knowledge, homological mirror symmetry and CCC. Then we will move to the functoriality of CCC, and possible extension to toric Artin stacks, based on Gaitsgory's (de-)equivariantization formalism.
