Reduction cohomology on Riemann surfaces

2021/06/10 Thu 16:00 - 17:30
Alexander Zuevsky
Czech Academy of Sciences

We define and compute a cohomology of the space of Jacobi forms based on precise analogues of Zhu reduction formulas derived by Bringmann-Krauel-Tuite. It is shown that the reduction cohomology for Jacobi forms is given by the cohomology of $n$-point connections over a deformed vertex algebra bundle defined on the torus. The reduction cohomology for Jacobi forms for a vertex algebra is determined in terms of the space of analytical continuations of solutions to Knizhnik-Zamolodchikov equations.
A counterpart of the Bott-Segal theorem for the reduction cohomology of Jacobi forms on the torus is proven.
Algebraic, geometrical, and cohomological meanings of reduction formulas is clarified.

This will be a zoom seminar.
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