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.
Zoom URL: https://us02web.zoom.us/j/81065329363
Passcode: The order of the Weyl group of type $E_7$