Conjecture on theta-blocks of order one. Part 1: Siegel modular forms

Theta-blocks are special automorphic products which are holomorphic Jacobi forms. These objects are important in number theory, the theory of automorphic forms, Lie algebras, algebraic geometry and string theory. Conjecture on theta-blocks of order one was formulated by Gritsenko, Poor and Yuen in 2013. In two talks, November13 and 20, we give a solution of this problem in one of the most interesting cases, Jacobi theta-blocks of weight 2. In the first talk we give a general overview of the subject for all students with minimal knowledge on modular forms. In the second talk, November 20, we present the theory of Borcherds products and the solution of the theta-block conjecture.