Автоморфные формы и их приложения: B.Гриценко и Haowu Wang

Семинар «Автоморфные формы и их приложения» состоится во вторник 16 октября в 18:00 в аудитории 306. На семинаре выступят:

1) Валерий Гриценко (University of Lille и НИУ ВШЭ) с докладом «Differential operators on the space of Jacobi forms.».

Аннотация:
The modular differential operators will play an important role in different aspects of the theory of reflective modular forms. The first two interesting illustrations will be given in the talks of Haowu Wang and Dimitri Adler in October and November. In this talk I give an overview of quasi-modular forms, modular differential operators on Jacobi forms in many variables and Taylor expansions of Jacobi forms. The talk will be oriented on non-specialists. At the end I’ll formulate a pair of working problems.

2) Haowu Wang (LabEx CEMPI, University of Lille) с докладом «Non-existence of reflective modular forms».

Аннотация:
A non-constant holomorphic modular form for an even lattice M of signature (2,n) is called reflective (resp. 2-reflective) if the support of its divisor is contained in the union of rational quadratic divisors determined by reflective vectors (resp. 2-reflective vectors) of M. Classification of reflective modular forms is an old open problem and has been investigated by several mathematicians (Borcherds, Gritsenko, Nikulin, Looijenga, Scheithauer, Ma, ...). In this talk, I will prove two non-existence results based on the theory of Jacobi forms. The first one is that if M admits a 2-reflective modular form then n<15, or n=19, or M is isomorphic to the unimodular lattice of signature (2,18) or (2,26). The second is that if M admits a reflective modular form then n