Automorphic Forms and Applications: Haowu Wang (LabEx CEMPI, University of Lille)
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The Seminar Automorphic Forms and Applications will take place on Nov 27 at 18:00 in the room 306
Haowu Wang (LabEx CEMPI, University of Lille) will give a talk «Siegel paramodular forms of small weights»
Abstract:
Paramodular forms are Siegel modular forms with respect to the paramodular groups of polarisation (1,t) and genus 2. The construction of paramodular forms of small weights is quite a difficult problem, equivalent to the proof of the non-triviality of the third cohomology groups or proof of general type of Siegel modular 3-folds.
Paramodular forms are Siegel modular forms with respect to the paramodular groups of polarisation (1,t) and genus 2. The construction of paramodular forms of small weights is quite a difficult problem, equivalent to the proof of the non-triviality of the third cohomology groups or proof of general type of Siegel modular 3-folds.
In this talk, we first give a brief overview of the subject and some necessary preliminary materials will be given, such as the notions of paramodular forms, Jacobi forms, theta-blocks, additive lifting and Borcherds products. Then we construct an infinite family of paramodular forms of weight 2 which are simultaneously Borcherds products and Gritsenko lifting (i.e. identities of type `infinite product=infinite sum'). This proves the conjecture of Gritsenko-Poor-Yuen (2013) for the known infinite series of theta blocks of weight 2. We also construct infinite families of antisymmetric paramodular forms of weights 3 and 4. These paramodular forms are obtained as quasi pull-backs of certain remarkable reflective modular forms of singular weights for the root lattices A_4 and A_6. The talk is based on a joint work with Valery Gritsenko.
Date
27 November
18:00
Address
Усачёва 6, ауд. 306