Jacobi forms of lattice index (3 lecture serisi verildi)

Abstract

Part 1: Workshop on Jacobi forms of lattice indexOrganizers: Prof. M. Manickam, Prof. Ramakrishnan B., Prof. Nils Peter SkoruppaLecturers: Hatice Boylan (Istanbul Üniversitesi and Max­Planck­Institute Bonn), Fabien Cléry (University of Siegen), Nils­Peter Skoruppa(University of Siegen and Max­Planck­Institute Bonn)Overview: The workshop aims to give a careful and thorough introduction into the theory of Jacobi forms of lattice index with emphasis onexplicit constructions, in particular, for low weights and maximal lattices as index. In addition, it will be shown how Jacobi forms can be used toconstruct other types of automorphic forms via the so­called additive and multiplicative liftings.Subjects:● Basic notions: Lattices, shadows, discriminant modules, definition of Jacobi forms, discussion of the definition, first examples, functorialproperties● Jacobi forms as theta functions: vector valued modular forms, relation between Jacobi forms and vector valued modular forms, dimensionformulas● Explicit constructions of Jacobi forms: Taylor expansion around 0, Theta blocks, invariants of Weil representations● Maximal lattices as index, explicit description of forms of singular and critical weight and maximal index● Additive and multiplicative liftings, product expansionsSchedule:Friday to Sunday: each day 3 lectures of 90 min and 60 minutes for discussions, questions and problem session