Jacobi forms of lattice index (3 lecture serisi verildi)

Boylan H.

Workshop and international conference on Automorphic forms and number theory , Kozhikkod, Hindistan, 30 Ağustos - 03 Eylül 2013, ss.1

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Kozhikkod
  • Basıldığı Ülke: Hindistan
  • Sayfa Sayıları: ss.1
  • İstanbul Üniversitesi Adresli: Evet

Özet

Part 1: Workshop on Jacobi forms of lattice index

Organizers: Prof. M. Manickam, Prof. Ramakrishnan B., Prof. Nils Peter Skoruppa

Lecturers: 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 on

explicit constructions, in particular, for low weights and maximal lattices as index. In addition, it will be shown how Jacobi forms can be used to

construct 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, functorial

properties

● Jacobi forms as theta functions: vector valued modular forms, relation between Jacobi forms and vector valued modular forms, dimension

formulas

● 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