The theta correspondence
MATH-670 / 3 crédits
Enseignant: Michel Philippe
Langue: Anglais
Remark: After several weeks of introductory lectures by the PI the participants are expected to give presentations of some specific aspects of the course.
Frequency
Only this year
Summary
In the course we will discuss some introductory aspects of the local/global theta correspondence for automorphic forms/representation for various dual pairs. One of the objectives will be to prove Waldspurger's formula relating SO(2) periods to L-functions.
Content
In the course we will discuss some introductory aspects of the local/global theta correspondence for automorphic forms/representation for various dual pairs. After several weeks of introductory lectures by the PI the participants are expected to give presentations of some specific aspects of the course.
- Generalities on automorphic forms and representations (in the adelic language)
- Generalities on the Weil representation.
- The theta correspondance for Orthogonal/Symplectic pairs. Local aspects. Multiplicity one and seesaw duality.
- The theta correspondance for Symplectic/Orthogonal pairs. Global aspects. The Siegel-Weil formula.
- The theta correspondence for special Symplectic/Orthogonal pairs: the Shimizu correspondence and Waldspurger's formula.
- The theta correspondance for some exceptional dual pair.
Keywords
theta correspondence, Weil representation, automorphic forms, see-saw duality, automorphic periods, L-functions
Learning Prerequisites
Required courses
MATH-417: Adelic Number Theory
MATH-511: Modular forms
MATH-603: Subconvexity, Periods and Equidistribution
Learning Outcomes
By the end of the course, the student must be able to:
- Define the general aspects of the theta correspondence and its possible modern applications
Dans les plans d'études
- Nombre de places: 20
- Forme de l'examen: Exposé (session libre)
- Matière examinée: The theta correspondence
- Cours: 28 Heure(s)
- TP: 28 Heure(s)
- Type: optionnel