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Automorphic Forms Summer School

2022.08.29. - 2022.09.02.
Erdős Center


The theory of automorphic forms is a central area of modern mathematics due to its depth and connections to a large number of other disciplines. This feature makes it attractive but also difficult to enter. The summer school will provide a motivated introduction to this rich field through exciting recent developments. It is aimed at graduate students and early career researchers. Four minicourses will be given by top researchers of the younger generation. Financial support will be provided to selected participants in the form of accommodation and catering (details to be shared later).

Minicourses by:

  • Jasmin Matz (University of Copenhagen): Equidistribution in automorphic families

Abstract: Automorphic forms and representations often naturally appear in families, for example, the family of all Hecke characters of a fixed number field, the family of holomorphic modular forms of growing level, or the family of Hecke-Maass forms of growing Laplace eigenvalue. It thus often makes sense to study families instead of single forms or representations, as this allows for more analytic methods to be used, and thus often makes certain conjectures that are otherwise out of reach more accessible (at least their probabilistic versions).

In addition, such families are conjectured to have additional underlying structure, so-called symmetry types, which are supposed to govern the distribution of the spectral parameters in those families. In this minicourse I want to discuss several instances of families, equidistribution results (known and conjectured), and their connection to conjectures such as the (vertical) Sato-Tate Conjecture and the Katz-Sarnak Conjectures on low-lying zeros in families of automorphic L-functions.

  • Paul Nelson (IAS Princeton): Estimates for L-functions

Abstract: A recurring problem in analytic number theory is to give estimates for special values of L-functions, either individually ("subconvexity") or on average over a family ("moments").  This problem can be approached via the theory of automorphic forms and their integral representations. I will give an introduction to recent results pursuing this approach, such as those in 

The main local issue is to choose, in a given automorphic representation, vectors that make the integral representation well-suited for estimation. The main global issue is to provide nontrivial estimates for integrals of automorphic forms, which has been addressed in certain cases via Ratner theory or the pretrace formula. In addressing both the local and global issues, a key role is played by microlocal analysis on Lie group representations and the invariant theory of Gan--Gross--Prasad pairs.

  • Danylo Radchenko (ETH Zürich): Modular forms, sphere packing, and energy minimization

Abstract: In this minicourse I will explain some old and new geometric applications of modular forms, from the classical theory of theta functions of lattices to the recent works of Viazovska on the sphere packing problem and of Cohn-Kumar-Miller-Radchenko-Viazovska on universal optimality for the energy minimization problem in dimensions 8 and 24.

  • Benjamin Schraen (Université Paris-Sud, Orsay):  Introduction to the p-adic Langlands Program

Absctract : The goal of the lectures will be to give an introduction to the p-adic Langlands Program, through the case of the group GL2(Qp). The p-adic Langlands corresondence relates p-adic 2-dimensional representations of the absolute Galois group of Qp and some representations of the group GL2(Qp) on p-adic Banach spaces. I will explain how such a correspondence is constructed and what it is useful in the theory of (p-adic) modular forms.

Application is now open. Application deadline: May 31, 2022.

The Erdős Center covers full lodging for selected participants. We try to support as many participants as possible. Please indicate in the application form if you wish to apply for this support.

MSc and PhD students applying to the summer school should also ask their supervisor to send a short recommendation (typically a few sentences) to the contact e-mail address

Link to the registration web-form of the summer school: 


Gergely Harcos (Rényi Institute)
Özlem Imamoḡlu (ETH Zürich)
Péter Maga (Rényi Institute)
Árpád Tóth (Rényi Institute & ELTE)
Gergely Zábrádi (ELTE)

Invited Speakers

Jasmin Matz (University of Copenhagen)
Paul Nelson (IAS Princeton)
Danylo Radchenko (ETH Zürich)
Benjamin Schraen (Université Paris-Sud, Orsay)


Csaba Anderlik            Eötvös Loránd University
Gergely Jakovác          Eötvös Loránd University
Bálint Mogyorósi          Eötvös Loránd University
Dávid Tóth                   BME VIK & ARIM
Mabud Ali Sarkar         The University of Burdwan
Khalil Besrour              University of Ottawa
Félicien Comtat           Queen Mary University of London
Agniva Dasgupta         Texas A&M University
Dragan Đokić              University of Belgrade
Shuaishuai Duan         HSE University Moscow
Wissam Ghantous       University of Oxford
Trajan Hammonds       Princeton University
Phillip Harris                 University of Wisconsin-Madison
Haojie Hong                  IM de Bordeaux
Jiaqi Hou                      University of Wisconsin-Madison
Amin Idelhaj                  University of Wisconsin-Madison
Tanmay Khale              UIUC
Doyon Kim                   Rutgers University
Filip Kovačević             ETH Zürich
Krishnarjun Krishnamoorthy HRI
Alessandro Lägeler      ETH Zürich
Wing Hong Leung        The Ohio State University
Chang Liu                     University of Göttingen
Thibaut Ménès              Université Paris 13
Duc Nam Nguyen         University of Lille
Mayank Pandey            Princeton University
Anish Ray                     University of Münster
Andrei Seymour-Howell    University of Bristol
Himanshu Shukla         University of Bayreuth
Radu Toma                   University of Bonn
Matt Tyler                      Stanford University
Théo Untrau                  IMB
Somnath Jha                IIT Kanpur
Shivani Goel                 IIIT Delhi
Ana Pavlaković             ETH Zürich
Ana Marija Vego            ETH Zürich
Svenja zur Verth           EPFL
Keshav Aggarwal         ARIM
Johann Birnick              ETH Zürich
Tim Davis                     QMUL
Gilles Felber                  MPIM Bonn & Bonn University
Robin Frot                     ARIM
Sumit Kumar                ISI Kolkata
Saikat Maity                  Pondicherry University
Lorenzo Sauras           T. U. Wien
Prahlad Sharma           TIFR Mumbai Mumbai
Semen Słobodianiuk    Warsaw University
Sarra Talbi                    USTHB
Biao Wang                   Hua Loo-Keng Center, AMSS, CAS