# Masterclass: Relative trace formulae

## University of Copenhagen 22-26 August 2022

This masterclass aims at offering an entrance door to the wide field of relative trace formulas, from different perspectives and with different applications ranging from representation theory to analytic number theory. Relative trace formulas are fundamental tools, and we bring together world-class experts to make them shine. The school will consist of three lecture series supplemented by problem sessions and further talks all related to different aspects of this area.

The masterclass is mostly intended to graduate students and young researchers, but everyone interested in relative trace formulas is welcome!

We can offer financial support of up to  DKK 500 per day (at most DKK 2500 in total) to a limited number of graduate students and other early career researchers to partly cover travel and accommodation expenses. If you want to apply for support, please fill out the appropriate parts of the registration form.

Lecture Series by

• Raphaël Beuzart-Plessis  (Aix-Marseille Université) on Comparison of relative trace formulas and factorization of automorphic period
Abstract: We will presentthe proof of Waldspurger's formula due to Jacquet and open towards Gan-Gross-Prasad conjectures.
• Valentin Blomer (Universität Bonn) on Relative trace formulas in analytic number theory
Abstract: The relative trace formula of Petersson-Bruggeman-Kuznetsov is a powerful tool to connect automorphic forms and number theory. It leads to a cross-fertilization of both fields: arithmetic problems can be solved by the theory of automorphic forms, and automorphic forms can be investigated by number theoretic methods. The course will present
various examples of this fascinating interplay, also for higher rank groups.
• Jayce Getz (Duke University) on Introduction to stabilization in the context of relative trace formulae
Abstract: A profitable strategy for proving cases of (relative) Langlands functoriality is to compare relative trace formulae. The geometric sides of relative trace formulae are indexed by the  set-theoretic quotients of the rational points of an affine variety by the rational points of a reductive group.  On the other hand, when  comparing relative trace formulae, it is often the case that one can only compare the rational points of the corresponding GIT quotient.  Thus one requires a reorganization of the relative trace formula into stable'' pieces indexed by a family of GIT quotients.  This course
will serve as an introduction to this process.

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The conference/masterclass will take place at the Department of Mathematical Sciences, University of Copenhagen. See detailed instructions on how to reach Copenhagen and the conference venue.

Tickets and passes for public transportation can be bought at the Copenhagen Airport and every train or metro station. You can find the DSB ticket office on your right-hand side as soon as you come out of the arrival area of the airport. DSB has an agreement with 7-Eleven, so many of their shops double as selling points for public transportation.

A journey planner in English is available.

We kindly ask the participants to arrange their own accommodation.

We recommend Hotel 9 Små Hjem, which is pleasant and inexpensive and offers rooms with a kitchen. Other inexpensive alternatives are CabInn, which has several locations in Copenhagen: the Hotel City (close to Tivoli), Hotel Scandinavia (Frederiksberg, close to the lakes), and Hotel Express (Frederiksberg) are the most convenient locations; the latter two are 2.5-3 km from the math department. Somewhat more expensive – and still recommended – options are Hotel Nora and  Ibsen's Hotel.

An additional option is to combine a stay at the CabInn Metro Hotel with a pass for Copenhagen public transportation (efficient and reliable). See information about tickets & prices.

The deadline for applying for financial support is June 26, 2022.
If you are not applying for funding, please register by July 24, 2022.

Please register early as we have a limit on the number of participants.

Registration form

Organisers:

• Didier Lesesvre (Université de Lille)
• Nils Matthes (University of Copenhagen)
• Jasmin Matz (University of Copenhagen)
• Morten Risager (University of Copenhagen)