ANERAUTOHI

Analytic and ergodic aspects of automorphic forms on higher rank groups

Coordinatore	EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZURICH    more  Organization address address: Raemistrasse 101 city: ZUERICH postcode: 8092 contact info Titolo: Prof. Nome: Roland Cognome: Siegwart Email: send email Telefono: +41 44 634 53 50 Fax: +41 44 634 53 51
Nazionalità Coordinatore	Switzerland [CH]
Totale costo	165˙865 €
EC contributo	165˙865 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2009-IEF
Funding Scheme	MC-IEF
Anno di inizio	2011
Periodo (anno-mese-giorno)	2011-09-01   -   2013-08-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZURICH  Organization address address: Raemistrasse 101 city: ZUERICH postcode: 8092 contact info Titolo: Prof. Nome: Roland Cognome: Siegwart Email: send email Telefono: +41 44 634 53 50 Fax: +41 44 634 53 51	CH (ZUERICH)	coordinator	165˙865.20

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 Obiettivo del progetto (Objective)

'Automorphic forms are an important subject in number theory and have many arithmetic applications. Some crucial results in the theory of (classical) automorphic forms include results on subconvexity, converse theorems and zeros of L-functions, to name only a few. However, so far the theory of higher rank groups is not as developed as the theory of (classical) automorphic forms and in the last years interest in higher rank groups and their application has increased. This can be seen from the number of workshops that deal with this topic, e.g. the American Institute of Mathematics (AIM) organized in the last two years three workshops that dealt with higher rank groups, namely the workshops "Computing arithmetic spectra", "Subconvexity bounds for L-functions", "Analytic theory of GL(3) automorphic forms and applications". In the proposed project we want to study a wide range of analytic aspects of higher rank groups, especially their L-functions and their applications (e.g. arithmetic quantum chaos in theoretical physics). It turns out that outstanding results on automorphic forms of groups of rank less than 1 have been very recently obtained via techniques largely inspired from ergodic theory. For instance, the subconvexity problem with respect to all the parameters at the same time for GL(1) and GL(2) automorphic forms was solved a few months ago. On the one hand, these techniques mimic the classical analytic methods but their main advantage lies in their softness. One purpose of this project is to master deeply these techniques and to determine how they could be used in the higher rank setting. On the other hand, the limit of these ergodic techniques (even in the rank 1 case) should shed some light on new analytic problems, which could possibly be attacked via classical techniques. Roughly speaking, the intricacies of the links between analytic and ergodic techniques are the core of this project.'