COUNTING CONJECTURES

Counting conjectures and characters of almost simple groups

Coordinatore	TECHNISCHE UNIVERSITAET KAISERSLAUTERN    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Germany [DE]
Totale costo	1˙444˙200 €
EC contributo	1˙444˙200 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2011-ADG_20110209
Funding Scheme	ERC-AG
Anno di inizio	2012
Periodo (anno-mese-giorno)	2012-04-01   -   2017-03-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	TECHNISCHE UNIVERSITAET KAISERSLAUTERN  Organization address address: GOTTLIEB-DAIMLER-STRASSE Geb. 47 city: KAISERSLAUTERN postcode: 67663 contact info Titolo: Mr. Nome: Berthold Cognome: Klein Email: send email Telefono: +49 631 205 3602 Fax: +49 631 205 4380	DE (KAISERSLAUTERN)	hostInstitution	1˙444˙200.00
2	TECHNISCHE UNIVERSITAET KAISERSLAUTERN  Organization address address: GOTTLIEB-DAIMLER-STRASSE Geb. 47 city: KAISERSLAUTERN postcode: 67663 contact info Titolo: Prof. Nome: Gunter Cognome: Malle Email: send email Telefono: +49 631 2052264 Fax: +49 631 2054427	DE (KAISERSLAUTERN)	hostInstitution	1˙444˙200.00

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 Obiettivo del progetto (Objective)

'This proposal has two major goals: to understand the irreducible complex characters of the finite almost simple groups, and to apply this knowledge to prove two longstanding famous conjectures in the representation theory of finite groups: the McKay conjecture and the Alperin Weight Conjecture.

The first goal requires the study of the action of outer automorphisms of finite groups of Lie type on their irreducible characters and the solution of extension problems. The determination of the irreducible characters of all almost simple groups is a fundamental task of group theory. For the second goal, we will build on the recent reductions (by the PI and others) of both conjectures to assertions on characters of finite simple groups. To prove these assertions, one needs to construct certain equivariant bijections with respect to outer automorphisms, which will involve the results from the first goal. Furthermore, we propose to extend the reduction of the McKay conjecture to include several refinements, in particular the block-wise version and congruences of character degrees.

The project will involve the interplay of methods from the theory of algebraic groups, character sheaves, block theory and modular character theory.'