Objective "In recent years there has been impressive development of the higher category theory and in particular development of the categorical counterpart of the Langlands conjecture over fields of finite characteristic. But until now, this development has had little bearing on the classical problems which deal with spaces of functions. The main goal of this proposal is to build the technique to apply the category theory to classical problems. Of course on the way I will have to deal with problems in the categorical realm.The first part of the proposal deals with construction of characters of irreducible representations of reductive groups over local nonarchimedian fields F in terms of traces of the Frobenious endomorphisms which should lead to the proof of the ""Stable center conjecture"" at least for representations of depth zero.The second part is on the extension of the definition of L-functions of representations of reductive F-groups corresponding to an arbitrary representation of the dual groups. As it is now, the definition is known only for very special representations of the dual group and only in the case of classical groups.The third part is on the extension of the classical theory to representations of Kac-Moody groups over local fields." Fields of science natural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsarithmeticsL-functions Keywords Representation theory Infinity categories l-adic sheaves Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-ADG-2014 - ERC Advanced Grant Call for proposal ERC-2014-ADG See other projects for this call Funding Scheme ERC-ADG - Advanced Grant Host institution THE HEBREW UNIVERSITY OF JERUSALEM Net EU contribution € 1 569 488,00 Address EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem Israel See on map Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 569 488,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all THE HEBREW UNIVERSITY OF JERUSALEM Israel Net EU contribution € 1 569 488,00 Address EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem See on map Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 569 488,00
