Explore the words cloud of the ModRed project. It provides you a very rough idea of what is the project "ModRed" about.
The following table provides information about the project.
UNIVERSITE CLERMONT AUVERGNE
|Coordinator Country||France [FR]|
|Total cost||882˙843 €|
|EC max contribution||882˙843 € (100%)|
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
|Duration (year-month-day)||from 2016-09-01 to 2021-08-31|
Take a look of project's partnership.
|1||UNIVERSITE CLERMONT AUVERGNE||FR (CLERMONT-FERRAND)||coordinator||710˙718.00|
|2||CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS||FR (PARIS)||participant||172˙125.00|
The main theme of this proposal is the Geometric Representation Theory of reductive algebraic groups over algebraically closed fields of positive characteristic. Our primary goal is to obtain character formulas for simple and for indecomposable tilting representations of such groups, by developing a geometric framework for their categories of representations. Obtaining such formulas has been one of the main problems in this area since the 1980's. A program outlined by G. Lusztig in the 1990's has lead to a formula for the characters of simple representations in the case the characteristic of the base field is bigger than an explicit but huge bound. A recent breakthrough due to G. Williamson has shown that this formula cannot hold for smaller characteristics, however. Nothing is known about characters of tilting modules in general (except for a conjectural formula for some characters, due to Andersen). Our main tools include a new perspective on Soergel bimodules offered by the study of parity sheaves (introduced by Juteau-Mautner-Williamson) and a diagrammatic presentation of their category (due to Elias-Williamson).
|year||authors and title||journal||last update|
Riche , Simon; Williamson , Geordie
Tilting modules and the p-canonical basis
published pages: 1-184, ISSN: 0303-1179, DOI:
Pramod N. Achar, Simon Riche
Reductive groups, the loop Grassmannian, and the Springer resolution
published pages: 289-436, ISSN: 0020-9910, DOI: 10.1007/s00222-018-0805-1
|Inventiones mathematicae 214||2019-07-08|
Pramod N. Achar, Shotaro Makisumi, Simon Riche, Geordie Williamson
Koszul duality for Kacâ€“Moody groups and characters of tilting modules
published pages: 261-310, ISSN: 0894-0347, DOI: 10.1090/jams/905
|Journal of the American Mathematical Society 32/1||2019-04-18|
Achar , Pramod ,; Cooney , Nicholas; Riche , Simon
The parabolic exotic t-structure
published pages: , ISSN: 2491-6765, DOI:
|Epijournal de GÃ©omÃ©trie AlgÃ©brique 2||2019-04-18|
Carl Mautner, Simon Riche
Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the MirkoviÄ‡â€“Vilonen conjecture
published pages: 2259-2332, ISSN: 1435-9855, DOI: 10.4171/jems/812
|Journal of the European Mathematical Society 20/9||2019-04-18|
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