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ModRed SIGNED

The geometry of modular representations of reductive algebraic groups

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

ModRed project word cloud

Explore the words cloud of the ModRed project. It provides you a very rough idea of what is the project "ModRed" about.

obtaining positive tilting elias area theory nothing breakthrough base groups algebraic andersen formula hold except bound representation framework representations explicit geometric huge closed theme 1990 sheaves williamson bigger tools juteau soergel conjectural formulas primary character diagrammatic outlined categories smaller characters mautner lusztig perspective obtain 1980 bimodules indecomposable modules shown presentation algebraically parity reductive category

Project "ModRed" data sheet

The following table provides information about the project.

Coordinator	UNIVERSITE CLERMONT AUVERGNE Organization address address: 49 BOULEVARD FRANCOIS MITTERRAND city: CLERMONT-FERRAND postcode: 63000 website: http://creation-uca.fr/ contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.
Coordinator Country	France [FR]
Total cost	882˙843 €
EC max contribution	882˙843 € (100%)
Programme	1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
Code Call	ERC-2015-STG
Funding Scheme	ERC-STG
Starting year	2016
Duration (year-month-day)	from 2016-09-01 to 2021-08-31

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	UNIVERSITE CLERMONT AUVERGNE UNIVERSITE CLERMONT AUVERGNE Organization address address: 49 BOULEVARD FRANCOIS MITTERRAND city: CLERMONT-FERRAND postcode: 63000 website: http://creation-uca.fr/ contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	FR (CLERMONT-FERRAND)	coordinator	710˙718.00
2	CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Organization address address: RUE MICHEL ANGE 3 city: PARIS postcode: 75794 website: www.cnrs.fr contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	FR (PARIS)	participant	172˙125.00

Map

Project objective

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).

Publications

List of publications.
year	authors and title	journal	last update
2018	Riche , Simon; Williamson , Geordie Tilting modules and the p-canonical basis published pages: 1-184, ISSN: 0303-1179, DOI:	AstÃ©risque 397	2019-07-08
2019	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
2019	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
2018	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
2018	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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