CORDIS

EU research results

CORDIS

Harmonic Analysis and l-adic sheaves

Fact Sheet

Reporting

Results

Project information

HAS

Grant agreement ID: 669655

Status

Ongoing project

Start date

1 October 2015
End date

30 September 2021

Funded under:

H2020-EU.1.1.

Overall budget:

€ 1 569 488
EU contribution

€ 1 569 488

Hosted by:

THE HEBREW UNIVERSITY OF JERUSALEM

Israel

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."

Programme(s)

H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)

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

Address

Edmond J Safra Campus Givat Ram
91904 Jerusalem

Israel

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 1 569 488

Website

Contact the organisation

Beneficiaries (1)

Sort alphabetically

Sort by EU Contribution

Expand all

THE HEBREW UNIVERSITY OF JERUSALEM

Israel

EU Contribution

€ 1 569 488

Project information

HAS

Grant agreement ID: 669655

Status

Ongoing project

Start date

1 October 2015
End date

30 September 2021

Funded under:

H2020-EU.1.1.

Overall budget:

€ 1 569 488
EU contribution

€ 1 569 488

Hosted by:

THE HEBREW UNIVERSITY OF JERUSALEM

Israel

Project information

HAS

Grant agreement ID: 669655

Status

Ongoing project

Start date

1 October 2015
End date

30 September 2021

Funded under:

H2020-EU.1.1.

Overall budget:

€ 1 569 488
EU contribution

€ 1 569 488

Hosted by:

THE HEBREW UNIVERSITY OF JERUSALEM

Israel

Periodic Reporting for period 2 - HAS (Harmonic Analysis and l-adic sheaves)

Reporting period: 2017-04-01 to 2018-09-30

Summary of the context and overall objectives of the project

The main goal of this project is the study of the category C(G) of smooth representations of reductive group G over a local non-archimedian field F.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

There are five different directions of my research which are stated in the order of their importance in my eyes.

a) The first is the development of the affine analogue of Lusztig's theory of character sheaves. Lusztig used successfully the algebra-geometric theory of perverse sheaves to study representations of reductive group over finite fields. Reductive groups over local non-archimedian fields can be considered as infinite dimensional variety over a finite field.

My goal is to extend the theory of perverse sheaves to such varieties and to use this new theory for the study of representations of reductive groups over local non-archimedian fields. An important step of this program is achieved in the preprint “Perverse sheaves on certain infinite-dimensional stacks and affine Springer theory” (a joint paper with A. Bouthier and Y. Varshavsky).

b) In the paper “IwahoriHecke algebras for p-adic loop groups” (a joint paper with A. Braverman and M. Patnaik) we defined and study the Iwahori-Hecke algebras for loop groups over non-archimedian local fields. We show that this algebra is closely related to Cherednik’s double affine Hecke algebra and gave an explicit description of the affine Satake isomorphism. This work could lead to a construction of the KL-basis in these algebras.

c) The natural map from the center of C(G) to its cocenter fails to be an isomorphism and this failure is a source of many difficulties.

The second part of the project is on a definition of a variant C'(G) of the category C(G) such that the map from the center of C'(G) to its cocenter is an isomorphism and on an application of this construction to the study of C(G). The first construction of C'(G) and study of some of its properties is in the paper “Remarks on the asymptotic Hecke algebra” (a joint work with A. Braverman).

d) In the paper “Character values and Hochschild homology” (a joint work with R. Bezrukavnikov) we present a conjecture (and a proof for G = SL(2)) generalizing a result of J. Arthur which expresses a character value of a cuspidal representation of a group over a non-archimedian local field as a weighted orbital integral of its matrix coefficient.

e) In the paper “A spectral decomposition of orbital integrals for PGL(2, F)” I described the spectral decomposition of functionals of elliptic orbital for the group PGL(2, F).

Now I am finishing (in a joint work with S. Debacker) an extension of this result to the case of G=PGL(3, F).

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

A construction of the theory of character sheaves of depth zero.

summary-of-the-major-achievement-page-1.jpg

summary-of-the-major-achievement-page-2.jpg

Project information

HAS

Grant agreement ID: 669655

Status

Ongoing project

Start date

1 October 2015
End date

30 September 2021

Funded under:

H2020-EU.1.1.

Overall budget:

€ 1 569 488
EU contribution

€ 1 569 488

Hosted by:

THE HEBREW UNIVERSITY OF JERUSALEM

Project information

HAS

Grant agreement ID: 669655

Status

Ongoing project

Start date

1 October 2015
End date

30 September 2021

Funded under:

H2020-EU.1.1.

Overall budget:

€ 1 569 488
EU contribution

€ 1 569 488

Hosted by:

THE HEBREW UNIVERSITY OF JERUSALEM

Israel

Deliverables

Deliverables not available

Publications

Peer reviewed articles (11)

Deligne–Lusztig duality and wonderful compactification

Author(s): Joseph Bernstein, Roman Bezrukavnikov, David Kazhdan

Published in: Selecta Mathematica, Issue 24/1, 2018, Page(s) 7-20, ISSN 1022-1824

DOI: 10.1007/s00029-018-0391-5

Scattering amplitude annihilators

Author(s): Andrea Nützi, Michael Reiterer

Published in: Journal of High Energy Physics, Issue 2020/2, 2020, ISSN 1029-8479

DOI: 10.1007/jhep02(2020)020

Bernstein components via the Bernstein center

Author(s): Alexander Braverman, David Kazhdan

Published in: Selecta Mathematica, Issue 22/4, 2016, Page(s) 2313-2323, ISSN 1022-1824

DOI: 10.1007/s00029-016-0277-3

Deligne Categories and the Limit of Categories $\operatorname{\mathbf{Rep}}\!\boldsymbol{(GL(m|n))}$

Author(s): Inna Entova-Aizenbud, Vladimir Hinich, Vera Serganova

Published in: International Mathematics Research Notices, 2018, ISSN 1073-7928

DOI: 10.1093/imrn/rny144

Categorical actions and multiplicities in the Deligne category R e p _ ( G L t

Author(s): Inna Entova-Aizenbud

Published in: Journal of Algebra, Issue 504, 2018, Page(s) 391-431, ISSN 0021-8693

DOI: 10.1016/j.jalgebra.2018.02.016

Skeletons and moduli of Stokes torsors

Author(s): Jean-Baptiste Teyssier

Published in: Annales Scientifiques de l'École Normale Supérieure, 2019, ISSN 0012-9593

A spectral decomposition of orbital integrals for PGL(2, F) (with an appendix by S. Debacker)

Author(s): David Kazhdan

Published in: Selecta Mathematica, Issue 24/1, 2018, Page(s) 473-497, ISSN 1022-1824

DOI: 10.1007/s00029-017-0321-y

On the depth r Bernstein projector

Author(s): Roman Bezrukavnikov, David Kazhdan, Yakov Varshavsky

Published in: Selecta Mathematica, Issue 22/4, 2016, Page(s) 2271-2311, ISSN 1022-1824

DOI: 10.1007/s00029-016-0278-2

Iwahori–Hecke algebras for p-adic loop groups

Author(s): Alexander Braverman, David Kazhdan, Manish M. Patnaik

Published in: Inventiones mathematicae, Issue 204/2, 2016, Page(s) 347-442, ISSN 0020-9910

DOI: 10.1007/s00222-015-0612-x

Geometric approach to parabolic induction

Author(s): David Kazhdan, Yakov Varshavsky

Published in: Selecta Mathematica, Issue 22/4, 2016, Page(s) 2243-2269, ISSN 1022-1824

DOI: 10.1007/s00029-016-0275-5

Translation functors and decomposition numbers for the periplectic Lie superalgebra p(n)

Author(s): Martina Balagovic, Zajj Daugherty, Inna Entova-Aizenbud, Iva Halacheva, Johanna Hennig, Mee Seong Im, Gail Letzter, Emily Norton, Vera Serganova, Catharina Stroppel

Published in: Mathematical Research Letters, 2019, ISSN 1073-2780

Other (17)

Quantum geometry of moduli spaces of local systems and representation theory

Author(s): Alexander Goncharov, Linhui Shen

Published in: 2019

Vertex operators, solvable lattice models and metaplectic Whittaker functions

Author(s): Ben Brubaker, Valentin Buciumas, Daniel Bump, Henrik Gustafsson

Published in: 2018

On the pro-p-Iwahori invariants of supersingular representations of unramified U(2,1)

Author(s): Peng Xu

Published in: 2018

A toy model for the Drinfeld-Lafforgue shtuka construction

Author(s): D. Gaitsgory, D. Kazhdan, N. Rozenblyum, Y. Varshavsky

Published in: 2019

An analytic version of the Langlands correspondence for complex curves

Author(s): Pavel Etingof, Edward Frenkel, David Kazhdan

Published in: 2019

A homotopy BV algebra for Yang-Mills and color-kinematics

Author(s): Michael Reiterer

Published in: 2019

A Yang-Baxter equation for metaplectic ice

Author(s): Ben Brubaker, Valentin Buciumas, Daniel Bump

Published in: 2018

Faisceaux pervers sur les espaces d'arcs

Author(s): Alexis Bouthier, David Kazhdan

Published in: 2017

The affine VW supercategory

Author(s): Martina Balagovic, Zajj Daugherty, Inna Entova-Aizenbud, Iva Halacheva, Johanna Hennig, Mee Seong Im, Gail Letzter, Emily Norton, Vera Serganova, Catharina Stroppel

Published in: 2018

Regularity of the superstring supermeasure and the superperiod map

Author(s): Giovanni Felder, David Kazhdan, Alexander Polishchuk

Published in: 2019

On triple product L-functions

Author(s): Jayce R. Getz

Published in: 2019

Semiglobal non-oscillatory big bang singular spacetimes for the Einstein-scalar field system

Author(s): Andrea Nützi, Michael Reiterer, Eugene Trubowitz

Published in: 2020

Gröbner cells of punctual Hilbert schemes in dimension two

Author(s): Ivan Cherednik

Published in: 2020

Alexander type invariants of tangles

Author(s): Iva Halacheva

Published in: 2016

Tangent categories of algebras over operads

Author(s): Yonatan Harpaz, Joost Nuiten, Matan Prasma

Published in: 2018

On certain Iwahori representations of unramified U(2,1) in characteristic p

Author(s): Peng Xu

Published in: 2018

Perverse sheaves on infinite-dimensional stacks, and affine Springer theory

Author(s): Alexis Bouthier, David Kazhdan, Yakov Varshavsky

Published in: 2020

Conference proceedings (2)

Character values and Hochschild homology

Author(s): Roman Bezrukavnikov, David Kazhdan

Published in: Proceedings of Symposia in Pure Mathematics, 2018

Schwartz space of parabolic basic affine space and asymptotic Hecke algebras

Author(s): Alexander Braverman, David Kazhdan

Published in: """Representations of Reductive Groups""", 2018

Project information

HAS

Grant agreement ID: 669655

Status

Ongoing project

Start date

1 October 2015
End date

30 September 2021

Funded under:

H2020-EU.1.1.

Overall budget:

€ 1 569 488
EU contribution

€ 1 569 488

Hosted by:

THE HEBREW UNIVERSITY OF JERUSALEM

Project information

HAS

Grant agreement ID: 669655

Status

Ongoing project

Start date

1 October 2015
End date

30 September 2021

Funded under:

H2020-EU.1.1.

Overall budget:

€ 1 569 488
EU contribution

€ 1 569 488

Hosted by:

THE HEBREW UNIVERSITY OF JERUSALEM

Israel

Project information

HAS

Grant agreement ID: 669655

Status

Ongoing project

Start date

1 October 2015
End date

30 September 2021

Funded under:

H2020-EU.1.1.

Overall budget:

€ 1 569 488
EU contribution

€ 1 569 488

Hosted by:

THE HEBREW UNIVERSITY OF JERUSALEM

Download

PDF

XML

Last update: 11 May 2020

Record number: 197450

Permalink: https://cordis.europa.eu/project/id/669655/results

CORDIS

Project information

Objective

Host institution

Beneficiaries (1)

Project information

Project information

Periodic Reporting for period 2 - HAS (Harmonic Analysis and l-adic sheaves)

Project information

Project information

Deliverables

Publications

Project information

Project information

Project information

Share this page

Download