# Oberseminar Representation Theory, Sommer Term 2017

Contact:

Catharina Stroppel email

Daniel Tubbenhauer email

## Where and when?

- Seminar room 1.008, Mathematik-Zentrum, Endenicher Allee 60, 53115 Bonn, Germany
- Every Friday from 14:15-15:15 (with some exceptions)
- First talk: Friday 21.04.2017
- Olivier Schiffmann's talk (scheduled for the 26.05.2017) is canceled, but there is another talk (by Dmitry Kaledin) the same time and place
- There will be two talks on Friday the 30th of June: Laura Rider (12:15-13:15) and Ivan Mirković (14:15-15:15), both in the seminar room 1.008

## Schedule

- Friday 21.04.2017,
**Speaker**: Ruslan Maksimau (Université de Montpellier),**Title**: Higher level affine Hecke algebras - Friday 28.04.2017,
**Speaker**: Iuliya Beloshapka (Steklov Mathematical Institute),**Title**: Irreducible representations of finitely generated nilpotent groups - Friday 05.05.2017,
**Speaker**: Hankyung Ko (University of Virginia),**Title**: Cohomological difference between quantum groups and algebraic groups - Friday 12.05.2017,
**Speaker**: Paolo Papi (Sapienza Università di Roma),**Title**: Covariants in the exterior algebra of a simple Lie algebra - Friday 19.05.2017,
**Speaker**: Stéphane Gaussent (Université Jean-Monnet-Saint-Étienne),**Title**: A Macdonald formula for Kac-Moody groups - Friday 26.05.2017,
**Speaker**: Talk canceled! Olivier Schiffmann (Université de Paris-Sud Orsay),**Title**: TBA - Friday 26.05.2017,
**Speaker**: Dmitry Kaledin (Steklov Mathematical Institute),**Title**: Non-commutative Hodge-to-de Rham degeneration, for complexes and for spectra - Friday 02.06.2017,
**Speaker**: Left free,**Title**: None - Friday 09.06.2017,
**Speaker**: Matthew Hogancamp (University of Southern California),**Title**: Khovanov-Rozansky homology and $q,t$ Catalan numbers - Friday 16.06.2017,
**Speaker**: Gwyn Bellamy (University of Glasgow),**Title**: Graded algebras admitting a triangular decomposition - Friday 23.06.2017,
**Speaker**: Left free (due to the Mathematische Arbeitstagung),**Title**: None - Friday 30.06.2017,
**Speaker**: Laura Rider (University of Georgia),**Title**: Formality for the nilpotent cone and the generalized Springer correspondence - Friday 30.06.2017,
**Speaker**: Ivan Mirković (University of Massachusetts),**Title**: TBA - Friday 07.07.2017,
**Speaker**: Bea Schumann (Universität zu Köln),**Title**: Combinatorics of canonical bases and cluster duality - Friday 14.07.2017,
**Speaker**: Left free,**Title**: None - Friday 21.07.2017,
**Speaker**: Left free,**Title**: None - Friday 28.07.2017,
**Speaker**: Valentin Buciumas (Stanford University),**Title**: Hecke algebra modules from representations of $p$-adic groups and quantum groups

## Abstracts

Ruslan Maksimau,

**Title**: Higher level affine Hecke algebras

KLR algebras were introduced by Khovanov-Lauda and Rouquier to categorify quantum groups. For each weight $\Lambda$, the KLR algebra $R$ has a special quotient $R^\Lambda$ (called cyclotomic quotient) that categorifies the simple module $L(\Lambda)$ over a quantum group. It is proved by Brundan--Kleshchev and Rouquier that the cyclotomic quotient $R^\Lambda$ is isomorphic to some similar quotient of the affine Hecke algebra.

Ben Webster has defined new algebras (called tensor product algebras) that generalize KLR algebras. The cyclotomic quotients of the tensor product algebras categorify tensor products of simple modules over a quantum group. However, tensor product algebras have no known analogue from the Hecke side.

In my talk I introduce such an analogue called “higher level affine Hecke algebra”. This new algebra contains the usual affine Hecke algebra. This algebra also has a special quotient that is isomorphic to the cyclotomic quotient of the tensor product algebra.

Iuliya Beloshapka,

**Title**: Irreducible representations of finitely generated nilpotent groups

Hankyung Ko,

**Title**: Cohomological difference between quantum groups and algebraic groups

Paolo Papi,

**Title**: Covariants in the exterior algebra of a simple Lie algebra

Stéphane Gaussent,

**Title**: A Macdonald formula for Kac-Moody groups

Olivier Schiffmann,

**Title**: Talk canceled!

Dmitry Kaledin,

**Title**: Non-commutative Hodge-to-de Rham degeneration, for complexes and
for spectra

Matthew Hogancamp,

**Title**: Khovanov-Rozansky homology and $q,t$ Catalan numbers

Gwyn Bellamy,

**Title**: Graded algebras admitting a triangular decomposition

This is based on joint work with U. Thiel.

Laura Rider,

**Title**: Formality for the nilpotent cone and the generalized Springer correspondence

Ivan Mirković,

**Title**:
TBA

Bea Schumann,

**Title**: Combinatorics of canonical bases and cluster duality

Valentin Buciumas,

**Title**: Hecke algebra modules from representations of $p$-adic groups and quantum groups

## Aktuelles

21./22.11.: Eröffnungsveranstaltung GlobalMathNetwork

Hausdorff-Kolloquium im WS 2017/18

Toeplitz Kolloquium zur "Didaktik und Geschichte der Mathematik" im WS 2017/18

Berufspraktisches Kolloquium im WS 2017/18

Prof. Daniel Huybrechts wurde zum Mitglied der Academia Europaea gewählt.

Bonner Mathematik im Shanghai-Ranking auf Platz 32 und bundesweit führend

Prof. Peter Scholze ist plenary speaker auf dem ICM 2018

Prof. Dr. Gerd Faltings erhält Cantor-Medaille der DMV

Prof. Peter Scholze in die Akademie der Wissenschaften und der Literatur aufgenommen

Prof. Peter Scholze erhält einen der zehn EMS-Preise

Humboldt-Forschungspreis für Daniel Tataru

Prof. Peter Scholze erhält den Gottfried Wilhelm Leibniz-Preis 2016