# Trimester Seminar

**Venue:** HIM lecture hall, Poppelsdorfer Allee 45**Organizers:** Steffen König, Peter Littelmann, Jan Schröer, Catharina Stroppel

## Monday, January 17

**15:00 - 16:00** Harry Tamvakis (University of Maryland): A Giambelli formula for classical G/P spaces ** Abstract:** The cohomology ring of the Grassmannian X of m-planes in complex N-space is generated by certain special Schubert classes, which are the Chern classes of the universal quotient bundle over X. The classical Giambelli formula expresses any Schubert class in H*(X) as a determinant in these special classes. We will discuss a combinatorially explicit analogue of this result which holds in the cohomology ring of any partial flag variety G/P, where G is a classical Lie group and P an arbitrary parabolic subgroup of G.

**16:30 - 17:30 **Eric Opdam: The Euler-Poincaré pairing and affine Hecke algebras ** Abstract:** Let π, π be tempered representations of an affine Hecke algebra with positive parameters. We give a direct computation of the Euler-Poincaré pairing EP(π,π), the alternating sum of the dimensions of the Ext-groups. The answer is expressed by a simple formula involving the analytic R-groups of the affine Hecke algebra, and is analogous to a formula of Arthur for the elliptic pairing of tempered characters in the setting of reductive p-adic groups. Our proof applies equally well to affine Hecke algebras and to reductive groups over nonarchimedean local fields of arbitrary characteristic. This sheds new light on Arthurs original formula and on Kazhdans conjecture for the elliptic pairing of admissible characters.

## Thursday, January 20

**15:00 - 16:00 **Ivan Losev (MIT): Classification of irreducible finite dimensional representations of W-algebras.

Abstract: I am going to explain how to classify irreducible finite dimensional modules over finite W-algebras for arbitrary semisimple Lie algebras. I will mostly concentrate on the case of regular integral central character which is a joint work with Victor Ostrik.

**16:30 - 17:30 **Ralf Schiffler (University of Connecticut): On cluster algebras arising from surfaces.

## Monday, January 24

**15:00 - 16:00** Henning Haahr Andersen (Aarhus): Cohomology of line bundles on flag varieties This talk will be a survey of known results together with a discussion of open problems.

**16:30 - 17:30** Ahmet Seven (Ankara): Mutation classes of skew-symmetrizable matrices ** Abstract:** In this talk, I will discuss some properties of Fomin-Zelevinskys mutation operation on skew-symmetrizable matrices. In particular, I will describe some algebraic / combinatorial invariants associated with the mutation operation. Furthermore, I will give a classification of the mutation classes of skew-symmetrizable matrices in size three and discuss generalizations.

## Thursday, January 27

**15:00 - 16:00** Idun Reiten (Trondheim): Invariant rings and generalised cluster categories

**16:30 - 17:30** Alistair Savage (Ottawa): Hecke algebras and Heisenberg categorification**Abstract:** We will present a graphical category in terms of certain planar braid-like diagrams. The definition of this category is inspired by the representation theory of Hecke algebras of type A (which are certain deformations of the group algebra of the symmetric group). The Heisenberg algebra (in infinitely many generators) injects into the Grothendieck group of our category, yielding a "categorification" of this algebra. We will also s ee that our graphical category acts on the category of modules of Hecke algebras and of general linear groups over finite fields. Additionally, other algebraic structures, such as the affine Hecke algebra, appear naturally. This is joint work with Anthony Licata and inspired by work of Mikhail Khovanov.

## Monday, January 31

**15:00 - 16:0**0 Steen Ryom-Hansen (Talca): The seminormal basis and the Khovanov-Lauda algebra

**16:30 - 17:30** Martina Lanini (Rome/Erlangen): Kazhdan-Lusztig combinatorics in the moment graph setting

## Thursday, February 3

**15:00 - 16:00** Ghislain Fourier (Köln): Weyl modules for map algebras

**16:30 - 17:30** Anne Schilling (Davis): The Murnaghan-Nakayama rule for k-Schur functions

## Monday, February 7

**15:00 - 16:00** Hans Wenzl (San Diego): Module tensor categories and another q-Brauer algebra

**16:30 - 17:30** Jorge Vitoria (Stuttgart): Bounded t-structures for piecewise hereditary algebras

## Thursday, February 10

**15:00 - 16:00** Evgeny Feigin (Moscow): Representations and flag varieties for PBW degeneration in type A

**16:30 - 17:30** Markus Reineke (Wuppertal): Degenerate Cohomological Hall algebra and quantized Donaldson-Thomas invariants

## Monday, February 14

**15:00 - 16:00** Hiraku Nakajima (Kyoto): Quantum unipotent subgroup and dual canonical basis (after Y. Kimura)

**16:30 - 17:30** Selene Sanchez-Flores (Stuttgart): On the Gerstenhaber bracket for monomial algebras

## Thursday, February 17

**15:00 - 16:0**0 Gunter Malle (Kaiserslautern): Quasi-isolated blocks and decomposition of RLG

**16:30 - 17:30** Michel Brion (Grenoble): Homogeneous bundles over abelian varieties

## Monday, February 21

**15:00 - 16:00** Dong Liu (Köln): Classification of Harish-Chandra modules over some Lie algebras and superconformal algebras related to the Virasoro algebra

**16:30 - 17:30** Giovanni Cerulli Irelli (Rome): Positivity in Cluster Algebras

## Thursday, February 24

**15:00 - 16:00** Joachim Hilgert (Paderborn): Okounkov bodies for line bundles over flag varieties

**16:30 - 17:30** Karl-Hermann Neeb (Erlangen): Unitary representations of automorphism groups of infinite dimensional symmetric spaces

## Monday, February 28

**15:00 - 16:00** Daisuke Sagaki (Tsukuba): Tensor products and Minkowski sums of Mirkovic-Vilonen polytopes

**16:30 - 17:30** Armin Shalile (Stuttgart): On the center of Brauer algebras and modular character theory

## Thursday, March 3

**15:00 - 16:00** Frederike Stoll (Stuttgart): The Levi subalgebra of the rational q-Schur algebra and Schur-Weyl duality

## Monday, March 7

**15:00 - 16:00** Sergey Loktev (Moscow): Two-variable Weyl modules as generalized fusion modules

**16:30 - 17:30** Changchang Xi (Beijing): Derived categories from infinitely generated tilting modules

## Thursday, March 10

**15:00 - 16:00** Stephanie Cupit-Foutou (Cologne): Real structures on wonderful varieties

**16:30 - 17:30** Boris Feigin (Moscow): Representations of W-algebras and toroidal algebras. A geometrical approach

## Monday, March 14

**15:00 - 16:00** Mauritio Martino (Bonn): Blocks of restricted rational Cherednik algebras

## Thursday, March 17

**15:00 - 16:00** Luca Moci (Rome): Kostant partition function, toric arrangements, and Tutte polynomials

**16:30 - 17:30** Masaki Kashiwara (Kyoto): Crystal bases of the quantum queer superalgebras

## Monday, April 4

**15:00 - 16:00** Stavros Kousidis (Köln): Statistics of affine Demazure characters

**16:30 - 17:30** Andrei Zelevinsky (Boston): Tropical dualities in cluster algebras

## Thursday, April 7

**15:00 - 16:00** Dylan Rupel: Positivity in Rank 2 Quantum Cluster Algebras

**16:30 - 17:30** Josh Sussan: Categorifications of the Jones-Wenzl Projector

## Monday, April 11

**15:00 - 16:00** Sebastian Zwicknagl (Bonn): Poisson ideals in cluster algebras and primitive ideals in quantum groups

**16:30 - 17:30** Christof Geiß (Mexico City): Cluster structures on quantum coordinate rings

## Thursday, April 14

**15:00 - 16:00** Hanno Becker (Bonn): Khovanov-Rozansky Homology via Cohen-Macaulay Modules and Soergel Bimodules

**16:30 - 17:30** Vanessa Miemietz (Norwich): Ext algebras for GL_{2}

## Monday, April 18

**15:00 - 16:00** Toshiro Kuwabara (MPIM/Seoul): Representation theory of the rational Cherednik algebra for cyclic groups via microlocal analysis

**16:30 - 17:30** Sergey Fomin (Michigan): Cluster structures in classical rings of invariants

## Thursday, April 21

**15:00 - 16:00** Felix Dietlein (Köln): Spectral Properties in Auslander-Reiten-Theory