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 - 16:00 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 - 16:00 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 GL2

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