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