Oberseminar Darstellungstheorie - Representation Theory

Prof. Dr. Catharina Stroppel, Dr. Olaf Schnürer.

Time: Mondays, 16.30-17.30. Tea at 16.15 in the Plücker room 1.015.
Place: Seminar room 0.006, Mathematik-Zentrum, Endenicher Allee 60.

Talks

  • October 21: Carl Mautner: Hypertoric geometry and Ringel duality
  • October 28, 17.30-18.30 (due to the Plücker lecture), Daniel Tubbenhauer: sl3-web bases, intermediate crystal bases and categorification, abstract
  • November 4: Greg Stevenson: Derived categories of quivers over Noetherian rings
    Abstract: Given a Noetherian ring R, or a Dynkin quiver Q and a field k, one can consider the unbounded derived categories D(R) and D(kQ), of R-modules, and of representations of the path algebra kQ, respectively. These triangulated categories are somewhat well understood in the sense that one has, in both cases, a full classification of the localising subcategories. It's thus natural to ask if one can combine these classification results to say something about D(RQ), the unbounded derived category of the R-linear path algebra. I'll discuss joint work with Ben Antieau which shows that not only can one combine these classifications, but that it is possible to reduce such classification problems to the case of fields in a quite general setting.
  • November 11: Cristian Lenart: Specialized Macdonald polynomials, quantum K-theory, and Kirillov-Reshetikhin modules
    Abstract: The Macdonald polynomials are Weyl group invariant polynomials with rational function coefficients (in q,t), which specialize to the irreducible Lie algebra characters upon setting q=t=0. Quantum K-theory is a K-theoretic generalization of quantum cohomology. Kirillov-Reshetikhin (KR) modules are certain finite-dimensional modules for affine Lie algebras. Braverman and Finkelberg related the Macdonald polynomials specialized at t=0 to the quantum K-theory of flag varieties. With S. Naito, D. Sagaki, A. Schilling, and M. Shimozono, we proved that the same specialization of Macdonald polynomials equals the graded character of a tensor product of (one-column) KR modules. I will discuss the combinatorics underlying these connections.
  • Friday, November 22, 10.15: Igor Burban: Hall algebra of a weighted projective line and quantized enveloping algebras
  • November 25:
  • Tuesday, December 3, 16.15, room 0.008: Valery Lunts: Categorical Lefschetz trace formula
  • December 9: Dmytro Shklyarov: On Hodge theoretic and categorical invariants of singularities
  • December 16:
  • January 6: Andrew Hubery: Ringel-Hall algebras of cyclic quivers
    Abstract: We will discuss the structure of the Ringel-Hall algebra of a cyclic quiver, in particular computing its centre and showing it is canonically isomorphic to the ring of symmetric functions. We will finish with a conjecture relating the (dual) canonical basis and the (dual) Schur functions.
  • January 13: Tobias Dyckerhoff: Crossed simplicial groups and invariants of structured surfaces
  • January 20:
  • January 27: Ingo Runkel: Orbifold equivalent potentials for matrix factorisations
  • February 3: