** 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
**

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.

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.

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.

## News

Hausdorff-Kolloquium im SS 2018

Toeplitz Kolloquium zur "Didaktik und Geschichte der Mathematik" im SS 2018

Berufspraktisches Kolloquium im SS 2018

15.06.18: Colloquium in commemoration of Felix Hausdorff

10.-25.04.18: Felix Klein Lectures: The hyperbolic Yang-Mills equation by Daniel Tataru

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 erhält einen der zehn EMS-Preise

Humboldt-Forschungspreis für Daniel Tataru

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