** Oberseminar Darstellungstheorie - Representation Theory
**

Prof. Dr.
Catharina Stroppel,
Dr.
Olaf Schnürer.
Time: Mondays, 17.15-18.15 (maybe tea at 17.00 in the Plücker room 1.015).

Place: Seminar room 1.007, Mathematik-Zentrum, Endenicher Allee 60.

** Talks
**

** Abstracts
**

In this talk I will review recent work of mine, partially in collaboration with H. Ruddat, D. Treumann and E. Zaslow, which centers on various aspects of Kontsevich's Homological Mirror Symmetry in the large complex limit. The one-dimensional case will be emphasized, as a convenient testing ground for more general constructions.

We show that two varieties $X$ and $Y$ with isomorphic endomorphism semigroups are isomorphic up to a field automorphism if one of them is affine and contains a copy of the affine line. We also show that there exist smooth affine varieties in any dimension without endomorphisms except the identity and the constant maps.

The BMW algebra is a deformation of the Brauer algebra, and has the Hecke algebra of type A as a quotient. Its specializations play a role in types B, C, D akin to that of the symmetric group in Schur-Weyl duality. One can enlarge these algebras by a commutative subalgebra $X$ to an affine, or annular, version. Unlike the affine Hecke algebra, the affine BMW algebra is not of finite rank as a right $X$-module, so induction functors are ill-behaved, and many of the classical Hecke-theoretic constructions of simple modules fail. However, the affine BMW algebra still has a nice class of $X$-semisimple, or calibrated, representations, that don't necessarily factor through the affine Hecke algebra. I will discuss Walker's TQFT-motivated 2-handle construction of the $X$-semisimple, or calibrated, representations of the affine BMW algebra. While the construction is topological, the resulting representation has a straightforward combinatorial description. This is joint work with Kevin Walker.

## 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