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

  • April 14: Nicolo Sibilla (Bonn): Ribbon graphs, skeleta and homological mirror symmetry
  • Friday, April 25, SR 1.008, 14.00: Markus Reineke (Wuppertal): Arithmetic of character varieties of free groups
  • April 28: no talk
  • May 5: Hanspeter Kraft (Basel): Varieties Characterized by their Endomorphisms
  • May 12: Monica Vazirani (UC Davis): Representations of the affine BMW algebra
  • May 19: no talk
  • May 26: Steffen Oppermann (Trondheim): Geigle-Lenzing weighted projective varieties
  • June 2: Hans Franzen (Wuppertal): Cohomology of Non-Commutative Hilbert Schemes as CoHa-Modules
  • June 9: no talk (Whit Monday)
  • June 16: free
  • June 23: Nathan Broomhead (Hannover): Discrete derived categories
  • June 30: Antonio Sartori (York): Tensor product categorification and category O
  • July 7: Rainer Weissauer (Heidelberg): Cohomological tensor functors and representations of linear supergroups
  • July 14: free

  • Abstracts

  • April 14: Nicolo Sibilla (Bonn): Ribbon graphs, skeleta and homological mirror symmetry.
    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.
  • May 5: Hanspeter Kraft (Basel): Varieties Characterized by their Endomorphisms (joint work with Raffael Andrist).
    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.
  • May 12: Monica Vazirani (Davis): Representations of the affine BMW algebra
    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.