Special Invited Seminars in Algebraic Geometry - Winter Semester 2015/2016

Schedule 2015

Magnus Engenhorst: Stability for quiver categories // 4pm 15.10.2015, SR 025/26 Arnimallee 6
Stable representations of quivers are an analogue of stable vector bundles on curves. They are closely related to so called maximal green sequences for the associated derived categories. Maximal green sequences were originally introduced as combinatorical counterpart for Donaldson-Thomas invariants for quivers with potential by Bernhard Keller. In the case of preprojective algebras we show that a quiver has a maximal green sequence if and only if it is of Dynkin type.

Arne Rüffer: Holomorphic triples and t-structures // 10am 18.11.2015, SR 005 Arnimallee 3
Stability conditions on triangulated categories were introduced by Bridgeland. They can be given by a t-structure together with a stability function on its heart. To study stability conditions we start by looking for t-structures and descriptions of their hearts. In my talk I will endeavour to discuss how hearts of t-structures can be studied in the case of the bounded derived category of holomorphic triples on an elliptic curve.

Ben Davison: Donaldson Thomas theory and the cohomology of character varieties // 4pm 24.11.2015, SR 119 Arnimallee 3
In this talk I will explain how a recent joint theorem with Sven Meinhardt, a proof of a refined version of the motivic integrality conjecture of Kontsevich and Soibelman, gives a way to identify the pure part of the cohomology of the stack of representations of the fundamental group of a Riemann surface. I'll also sketch how this implies a stack-theoretic analogue of the conjecture of Hausel and Villegas on the pure part of this cohomology.

Tarig Abdelgadir: Tensor McKay Correspondence // 4pm 26.11.2015, Horsaal 1 Arnimallee 3
Given a finite group G in the SL(n), the derived McKay correspondence conjecture states that a crepant resolution of the corresponding singularity is derived equivalent to the corresponding orbifold. A theorem of Balmer implies that nontrivial derived equivalences induce/arise-from a change in the tensor product of the derived category. The aim is to examine this variation of tensor products in the McKay case. This is a joint project with Alastair Craw and Alastair King. Since this is a work in progress, we will restrict ourselves to the simplest of cases.