Title: Infinite mutations on marked surfaces Speaker: Sira Gratz (University of Oxford, UK)
Time: Wednesday, March 29, 2017 at 3:30 pm Place: MONT 313

Title: Linearity of Stability Conditions -- Northeastern-UConn Joint Seminar in Representation Theory Speaker: Kiyoshi Igusa (Brandeis University)
Time: Friday, March 31, 2017 at 3:00 pm Place: MONT 214Abstract: In 2002 Markus Reineke conjectured that there is a linear stability condition (given by a central charge Z) making all roots of a Dynkin quiver stable. This is reported to be solved by Hille and Juteau in an unpublished work. In 2014 Yu Qiu posted a solution of this conjecture along with many other results in the Dynkin case. The point is that there is an easy nonlinear stability condition, given by a maximal green sequence (MGS), which makes all roots stable. This becomes obvious given the equivalence between MGSs and Harder-Narasimhan (HN) stratification of mod H for any hereditary H, a result obtained by Yu Qiu in the Dynkin case. This talk is an updated version of talks with the same title given in Sherbrooke and in Hong Kong. New since Hong Kong: we extended results (same proofs!) to any finite dimensional algebra over any field. Namely, there is a notion of maximal green sequence for any algebra. Key properties of these generalized maximal green sequences are presented with an application: In joint work with PJ Apruzzese, an undergraduate at Brandeis, we found the upper bound on the length of a MGS with any cyclic quiver including the oriented cycle and give an explicit central charge attaining the upper bound showing that it is given by a linear MGS for any orientation of a circular quiver.