2019-10-29

Speaker: Yu Qiu (Tsinghua University)

Title: Cluster exchange groupoids and framed quadratic differentials

Abstract: We introduce the cluster exchange groupoid to show that any connected component (which are all isomorphic) of the moduli space of framed quadratic differentials on a decorated marked surface S_Delta is simply connected. We also impove the result of Bridgeland-Smith, that such a space can be identified with the principal component of the space of stability conditions on the associated Calabi-Yau-3 categories of S_Delta.

2019-10-15

【1】15:20 - 16:20

Speaker: Aslak Bakke Buan (Norwegian University of Science and Technology)

Title: A reduction technique for tau-rigid objects

Abstract: For a tau-rigid A-module M , Jasso considers a subcategory J(M), which he proves is (equivalent to) the module-category of a smaller algebra.

Then he shows that the complements of M as a support tau-tiling module are in correspondence with the support tau-tilting modules in J(M).

Applying Jasso's framework, we prove a slightly different version of this bijection, where we compare instead certain indecomposable objects in mod A with tau-rigid indecomposable objects in J(M).

Then we extend this bijection to a slightly bigger category, suitable for the study of (signed) tau-exceptional sequences and support tau-tilting objects.

This extension involves passing from a support tau-tilting set-up, to studying related 2-term silting objects in the bounded homotopy category.

Based on joint work with R.J. Marsh.

【2】16:30 - 17:30

Speaker: Xiaoting Zhang (Uppsala University)

Title: 2-representations of Soergel bimodules of finite Coxeter groups

Abstract: In this talk, I will introduce the 2-representation theory of Soergel bimodules for a finite Coxeter group and establish a precise conncection between the 2-representation theory of this non-semisimple 2-category and that of the associated semisimple asymptotic bicategory. This allows us to formulate a conjectural classification of simple transitive 2-representations of Soergel bimodules, which we prove in almost all Weyl type. This is a joint work with with M. Mackaay, V. Mazorchuk, V. Miemietz and D. Tubbenhauer.