Combinatorics Seminar 2018

Speaker: Yu Qiu (邱宇), Tsinghua University

Date: Thu, Jan 10, 2019

Time: 17:10 - 18:00

Venue: Xiayuan 211

Title: Cluster exchange groupoids and quadratic differentials


We introduce the cluster exchange groupoid associated to a non-degenerate quiver with potential, as an enhancement of the cluster exchange graph. In the case of the decorated marked surface $S$, the universal cover of this groupoid can be constructed using decorated triangulations of $S$. Such a covering graph is a skeleton for a space of suitably framed quadratic differentials on $S$, which in turn models the space $Stab(S)$ of Bridgeland stability conditions for the 3-Calabi-Yau category associated to $S$. Finally, we show that $Stab(S)$ is simply connected.

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