Skip to the content.
Unlimited Blade Works Background Research Tex Art
無限劍宇 背景 研究 数·图

Qiu Yu 邱宇


Hand Writing talk slide

Cluster Exchange Groupoids and Framed Quadratic Differentials

Abstract: We introduce the cluster exchange groupoid associated to a quiver with potential. In the case of the decorated marked surface S, the universal cover of this groupoid 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 (Fukaya) category associated to S. Finally, we show that Stab(S) is simply connected. This is a joint work with Alastair King.

q-Deformations of Categories, Stability Conditions and Quadratic Differentials

Abstract: We introduce Calabi-Yau-X categories D_X as q-deformation of topological Fukaya categories TFuk whose Calabi-Yau-N orbit categories are (subcategories of) derived Fukaya categories. Moreover, we show that TFuk is equivalent to the cluster categories associated to D_X. I will also mention q-deformation of stability conditions (and q-quadratic differentials). This is a joint work with Akishi Ikeda.