Unlimited Blade Works	Background	Research	Tex Art
無限劍宇	背景	研究	数·图

Qiu Yu 邱宇

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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.