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Abstract：We will explain the concept of Lagrangian Dehn twists and its significance in mirror symmetry. There is a conjecture due to Paul Seidel, which asserts the composition of a sequence of Lagrangian Dehn twists can be computed as a mapping cone between the Floer chain complex of the identity, as well as a cube complex formed by the Hochschild complex of a directed subcatgory with spherical objects. We give two proofs of this conjecture, one is purely algebraic, the other is more geometric and is of independent interests. We will also explain the relation between this work and other problems. This is a joint work with Cheuk-Yu Mak and Shuo Zhang.
Bio：吴惟为，浙江大学长聘副教授。2012年获明尼苏达双城分校博士学位，曾在密歇根州立大学，蒙特利尔大学任博士后；并于2016-2021在University of Georgia 任助理教授，2021-2022 受聘为副教授。吴惟为教授在2023年加入浙江大学。吴惟为教授在辛拓扑和同调镜对称等领域作出了一系列具有国际影响力的工作，相关论文发表在Geom. Top., Crelle's journal, Adv. Math., Compositio, J. Differential Geom., Math. Ann. Selecta Math. 等杂志上。