中科院数学与系统科学研究院

数学研究所

学术报告

拓扑研讨班

报告人：吴惟为教授 (浙江大学)

题  目：Floer cohomology of compositions of Lagrangian Dehn twists

时  间：2024.07.10（星期三）11:00-12:00

地  点：数学院南楼N602

摘  要： There is a conjecture due to Paul Seidel, that 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 subcategory with spherical objects.  We give two proofs of this conjecture, one is purely algebraic, and the other relies on clean surgery and should be of independent interest.  This result was previously announced by Sikimeti M'au and Tim Perutz, but either approach we present in this talk is different from their solution.  This is partly an upcoming work of Shuo Zhang, and partly a joint work in progress with Cheuk-Yu Mak and Shuo Zhang.

报告人：李文远博士(南加州大学)

题  目：Relative Calabi-Yau structures for microlocal sheaves/Fukaya categories

时  间：2024.07.10（星期三）10:00-11:00

地  点：数学院南楼N602

摘  要：For a Liouville manifold with a Liouville hypersurface at infinity, one can associate a pair of (partially) wrapped Fukaya categories to the pair of Liouville manifolds. The result of Ganatra-Pardon-Shende shows that the Fukaya categories are equivalent to certain categories coming from microlocal sheaf theory. We consider cotangent bundles with Weinstein hypersurfaces, study duality and exact sequences that arise from the pair of categories and show that this pair admits a strong relative Calabi-Yau structure, such that the wrap-once functor gives the inverse dualizing bimodule. This is a non-commutative analogue of the Poincare-Lefschetz duality on manifolds with boundary. This is joint work in preparation with Chris Kuo.