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：高鸿灏（清华大学）
题 目：Legendrian knots and cluster algebras via augmentations
时 间：2022.11.09（星期三） 14:30-15:30
地 点： 数学院南楼N533
摘 要：Legendrian knots and their exact Lagrangian fillings are central objects to study in low dimensional contact and symplectic topology. In recent developments, cluster algebras have proven to be powerful tools to classify Lagrangian fillings. For a positive braid link, we introduce a cluster K2 structure on its augmentation variety. Using the perspective of Ekholm-Honda-
Kalman theory, we prove that admissible exact Lagrangian fillings, a subset of decomposable ones, induce cluster seeds in the cluster K2 augmentation variety. We provide an algorithm to compute these cluster seeds. We also use the cluster Donaldson-Thomas transformation to produce infinitely many Lagrangian fillings. This is a joint work with L. Shen and D. Weng.
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