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 博士（Michigan State University）
题 目：Rigidity in contact topology
时 间：2022.01.21（星期五），09:00-10:00
地 点：数学院南楼N202室 腾讯会议：713 831 373
摘 要：Legendrian links play a central role in low dimensional contact topology. A rigid theory uses invariants constructed via algebraic tools to distinguish Legendrian links. The most influential and powerful invariant is the Chekanov-Eliashberg differentialgraded algebra (Chekanov, Inventiones, 2002), which set apart the first non-classical Legendrian pair and stimulated many subsequent developments. The functor of points for the dga is a moduli space which acquires algebraic structures and can distinguish exactLagrangian fillings. Such fillings are difficult to construct and to study, whereas the only known classification is the unique filling for Legendrian unknot (Eliashberg-Polterovich, Annals, 1996). A folklore belief was that exact Lagrangian fillings mightbe scarce. In this talk, I will report a joint work with Roger Casals, where we applied the techniques from contact topology, microlocal sheaf theory and cluster algebras, and successfully found the first examples of Legendrian links with infinitely many Lagrangianfillings.
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