清华主页 EN
导航菜单

Rigidity in contact topology

来源: 11-22

时间:2022-11-22, TUESDAY 13:30-14:30

地点: Venue / 地点 Zoom ID: 405 416 0815, PW: 111111

组织者:陈伟彦、高鸿灏、黄意、林剑锋、江怡

主讲人:Honghao GAO 高鸿灏, YMSC

Abstract

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 differential graded algebra, which set apart the first non-classical Legendrian pair and stimulated many subsequent developments. The functor of points for the dga forms a moduli space which acquires algebraic structures and can be used to distinguish exact Lagrangian fillings. Such fillings are difficult to construct and to study, whereas the only known complete classification is the unique filling for Legendrian unknot. A folklore belief was that exact Lagrangian fillings might be scarce. In this talk, I will report a joint work with Roger Casals, where we applied techniques from contact topology, microlocal sheaf theory and cluster algebras to find the first examples of Legendrian links with infinitely many Lagrangian fillings.


Speaker

Dr. Honghao Gao is an Associate Professor at Yau Mathematical Sciences Center. He obtained his PhD from Northwestern University. His area of research is contact and symplectic topology, and their relations with knot theory, microlocal sheaf theory and cluster algebras.

返回顶部
相关文章
  • Introduction to contact topology

    Description: This is an introductory course to contact topology. We will give a first glance at topics in contact topology and its relationship with peripheral subjects such as knot theory and symplectic topology. The course will be suitable for advanced undergraduate students and PhD students.Reference:Geiges, An Introduction to Contact TopologyKashiwara and Schapira, Sheaves on Manifold

  • Renormalization and Rigidity in Dynamical Systems

    Abstract:The ideas of renormalization was introduced into dynamics around 40 years ago. By now renormalization is one of the most powerful tools in the asymptotic analysis of dynamical systems. In this talk I will discuss the main conceptual features of the renormalization approach,and present a selection of recent results. I will also discuss open problems and formulate related conjectures.Sp...