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Exact Lagrangian fillings of D-type Legendrian Links

Student-Run Research Seminar

Speaker: James Hughes, UC Davis
Location: (Online) Zoom
Start time: Thu, May 6 2021, 11:00AM

A Legendrian link L in contact R^3 is a smooth link with the additional requirement that its tangent space is contained in the 2-plane field defined by the contact structure. An exact Lagrangian filling of L is a surface in the symplectic 4-ball with boundary equal to L and which satisfies certain properties. In this talk, we describe a method of constructing and distinguishing exact Lagrangian fillings of a certain family of links. In particular, we show that this family has at least (an integer multiple of) a Catalan number of fillings, or as many as cluster seeds in the D-type cluster algebra. No prior knowledge of contact topology or cluster algebras is assumed.



Snacks provided by attendees from their kitchens.