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GRT at home seminar

Roger Casals, UC Davis

Legendrian knots and Algebraic Structures

Organizer's time: 2020-12-01 17:00 Europe/Vienna

Duration: 1 hour 15 minutes

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In this talk, I will discuss the algebraic structures that arise in the study of Legendrian knots. In particular, I will explain how to use cluster structures in certain moduli spaces associated to Legendrian knots to solve some problems in 3-dimensional contact topology. First, I will introduce the contact topological setting: with the basic definitions and examples of Legendrian links. Second, we discuss the algebraic varieties associated to Legendrian links, including their symplectic geometric meaning and motivation. Then, I will explain how to study these algebraic varieties (and thus the Legendrian links) via a diagrammatic calculus, and the use of cluster algebras. The diagrammatic calculus, of symplectic geometric origin, can be understood, in a sense, as the open analogue of Elias-Khovanov Soergel calculus.

Submitted by: Anton Mellit