Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

The talk will focus on studying Legendrian knots in the standard 3-dimensional contact Darboux ball, with an emphasis on the moduli space of Lagrangian fillings. First, I will discuss some of the algebraic geometric techniques that we currently use to understand Legendrian knots and their Lagrangian fillings. Then, we will motivate the notion of a cluster algebra through the lens of algebraic geometry and present one of the new results in this area: the existence of cluster algebras associated to a large class of Legendrian knots, including all positive braids. This is joint work with D. Weng.