Lenhard Ng Department of Mathematics Duke University Lenhard Ng's website Monday, February 17, 2025 - 3:00pm Boyd 322 Braid varieties from several perspectives Abstract: In this talk, I'll introduce a family of algebraic varieties that has recently appeared in several distinct areas of mathematics. This family goes by the name of "braid varieties" and associates a variety to any positive braid. I'll discuss how braid varieties arise in algebraic geometry through flags and constructible sheaves; in algebraic combinatorics through cluster theory; and finally in symplectic topology. We'll use braid varieties to explore the symplectic problem of classifying Lagrangian fillings of Legendrian links, and we'll talk about how cluster theory provides some new insight into this old problem.
