Speaker: Amanda Burcroff
Harvard
Will give a Discrete Mathematics Seminar entitled:
Positivity for Generalized Cluster Algebras
Abstract: Cluster algebras provide a powerful combinatorial framework for understanding the structure of algebraic and geometric spaces. They are especially notable for their remarkable positivity properties, which reveal deep and often unexpected connections across mathematics and physics. In this talk, we explore positivity from both combinatorial and mirror symmetric perspectives to develop a directly computable, manifestly positive, and elementary (yet highly nontrivial) formula describing scattering diagrams in rank 2. Using this formula, we prove Laurent positivity for generalized cluster algebras of arbitrary rank, resolving a conjecture of Chekhov and Shapiro from 2014. This is joint work with Kyungyong Lee and Lang Mou.
Date: 05-08-2025
Time: 1:00 pm
Location: 125 HH
Zoom URL: notredame.zoom.us/j/