Deformation Theory for Finite Cluster Complexes

Explore the intricate world of cluster complexes in this 59-minute lecture by Alfredo Najera from the University of Miami. Delve into the geometric relationship between cluster varieties and cluster complexes, focusing on finite cluster types with universal coefficients. Learn how these cluster varieties can be obtained through a torus action on a specific Hilbert scheme constructed from the cluster complex. Gain insights into the potential generalization of this approach beyond the cluster setting. This talk, part of the "Geometry, Topology, Group Actions, and Singularities in the Americas" conference, bridges the fields of algebraic topology, algebraic geometry, and mathematical physics, offering a rich exploration of group actions in geometry and topology and their connections to singularity theory.