The Deep Locus of Cluster Varieties

Explore the intricacies of cluster varieties in this 38-minute mathematics lecture presented by Jose Simenthal at the Canada-Mexico-US Conference on Representation Theory, Noncommutative Algebra, and Categorification. Delve into the concept of the deep locus in cluster algebras, beginning with an explanation of how the Laurent phenomenon relates to cluster tori on the spectrum of a cluster algebra. Examine a comprehensive description of the deep locus for finite-type cluster varieties with really full rank, as well as select infinite-type cluster varieties, including maximal positroid strata in Gr(3,n). Gain insights into potential applications of this research to homological mirror symmetry of Grassmannians, based on collaborative work with Marco Castronovo, Mikhail Gorsky, and David Speyer. Enhance your understanding of advanced mathematical concepts in cluster theory and its connections to algebraic geometry and representation theory.