Singular Points on Positroid Varieties and Physics Applications

Explore a 56-minute seminar lecture that delves into the mathematical intricacies of positroid varieties and their applications in physics. Learn about the criteria for determining singularity at distinguished points within positroid varieties, and understand how this information can be used to assess the smoothness of entire positroid varieties through the examination of affine pipe dreams. Discover the partial ordering system for positroid varieties based on deletion and contraction, with special attention to closure properties of smooth varieties and the characterization of minimal singular elements. Gain insights into practical physics applications involving Postnikov's plabic diagrams, including the BCFW bridge decomposition and inverse soft factors. Building upon previous discussions of positroid varieties as Grassmannian subvarieties defined by cyclic rank conditions, examine their relationship to Schubert varieties and their significance in mathematical physics.