Algebraic Geometry Seminar: Alex Yong

This talk addresses the problem of how to analyze and discuss singularities of a variety X that "naturally'' sits inside a flag manifold. Our three main examples are Schubert varieties, Richardson varieties and Peterson varieties. The overarching theme is to use combinatorics and commutative algebra to study the "patch ideals", which encode local coordinates and equations of X. Thereby, we obtain formulas and conjectures about X's invariants. We will report on projects with (subsets of) Erik Insko (Florida Gulf Coast U.), Allen Knutson (Cornell), Li Li (Oakland University) and Alexander Woo (U. Idaho).