Speaker: Monty McGovern (University of Washington)

Title:  Pattern avoidance and singularity of K-orbit closures

Abstract:  Kazhdan-Lusztig-Vogan polynomials provide fairly complete information about the singularities of K-orbit closures in flag varieties; but in view of their complexity, it is often convenient to have weaker information available in a more explicit form.  The combinatorial notion of pattern avoidance provides a tool for doing this.  I will characterize smoothness and rational smoothness of K-orbit closures via pattern avoidance in all classical cases.  The conditions exhibit many similarities to but also intriguing differences from their counterparts for Schubert varieties.