Title: Understanding Schubert varieties using pattern avoidance  

Speaker: Sergio Da Silva (McMaster University)

Abstract: Many geometric properties of Schubert varieties in the full flag manifold GL_n/B can be described using pattern avoidance or interval pattern avoidance conditions. These convenient characterizations reduce difficult computations to simple combinatorics involving permutations. For example, a Schubert variety associated to a permutation w is smooth if and only if w pattern avoids 3412 and 4231. Similar descriptions exist for checking factoriality or Gorensteinness, among other properties.

I will start by providing any necessary background on Schubert varieties followed by an overview of known results regarding pattern avoidance. I will also discuss newer research on a combinatorial subword description for the Gorenstein property.

Location: Virtual

Zoom Link: https://mcmaster.zoom.us/j/92175988081?pwd=N0ZnWi8yQllzQ0lRcFkxVDFVclhHdz09

Meeting ID: 921 75988081

Please contact rajchgoj@mcmaster.ca for meeting password.

Website:  https://sites.google.com/view/McMasterAAGS/