Algebra and Algebraic Geometry Seminar - Sergio Da Silva - Understanding Schubert varieties using pattern avoidance
- Mathematics & Statistics
- 10.26.2020 10:30 am - 11:30 am
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.
Zoom Link: https://mcmaster.zoom.us/j/92175988081?pwd=N0ZnWi8yQllzQ0lRcFkxVDFVclhHdz09
Meeting ID: 921 75988081
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