Pattern avoidance and fiber bundle structure on Schubert varieties Travis Grigsby, Oklahoma State U Host: Siddiqur Rahman This is the first one of Travis's two talks.
Abstract: Permutation pattern avoidance has been used to describe smoothness and other geometric properties of Schubert varieties. Using a generalization of pattern avoidance called split pattern avoidance, Alland and Richmond were able to determine when projection from a Schubert variety to a Grassmannian is a fiber bundle. These projections are fiber bundles if and only if the indexing permutation avoids the split patterns 3|12 and 23|1. In this talk, we survey this area and discuss current progress towards generalizing this result to projections from Richardson varieties.
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