Michelle Snider

Michelle Snider
Ph.D. (2011) Cornell University

First Position

Government consulting job in Maryland


Affine Patches on Positroid Varieties and Affine Pipe Dreams


Research Area:
algebraic combinatorics

Abstract: The objects of interest in this thesis are positroid varieties in the Grassmannian, which are indexed by juggling patterns. In particular, we study affine patches on these positroid varieties. Our main result corresponds these affine patches to Kazhdan-Lusztig varieties in the affine Grassmannian. We develop a new term order and study how these spaces are related to subword complexes and Stanley-Reisner ideals. We define an extension of pipe dreams to the affine case and conclude by showing how our affine pipe dreams are generalizations of Cauchon and \Le-diagrams.