Abstract or Additional Information
Schubert varieties parametrize families of linear spaces intersecting certain hyperplanes in C^n in a predetermined way. In the 1970’s Hansen and Demazure independently constructed resolutions of singularities for Schubert varieties: the Bott-Samelson varieties. In this talk I will describe their relation with associahedra. I will also discuss joint work with Pechenick-Tenner-Yong linking Magyar’s construction of these varieties as configuration spaces with Elnitsky’s rhombic tilings. Finally, based on joint work with Wyser-Yong, I will give a parallel for the Barbasch-Evens desingularizations of certain families of linear spaces which are constructed using symmetric subgroups of the general linear group.
The first hour of the talk will be more elementary (aimed at graduate students) and will introduce (classical) Schubert varieties and Bott-Samelson varieties. These varieties contain lot of beautiful combinatorics and play important roles in geometric and combinatorial representation theory.