Colloquium - "Flag Varieties and Alcove Walks" - Elizabeth Milicevic
Please note that the room for the Colloquium talk has been changed to Hamilton Hall, Room 109
The refreshments will be served in the Math Cafe, Hamilton Hall at 3:00 pm
Title: Flag Varieties and Alcove Walks
Abstract: Flag varieties play a central role in the intersection of algebraic geometry, representation theory, and algebraic combinatorics. The points in this variety are defined as increasing chains of subspaces in a vector space, but these points also have a convenient combinatorial description given by taking a walk among the alcoves in a Euclidean geometric model for the flag variety. Because flag varieties and their generalizations can be quite large, it can be unwieldy to study the points individually, and so we often collect them into orbit of various groups. We will explain how folding the alcove walks in the geometric model provides a means for visualizing the de-composition of the flag variety into orbits of certain groups. The goal of this talk will be to explain precisely how these algebraic, geometric, and combinatorial stories coincide, primarily by drawing lots of pictures in concrete examples. No specialized background required.
This colloquium is part of the "Combinatorial Algebra meets Algebraic Combinatorics" conference being held at McMaster University from Jan. 26-28.