Rigidity and Flexibility of Schubert classes

Members' Seminar
Topic:Rigidity and Flexibility of Schubert classes
Speaker:Colleen Robles
Affiliation:Texas A & M University; Member, School of Mathematics
Date:Monday, January 27
Time/Room:2:00pm - 3:00pm/S-101
Video Link:https://video.ias.edu/members/2014/0127-ColleenRobles

Consider a rational homogeneous variety \(X\). (For example, take \(X\) to be the Grassmannian \(\mathrm{Gr}(k,n)\) of \(k\)-planes in complex \(n\)-space.) The Schubert classes of \(X\) form a free additive basis of the integral homology of \(X\). Given a Schubert class \([S]\), represented by a Schubert variety \(S\) in \(X\), Borel and Haefliger asked: aside from the Schubert variety, does \([S]\) admit any other algebraic representatives? I will discuss this, and related questions, in the case that \(X\) is Hermitian symmetric.