Monty McGovern: Singularities of K-orbit closures and pattern avoidance

Monty McGovern, University of Washington

Singularities of Schubert subvarieties of a flag variety are well known to play a major role in the representation theory of the corresponding complex reductive group.  Similarly, singularities of symmetric subvarieties of a flag variety have many connections with the representation theory of the corresponding real form of the group.  The first kind of singularities have been characterized via the classical combinatorial notion of pattern avoidance.  I will indicate how this plays out in the symmetric variety setting for real classical groups.