Colloquium: Transverse Spheres in Flag Manifolds

Abstract: Flag manifolds are natural objects in algebraic and differential geometry, generalizing familiar examples like projective space and Grassmannians. A subset of a flag manifold is called transverse when every pair of points is in general position. Transverse circles abound. Conversely, recent restriction results show that in certain cases transverse circles are maximally transverse. We shall detail a complementary result. Using spinors, we build arbitrarily large transverse spheres in real full flag manifolds. Previously, there were no known transverse subsets larger than a circle for these ambient spaces. The new spheres are, in fact, maximally transverse, as witnessed by topological K-theory. Time permitting, we discuss implications for Anosov representations. This project is joint with Max Riestenberg.

Host: Matt Kerr

Reception to follow at Cupples I, Room 200 (Lounge) from 2:00pm to 3:00pm