Morse-Bott functions on classical groups and a framed flow category

Abstract: Trace and quadratic trace functions on classical groups (and on more general spaces) are well-known Morse-Bott functions. Since more than half a century they have been providing bridges between geometry and combinatorics, relating one to the other through Schubert calculus. Following a joint work with I. Bozma and W.D. Gillam I will try to tell samples of these relations. I will finish by proposing a (possibly new) framed flow category.