Richard P. Stanley Seminar in Combinatorics: Nodal Count distribution for graph and signed graphs via Morse theory of eingenvalues
SEMINARS, HARVARD-MIT COMBINATORICS
Lior Alon - MIT
Discrete Morse theory, developed by Forman, is an efficient tool to determine the homotopy type of a regular CW complex. The theory has been reformulated by Chari in purely combinatorial terms of acyclic matchings on the face poset. In this talk, I will discuss explicit constructions of such acyclic matchings on Bruhat intervals using reflection orders. As an application, we show the totally nonnegative Springer fibres are contractible, verifying a conjecture of Lusztig. This is based on work in progress with Xuhua He.
For more info, see https://math.mit.edu/combin/