Richard P. Stanley Seminar in Combinatorics: Nodal Count distribution for graph and signed graphs via Morse theory of eingenvalues


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November 29, 2023 4:15 pm - 5:15 pm
MIT, Room 2-139

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.


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