Discrete gradient vector fields on simplicial complexes and rooted forests (Ivan Contreras Palacios)

Discrete Math Seminar on October 15, 2021

Abstract: Discrete Morse theory was originally formulated by R. Forman in 1998 as a CW-complex version of smooth Morse theory. In this talk we use a generalization of the graph Laplacian in simplicial complexes to find a generating function for the number of discrete gradient vector fields, in the case when the complex is a triangulation of an orientable manifold. We characterize a correspondence between discrete gradient vector fields for Morse functions and higher dimensional rooted forests of simplicial complexes. Based on joint work with Andrew Tawfeek (arXiv:2105.05388)