How to collapse a simplicial complex: theory and practice
Giovanni Paolini (AWS and Caltech)
Abstract: Sometimes one wants to answer topological questions about a simplicial complex: Is it contractible? Does it deformation retract onto a certain subcomplex? What is its homotopy type? What is its homology? In this talk, I will introduce discrete Morse theory, which allows approaching these questions in a purely combinatorial way, by constructing sequences of "elementary collapses" between pairs of simplices. Then I will outline algorithms and hardness results for collapsibility and discrete Morse theory.
computer science theorycombinatoricsgeometric topology
Audience: researchers in the discipline
Series comments: Password is on the seminar page. www.math.ucla.edu/~pak/seminars/CCSem-Fall-2020.htm