Plenary talk of Bruno Benedetti at the Applied Topology 2025 conference скачать в хорошем качестве

Plenary talk of Bruno Benedetti at the Applied Topology 2025 conference

Title: Random Simple Homotopy Theory Abstract: Discrete Morse Theory is a tool to understand simplicial complexes up to homotopy. It was introduced by Forman in 1999, though the main ideas go back to a 1939 paper by Whitehead. We discuss computational approaches via randomness, and drawbacks thereof. To bypass these drawbacks, we present a new strategy, closer in spirit to Whitehead’s original work. We implement an algorithm RSHT (Random Simple-Homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higherdimensional complexes. The RSHT algorithm combines elementary simplicial collapses with pure elementary expansions. It also generalizes the well-known “bistellar flip” algorithm for manifolds. At the moment, we do not know of a single contractible complex whose contractibility cannot be shown via the RSHT algorithm – a strong advantage with respect to discrete Morse theory. This is joint work with Frank Lutz and his students Crystal Lai, Davide Lofano. It was completed the same week of Frank’s sudden demise.