Henri Riihimäki: Excursions into directed networks: combinatorics, algebra, and topology with machine learning

Abstract

I will describe three recent works in the context of directed graphs/networks. The motivation and applications stem from brain networks of neurons and this perspective is interleaved in the talk. The three works I will describe are: 1) Machine learning pipeline for binary dynamics on a network, 2) New notion of a simplicial connectivity for directed graphs which extends Q-analysis of Atkin, and 3) How simplicial connectivities enable higher Hochschild homologies of directed graphs, going beyond degree 1 of the path algebra.