Explore homological methods in random noncommutative geometry through a 53-minute lecture by Hans Nguyen from the University of Nottingham, presented at the Fields Institute's Workshop on Noncommutative Geometry, Free Probability Theory and Random Matrix Theory. Delve into topics such as fuzzy spectral triples, Dirac operators, random matrix theory comparisons, and numerical evidence of phase transitions. Examine noncommutative diffeomorphisms, gauge transformations, and perturbations using the BV-formalism. Investigate the path integral computation, correlation functions, and draw analogies to the Higgs mechanism in this comprehensive exploration of random noncommutative geometry.