Homological Methods in Random Noncommutative Geometry

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.

Intro
Outline
Background
Fuzzy spectral triples
Dirac operator of fuzzy spectral triple
Examples: Fuzzy sphere
Random NCG and the path integral
Comparison with results from random matrix theory
Numerical evidence of phase transitions
Diffeomorphism symmetries?
NC diffeomorphisms
Gauge transformations
Perturbations
BV-formalism
Classical BV formalism
Shifted Poisson structure
BV quantisation
Computing the path integral
Correlation functions
Analogy Higgs mechanism
Summary