Renormalising Non-Commutative Singular (S)PDEs

When attempting to construct QFTs that include Fermions using the methods of Stochastic Quantisation, one is naturally forced to consider noncommutative stochastic PDEs. I shall show how to formulate SPDEs driven by noncommutative noises in terms of algebra-valued singular PDEs. Furthermore, I will describe how one can renormalise the singular products appearing in such equations for a set of algebras interpolating between Fermions and Bosons by appropriately modifying their topologies. This talk will be based on joint work with Ajay Chandra and Martin Hairer.