If one allows the base of the deformations to be non-commutative, then there are more deformations than usual deformations. The deformations over commutative base can sometimes be regarded as the first order approximation of more general higher order deformations. Though the formal theories of deformations are parallel and the extension to the non-commutative case is simple, some new phenomena and invariants appear. I will explain these by some examples.
This video was produced by the Japan-US Mathematics Institute and forms part of JAMI Conference 2022.
