Deformation theory

Richard Thomas.

Deformation theory is a formalisation of the idea that to study a nonlinear problem one can first study its linearisation at a point, then its quadratic behaviour, etc.

I'll review the functor of points formalism that Dougal showed you last term, then restrict it to small/infinitesimal ("Artinian") families. I'll concentrate mostly on first order deformations and obstructions, which we'll study through simple examples. If I'm successful I'll find a way to organise the material so we can touch on the "T^1-lifting" technique.

There are some notes from previous years.