Seminar

The noncommutative minimal model program (ncMMP) uses the techniques of Mori theory to classify noncommutative surfaces, which we assume to be finite over their centres. The main result is a very pleasing analogy with the commutative theory - a noncommutative surface is either birational to a unique minimal model, or a noncommutative ruled surface.

In this talk, I will explain how to associate a Brauer pair to a noncommutative surface, and how to run the ncMMP for these Brauer pairs. Although this is similar in spirit to the log MMP, there are some differences. Noncommutative ruled surfaces arise naturally in this context, and we will conclude with some structural results about them obtained by moduli theory.