Title: Noncommutative Minimal Models and applications to geometry.
Abstract: I will try and explain the ideas behind noncommutative minimal models (=MMAs) and why they should not only reprove parts of the MMP in dimension three, but also give us extra information that currently the geometry does not "see". This extra information (in the form of a quiver) should then allow us to run aspects of the MMP in a much easier way. The talk will mainly be example based, but as an application of the homological techniques, I will give (in the dimension three Gorenstein setting) a characterization of the Q-factorial property in terms of derived categories. This is joint with Iyama.
