Categorical resolutions of singularities (Kuznetsov)
I will discuss an approach to resolution of singularities of schemes
via derived categories of coherent sheaves. I will define what a categorical resolution
of singularities is, and will describe a construction of a categorical resolution
for any separable scheme of finite type over a field of characteristic zero (thus showing
that categorically any such singularity behaves as a rational singularity). Then I will
discuss the question of constructing small categorical resolutions, concentrating
on the notions of crepancy and explicit examples.