This semester will be devoted to resolution of singularities -- a process that modifies varieties at the singular locus so that the resulting variety becomes smooth. For many years this topic had the reputation of very technical and complicated, though rather elementary.
In fact, the same resolution algorithm can be described in various settings, including schemes, algebraic varieties or complex analytic spaces.
Recent trends in the field are that the resolution is, in fact, rather simple and conceptual, but simpler algorithms involve more advanced tools, such as orbifolds and log structures.
In this series of talks we will try to give a gentle introduction to the topic with the goal to discuss some new developments towards the end of the semester.
We do not assume serious familiarity with algebraic geometry. In particular, we will mainly work with varieties given by polynomial equations in C^n.
The first talk will be introductory with some classical examples of the main actors -- singularities, blow ups and resolutions.