Noncommutative crepant resolutions and some higher dimensional flops

Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half.

Abstract: We will talk about the theory noncommutative resolution of singularities. Noncommutative resolution is a noncommutative analog of usual (geometric) resolution of singularities, and allows us to generalise the idea of McKay correspondence to a large class of singularities.
In the first part of the talk, we discuss the classical McKay correspondence, the definition of noncommutative crepant resolution, and some known results in lower dimensions. In the second half, we will discuss some concrete examples of noncommutative crepant resolutions in higher dimensions.