Threefold flops and diffeomorphism groups
Abstract: Flops are elementary birational transformations which first appear in dimension 3. They are of great interest in algebraic geometry, as they play a key role in the minimal model program. They are also related to mirror symmetry, symplectic geometry, etc. The first example of a flop, known as the Atiyah flop, was found in Atiyah's paper of 1958. The Atiyah flop, essentially the simplest threefold flop, has many uses in low-dimensional topology. For instance, one can use it to prove that the moduli space of non-polarized K3 surfaces is non-Hausdorf. In this talk, I will show how one can use that flop to study the diffeomorphism groups of four-manifolds. In particular, I will focus on the fundamental group of the group of diffeomorphisms of algebraic surfaces.
This event will be held at 11am.