Advanced Minicourses
The target audience for these minicourses is faculty, graduate and advanced undergraduate students who are working in the field of Low-dimensional Topology.
Minicourse 1: Virtual Fibering Theorem
Virtual fibering Theorem - Stefan Friedl
A 3-manifold is called fibered if it is a surface bundle over the circle. Even though most 3-manifolds are not fibered it was shown by Ian Agol and Dani Wise about 10 years ago that most 3-manifolds admit a finite covering that is fibered. We will talk about some of the key ideas of this proof.
Minicourse 2: 4-manifolds
Topological 4-manifolds - Arunima Ray
I will describe the past, present, and (hopefully) future for the field of topological 4-manifolds. The key result in this area is Freedman's disc embedding theorem, which leads e.g. to the proof of the (topological) 4-dimensional Poincare conjecture. Here is the rough, optimistic plan for the talks:
Talk 1: Motivation and setup for the disc embedding theorem
Talk 2: Bing topology and outline of its application to the proof of the disc embedding theorem
Talk 3: Extending the disc embedding theorem to all compact surfaces
Talk 4: Open problems for topological 4-manifolds
Talk n will almost certainly spill into talk n+1 for n=1,2,3.