Schedule

13:30-14:30: Mathematical Colloquium: On classifying smoothings of \(\mathbb{R}^4\)
R. E. Gompf (U of Texas at Austin, US)

The colloquium will discuss the longstanding problem of classifying smooth structures on \(\mathbb{R}^4\), from its origin 45 years ago to the most recent development: There is a precise sense in which a complete solution is impossible. This follows by using tools from descriptive set theory, and is joint work with Aristotelis Panagiotopoulos. We will also briefly introduce joint work in progress that will be developed further in two lectures after the break, showing that various other uncountable manifold classification problems reach a much higher level of difficulty.

14:30-15:00 Coffee Break

15:00-15:30: Descriptive Obstructions to Classification
A. Panagiotopoulos (U Wien)

This seminar will introduce the Borel reduction hierarchy, a complexity theory for classification problems, it will survey recent developments in the area and will provide new upper bounds which show that manifolds in various categories are classifiable by countable structures.

15:50-16:30: Constructing unclassifiable families of manifolds
R. E. Gompf (U of Texas at Austin, US)

This seminar will present manifold-theoretic constructions which can be used to realize the complexity upper bounds introduced in the previous lecture.