This seminar series will explore recent interactions between manifold topology and descriptive set theory. The main Mathematical Colloquium lecture will discuss the longstanding problem of classifying smooth structures on, and how methods from descriptive set theory can be used to derive a strong form of unclassifiability for such smoothings.
Two accompanying lectures will develop the broader context and reach of these techniques.
The first 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. The second lecture will present manifoldtheoretic
constructions which can be used to realize these complexity upper bounds.

SCHEDULE:

13:30-14:30

Mathematical Colloquium:
On classifying smoothings of
R. E. Gompf, University of Texas

14:30-15:00

Coffee Break
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15:00-15:40

Descriptive Obstructions to Classification
A. Panagiotopoulos, University of Vienna

15:50-16:30

Constructing unclassifiable families of
manifolds
R. E. Gompf, University of Texas