Complexity of classification problems

Abstract: The notion of "Borel reducibility" gives a framework that allows us to compare the complexities of different classes of mathematical objects. I will give an introduction to this framework, including how it has been used to show that a number of proposed classification programmes in different areas of mathematics were impossible to realise. I'll then talk about using the framework to explain why the knot invariants called "quandles" are often considered to be too hard to work with (joint work with Sheila Miller), and finish with a discussion of what happens when the framework is extended to capture functoriality (joint work with Filippo Calderoni).

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.