# Borel complexity theory - Classification and structure

Boise Mathematics Colloquium, Boise, September 2021

*Abstract*: Like other scientific disciplines, mathematics has classification as as one of its primary aims. In sciences one may classify plants or pathologies; in math one classifies objects like functions, graphs, symmetries, and so on. Of course, some classifications are harder than others to carry out. Borel complexity theory is an area of math which provides the tools to identify and compare the complexities of classification problems in mathematics.

In this talk I will introduce Borel complexity theory and give a brief overview. Afterwards I will outline some of my recent work: (1) on identifying the complexity of the classification of symmetries of highly symmetric graphs; and (2) on applications of “jumps” in the structure of the Borel complexity hierarchy (with our colleague John Clemens).