# Borel complexity theory in mathematics

Boise Math Graduate Seminar, Boise, September 2016

*Abstract*: Given a mathematical problem it is natural to wonder how complicated it is, but it is hard to imagine how to make this question rigorous. Borel complexity theory is an area of set theory which provides a framework to measure the complexity of classification problems in mathematics. We will introduce this theory, and show how it has been applied to classification problems in group theory, graph theory, and functional analysis.