# Mathematical Conversations

**Topic: **Synthetic homotopy theory: going beyond set-level mathematics

**Speaker: **Guillaume Brunerie

**Affiliation: **Member, School of Mathematics

**Date & Time: **Wednesday March 14th, 2018, 6:00pm - 7:00pm

**Location: **Dilworth Room

In addition to offering a formal system for doing ordinary (or "set-level") mathematics, Vladimir Voevodsky’s Univalent Foundations also suggest a new way of studying homotopy theory, called "synthetic homotopy theory". I will show how synthetic homotopy theory emerges from the foundations of mathematics, and contrast it with set-level homotopy theory.