Synthetic homotopy theory: going beyond set-level mathematics

Mathematical Conversations
Topic:Synthetic homotopy theory: going beyond set-level mathematics
Speaker:Guillaume Brunerie
Affiliation:Member, School of Mathematics
Date:Wednesday, March 14
Time/Room:6:00pm - 7:00pm/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.