An introduction to univalent foundations and the equivalence principle

Please note: This is  talk will take place online only.

For zoom details contact: Barthel, Ozornova, Ray, Teichner.

The equivalence principle is an informal principle asserting that equivalent mathematical objects have the same properties. For example, isomorphic groups should have the same group-theoretic properties, and equivalent categories should have the same category-theoretic properties. Vladimir Voevodsky established Univalent Foundations (UF) as a foundation of mathematics based on Homotopy Type Theory with the conjecture that the equivalence principle cannot be violated in UF -- it is a theorem.

In this talk, I will introduce Univalent Foundations motivated by this perspective. I will also talk about joint work with Ahrens, Shulman, and Tsementzis which proves Voevodsky's conjecture.

This talk will be self-contained.