Logic and Its Applications

Homotopy Type Theory is a new, homotopical interpretation of constructive type theory. It forms the basis of the recently proposed Univalent Foundations of Mathematics program. Combined with a computational proof assistant, and including a new foundational axiom – the Univalence Axiom – this program has the potential to shift the theoretical foundations of mathematics and computer science, and to affect the practice of working scientists. This talk will survey the field and report on some of the recent developments.