Keynote: Higher Inductive Types in Homotopy Type Theory – Kristina Sojakova
Channel: Typelevel
Date: 2019-05-11

Homotopy type theory is a new field of mathematics based on the recently-discovered correspondence between constructive type theory and abstract homotopy theory. Higher inductive types, which form a crucial part of this new system, generalize ordinary inductive types such as the natural numbers to higher dimensions. We will look at a few different examples of higher inductive types such as the integers, circles, and the torus, and indicate how we can use their associated induction principles to reason about them, e.g., to prove that the torus is equivalent to the product of two circles.

* Event *

Typelevel Summit Philadelphia, April 2019: https://typelevel.org/event/2019-04-summit-philadelphia/

* About Speaker *

Kristina Sojakova is a postdoctoral researcher at Cornell University working with Greg Morrisett on the verification of cryptographic protocols. She received her PhD in 2016 from Carnegie Mellon University, where she worked on homotopy type theory, developing a universal mapping characterization of higher inductive types.

* Licensing *

This recording is licensed under CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/).