![Loading Events](https://cmsa.fas.harvard.edu/wp-content/plugins/the-events-calendar/src/resources/images/tribe-loading.gif)
- This event has passed.
Homotopy type theory and the quest for extensionality
April 21, 2021 @ 3:00 pm - 4:00 pm
![CMSA-New-Technologies-in-Mathematics-04.21.21](https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-04.21.21.png)
Speaker: Michael Shulman – Dept. of Mathematics, University of San Diego
Title: Homotopy type theory and the quest for extensionality
Abstract: Over the past decades, dependent type theory has proven to be a powerful framework for verified software and formalized mathematics. However, its treatment of equality has always been somewhat uncomfortable. Recently, homotopy type theory has made progress towards a more useful notion of equality, which natively implements both isomorphism-invariance in mathematics and representation-independence in programming. This progress is based on ideas from abstract homotopy theory and higher category theory, and with the development of cubical type theories it can be implemented as a true programming language. In this talk, I will survey these developments and their potential applications, and suggest some directions for further improvement.