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DTSTART;TZID=America/New_York:20210421T150000
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SUMMARY:Homotopy type theory and the quest for extensionality
DESCRIPTION:Speaker: Michael Shulman – Dept. of Mathematics\, University of San Diego \nTitle: Homotopy type theory and the quest for extensionality \nAbstract: 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. \n 
URL:https://cmsa.fas.harvard.edu/event/4-21-2021-new-tech-in-math-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
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