HoTT: The Language of Space
Groupoid Infinity Presentation (Slides) for Public Event f(cafe) 25 July 2018
Homotopy Type Theory (HoTT) is the most advanced programming language in the domain of intersection of several theories: algebraic topology, homological algebra, higher category theory, mathematical logic, and theoretical computer science. That is why it can be considered as a language of space, as it can encode any existent mathematics.
Speaker: Maxim Sokhatsky is an author of Privat24 deposits, 20 years of working experience as a programmer, one of the 30 top-commiters in Ukraine in Open Source, author of N2O, the best Erlang Web Framework, CEO of Synrc Research Center, author of several embedded operating system runtimes and production programming languages. Maxim is familiar with any programming language on the planet and had seen sources of all operating systems.
Now Maxim is doing his Ph.D. research (the second year of education) in HoTT, trying to encode as much mathematics in the programming language as possible along the way.
During this lecture, Maxim will try to smoothly guide you from the programming perspective to the pure space of mathematics and will show the evolution of mathematical provers from AUTOMATH to the family of Cubical Type Checkers. Also, this lecture is considered as a general introduction to HoTT course Maxim is preparing for his friends.