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Vladimir Voevodsky has died

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Re: Vladimir Voevodsky has died

#12
post #9
post #5

Earlier quoted context omitted.

Could you expand on his work, related to CS and/or his influence in your work? I've never heard of him so I'm curious, being a Field medalist and all.

Voevodsky won the Fields medal for A^1 homotopy theory: https://en.wikipedia.org/wiki/A%C2%B9_homotopy_theory It's quite technical to describe what that is, but the general idea is that he imported homotopy theory, a fundamental concept in mathematics which allows you to describe topology with an algebra of paths in that geometry, to algebraic geometry. This allowed him to solve some major open problems in the field.…

I think topology is mentioned in recent Microsoft Ignite Quantum Computing discussions from at least 1 panel who is a mathematician. I wonder how it might be related.

Re: Vladimir Voevodsky has died

#14
post #9

Earlier quoted context omitted.

Voevodsky won the Fields medal for A^1 homotopy theory: https://en.wikipedia.org/wiki/A%C2%B9_homotopy_theory It's quite technical to describe what that is, but the general idea is that he imported homotopy theory, a fundamental concept in mathematics which allows you to describe topology with an algebra of paths in that geometry, to algebraic geometry. This allowed him to solve some major open problems in the field.…

I think topology is mentioned in recent Microsoft Ignite Quantum Computing discussions from at least 1 panel who is a mathematician. I wonder how it might be related.

Topology of course is fundamental to all of physics, but in that context my guess would be on topological quantum computing: https://en.wikipedia.org/wiki/Topological_quantum_computer

I once attended a talk on the subject by Michael Freedman who is with Microsoft Station Q. They are trying to build just such a computer.

Re: Vladimir Voevodsky has died

#15
post #9
post #5

Earlier quoted context omitted.

Could you expand on his work, related to CS and/or his influence in your work? I've never heard of him so I'm curious, being a Field medalist and all.

Voevodsky won the Fields medal for A^1 homotopy theory: https://en.wikipedia.org/wiki/A%C2%B9_homotopy_theory It's quite technical to describe what that is, but the general idea is that he imported homotopy theory, a fundamental concept in mathematics which allows you to describe topology with an algebra of paths in that geometry, to algebraic geometry. This allowed him to solve some major open problems in the field.…

[deleted]

Re: Vladimir Voevodsky has died

#16
post #5

A great loss for mathematics! I became familiar with his work through HoTT -- > More recently he became interested in type-theoretic formalizations of mathematics and automated proof verification. He was working on new foundations of mathematics based on homotopy-theoretic semantics of Martin-Löf type theories. His new "Univalence Axiom" has had a dramatic impact in both mathematics and computer science. And some of…

Could you expand on his work, related to CS and/or his influence in your work? I've never heard of him so I'm curious, being a Field medalist and all.

I'm in a similar situation, I hope these couple of pieces about univalent foundations are useful: https://www.ias.edu/ideas/2014/voevodsky-origins, https://www.ias.edu/ideas/2013/awodey-coquand-univalent-foun...
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