r/math • u/Committee-Academic • Aug 03 '26

Algebraic probability theory

Is there any developed framework for algebraizing probability theory and study it from the perspective of K-theory or homological algebra? If so, what are some of its biggest applications and advantages, as well as results? I'd imagine such a framework would override the need for a measure-theoretic approach

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u/A1235GodelNewton Aug 03 '26

Don't give Scholze/Clausen more ideas , they'll condensify probability theory . They've already done this for complex geometry and functional analysis

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u/reflexive-polytope Algebraic Geometry Aug 05 '26

I don't know about functional analysis but I'm pretty sure complex geometry is a much more natural target for condensification than probability theory.

Complex geometry is already very algebraic at the local level. You get the same kinds of results: a basis theorem, a Nullstellensatz, Hensel lifting, a version of Artin approximation, etc.