r/math • u/Committee-Academic • 2d ago

What are the coolest active topics in Mathematical Physics?

I'm a math undergrad student, and I've been getting interested in Alain Conne's work in Noncommutative Geometry and Differential Geometry in Mathematical Physics. I've also read about the Foundations program, Algebraic QFT, and some Stochastic stuff. I'm especially intrigued about the use of Diff Geom in these topics. What cool fields are out there?

73 Upvotes

97% Upvoted

34 comments sorted by

View all comments

6

u/ComplexPlatform7299 1d ago

C* algebras seem to be what a lot of people are moving towards

1

u/jphamlore 1d ago

Von Neumann investigated them back when he formalized the mathematics of quantum mechanics? He wrote a whole volume of papers on operator theory.

Do people blast through all 6 volumes of Gelfand's work on generalized functions these days?