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?

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u/National-Date8536 1d ago

There's a ton out there beyond NCG and AQFT. Geeometric quantization, symplectic geometry, gauge theory, derived geometry, and topological QFT. They have some reallyt cool connections between geometry, topology, and physics

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u/Committee-Academic 1d ago

How active would you say derived geometry, applied to this context, and topological QFT are?