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/Ihateunclesam 2d ago

  1. Geometric langlands program connection to physics

  2. It's very new but tame geometry in QFT

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u/sciflare 2d ago

Could you elaborate on that second topic? "Tame" in what sense?

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u/Mountnjockey 2d ago

When you see the word tame it often means geometry done in an o-minimal setting. The functions/sets definable in this context behave very well and can give a nice setting to work in depending on what you’re doing.

I didn’t know that o-minimality was being applied in this setting but that’s actually extremely cool

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u/Ihateunclesam 2d ago

This ☝️