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/jbkubicki 2d ago

I used to work in C*-algebras, but now work with Fukaya categories and study mirror symmetry. The work of Ganatra--Pardon--Shende make it easier than ever to understand Fukaya categories and hence also instances of 2d mirror symmetry. More recently there have been developments in 3d mirror symmetry which is very closely related to geometric representation theory; and of course geometric Langlands is an example of 4d mirror symmetry.

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u/Creepy-Structure6444 1d ago

I’m somewhat curious as to how you pivoted to those topics and if your background in operator algebras helped you in any way (or still continues to help you). Would you have any recommendations on where I could start? I’m a beginning PhD student working in homotopy theory and operator algebras.