Mathematician Turning to Physics Research

[DogCow]

From Mathematics to Physics

Hey Everyone,

I've recently completed a BA and MSc in Mathematics at a great university. I've mostly been an Algebraist for the last four years and I've been successful so studying for a PhD would certainly be an option. While I still consider myself to be mostly a mathematician, I've always held an interest in Physics and I like the idea of working with problems in Mathematics that come from questions in Physics.

I understand that Lie Theory (which I love) is relevant to Particle Physics and that Differential Geometry is important in cosmology, but excluding these, I don't know what is relevant to current research. Quantum Groups? Symplectic Geometry? Representation theory? What are some hot areas of research that would make a good PhD project?

Thanks (and sorry for asking such a broad question).

 

[raam86]

I would love to know how Lie groups connect with physics.

*no sarcasm.

 

[Functor97]

Dogcow you could do research in any area connected to string theory. The thing is, no one knows what area of math is going to be relevant until the experimenters and phenomenologists provide more data.

 

[DogCow]

http://en.wikipedia.org/wiki/Particle_physics_and_representation_theory

(Lie Theory and its applications to Particle Physics)