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)

 

[Matrix0]

Hello there,

It's great to hear that you have a strong background in mathematics and are interested in exploring the field of physics research. I can assure you that there is a lot of overlap between mathematics and physics, and many exciting research opportunities await you in this field.

In terms of specific areas of research, it really depends on your interests and strengths. As you mentioned, Lie Theory, Differential Geometry, and Representation Theory are all relevant to physics research, but there are also many other areas that are currently being explored. For example, Symplectic Geometry is being used in the study of quantum mechanics and quantum field theory, while Quantum Groups are being applied to the study of quantum gravity and topological phases of matter.

Some hot areas of research that you may want to consider for your PhD project include quantum information theory, condensed matter physics, and astrophysics. These fields offer a wide range of interesting problems that require advanced mathematical techniques to solve. Additionally, there is currently a lot of research being done in the intersection of mathematics and artificial intelligence, which could also be a potential area of interest for you.

I would recommend doing some further research and reading in these areas to see which topics align with your interests and skills. And don't worry about asking a broad question – it's always better to ask and learn more about a topic than to not ask at all. Good luck in your future endeavors in physics research!