What Math Topics Bridge High Energy Physics and Theoretical Condensed Matter?

[the_kid]

Hi all,

I'm planning on doing a one-on-one tutorial my math department next semester. However, I don't know what topic I want to study, so I'm looking for some suggestions. Note that I'm interested in high energy physics (string theory, etc.) and theoretical condensed matter. I will be taking QFT next year.

My background: linear algebra, vector analysis, differential equations, real analysis, intro to functional analysis, and a graduate level mathematical methods in physics course.

The grad math methods course covered the following: advanced linear algebra, advanced real analysis, asymptotic expansions, advanced differential equations, analysis in Hilbert spaces, operator theory, and complex analysis. While it is impossible to learn all of these topics fully in a semester, the class has been remarkably difficult and I've learned more than I was expecting to.

So, what types of math are suggested?

Thanks!

 

[the_kid]

No suggestions?

 

[Klungo]

I can't help much with this but I'm sure if you list down your math interests, if you're okay with applied only or pure, and if it has to be directly useful for physics, someone more knowledgeable in graduate physics/math should be able to help.

It's too difficult to narrow down to a choice*when we're starting from the entire field of mathematics.

 

[the_kid]

I can't help much with this but I'm sure if you list down your math interests, if you're okay with applied only or pure, and if it has to be directly useful for physics, someone more knowledgeable in graduate physics/math should be able to help.

It's too difficult to narrow down to a choice*when we're starting from the entire field of mathematics.

Well, I'm looking for math is relevant to high energy theory and/or condensed matter theory. If I knew what types of math were most relevant to those subfields, I wouldn't be asking the question. I don't really know how to narrow it down other than that. I've heard things such as K-theory, cohomology, and differential forms are useful for string theory, but I'm not sure what the proper background is. I'm looking for my "next step."