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!