What background fits promising areas of mathematical physics

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T. Wentling
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I'm a graduate mathematics student and I did my undergrad in applied math. I also took the normal 10 hrs of physics foundations and then a semester of modern physics (basic quantum intro, special relativity, orbit states etc.). I was thinking about pursuing study in areas that would be closely related to mathematical physics and was looking for suggestions of topics that would line up well, particularly in higher abstract algebra topics. I'm not sure which areas are most closely related on the physics side, whether HEP or what, but am still interested in physics even though my proper course of study headed in a different direction. I am planning to go into a PhD program after finishing my masters next year.
 
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Physics is a broad area, from subatomic to cosmological scales.

A burgeoning area is computational physics, and one can find broad applications in both theoretical, experimental and applied physics.

Advanced algebra, partial differential equations, numerical analysis and multivariable statistics are just some of the areas of mathematics employed in physics.

Here is an example of some topics in contemporary mathematical physics.

http://www.worldscientific.com/worldscibooks/10.1142/5303

Another set of topics in theoretical physics
http://www.physics.rutgers.edu/~gmoore/Physics695/Admin_07.pdfOf course, one could look into topics in condensed matter physics in which folks employ density functional theory (DFT), or phase-field theory and molecular dynamics, among various tools.

For example - http://www.msm.cam.ac.uk/phase-trans/mphil/MP6-15.pdf

https://www.uam.es/personal_pdi/ciencias/jcuevas/Talks/JC-Cuevas-DFT.pdf
 
Lie algebras and lie groups have applications in particle physics and quantum computing. There are areas of combinatorics that are applicable to loop quantum gravity and statistical mechanics. Algebraic combinatorics has some connections to quantum groups and probably other areas as well.