Are higher branches of mathematics used in sub-fields of chemistry?
We use tensors in my research lab to analyze solid state NMR. 
In my research laboratory we use manifolds all the time for stimulating annealing calculations. 




There are several research groups in physical chemistry which utilize what you are describing, but it will never be an undergraduate topic. One particular group that comes to mind that uses this sort of stuff a lot is the Hirata group at the University of Illinois. They actually made a piece of software called the Tensor Contraction Engine. http://www.scs.illinois.edu/~sohirata/software.html