I am interested in pursuing a PhD in mathematics from a top ranked university with a faculty member researching something akin to the following description: applications of algebraic topology and/or differential geometry to numerical methods for PDEs.


A list of a few professors researching anything at all similar to the above description is what I am looking for.



Who is currently researching topics concerning applying algebraic topology and/or differential geometry to numerical methods?
M. Desburn at Caltech.


Anil Hirani at UIUC.


D. Arnold at Minnesota.


And a few more.


Quite a bit of the work in this area has originated from Jerry marsden or his collaborators.
Keywords "Discrete exterior calculus", "Discrete differential geometry",
"symplectic integrators" etc.


