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Research areas in the Penn Math Department include the following: algebra (number theory, algebraic geometry, ring theory), analysis (classical analysis, PDE's, functional analysis, operator algebras), geometry-topology (differential geometry, symplectic geometry, topology of manifolds, applied topology), logic (including mathematical foundations of computer science), combinatorics, probability, and applications such as mathematical physics, medical imaging and mathematical finance. A full list of faculty research interests can be found here.

A number of research projects in the department currently have funding to support Ph.D. students working in those areas. These are listed below. Grant proposals to support other projects or to renew existing projects are in progress. Applicants to our graduate program who wish to be considered for support on one of our projects should indicate this in their application.