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.

- Ted Chinburg

-- Cryptographic applications of capacity theory

--Secure and Trustworthy Cyberspace grant funded by the National Science Foundation

--Joint with Computer Science - Ted Chinburg

-- Chern classes in Iwasawa Theory

--Focused Research Group funded by the National Science Foundation

--Joint with the Universities of Arizona, Iowa, Washington, and Michigan State University. - Ted Chinburg, David Harbater, Florian Pop

-- Lifting problems and Galois theory

--Focused Research Group funded by the National Science Foundation

--Joint with USC and the University of Virginia - Rob Ghrist

--Topological Methods in Applied Mathematics

--Grant funding through a National Security Science & Engineering Faculty Fellowship

--Joint with AMCS and Penn Engineering - Phil Gressman

-- Radon transforms: geometric combinatorics, regularity, and applications

--Funded by the National Science Foundation - Julia Hartmann and David Harbater

-- Obstructions to Local-Global Principles and Applications to Algebraic Structures

--Focused Research Group funded by the National Science Foundation

--Joint with Emory and Univ. Georgia - Tony Pantev and Ron Donagi

--Mathematical physics and complex algebraic geometry

--Homological Mirror Symmetry --Simons Foundation Collaboration Grant

--Joint with Harvard, Berkeley, Columbia, Brandeis, Miami, IHES (Paris), SCGP - Andre Scedrov

--Science of Cyber Security: Modeling, Composition, and Measurement

--Grant funding through Multidisciplinary University Research Initiatives and the Office of Naval Research Cyber Security Program

--Joint with Computer Science - Robert Strain

-- Fluid dynamics with free boundaries, and Kinetic theory

--Funded by the National Science Foundation - Wolfgang Ziller

-- Curvature, group actions and geometric flows

--Funded by the National Science Foundation