Funded research projects at Penn Math
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), geometrytopology
(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 LocalGlobal 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
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