Philip T. Gressman
Department of Mathematics
University of Pennsylvania
David Rittenhouse Lab
209 South 33rd Street
Philadelphia PA 19104
Email:
Phone: (215) 898-7845
Office: DRL 3E5C
Office Hours Fall 2012
MATH 584: W 11:30-12:30, 2:00-2:30
MATH 241: T 2:15-3:00, Th 4:30-5:15
or by appointment
I am an Associate Professor in the
Department of Mathematics at the
Unversity of Pennsylvania. I am also affiliated with the
Applied
Mathematics and Computational Science (AMCS) program. My research interests lie at the intersection of harmonic analysis and geometry, including
the study of geometric averaging operators (generalizing the Radon transform), oscillatory integral operators, sublevel set estimates, the Fourier
restriction problem, and related objects and applications. Recently I have also worked on
applications of harmonic analysis to PDEs, specifically the Boltzmann equation and the Gross-Pitaevskii
Hierarchy. I am currently
supported by an Alfred P. Sloan Reasearch Fellowship and NSF grant DMS-1101393.
In case you are nostalgic, my old webpage can be found here. The
one before
that is available here.
Fall 2012 Courses
Math 241: Calculus IV Section 001. Sturm-Liouville problems, orthogonal functions, Fourier series, and partial differential equations including solutions of the wave, heat and Laplace equations, Fourier transforms. Introduction to complex analysis. Use of symbolic manipulation and graphics software.
Meets TTh
3:00-4:30 in DRL A2 with recitations on Wednesdays and Fridays at either
9 or 10. See the department calculus page for general
information and the section 001 blackboard page for more details. Also don't forget about Piazza.
Math 584: Mathematics of Medical Imaging and
Measurement.
In the last 25 years there has been a revolution in image reconstruction techniques in fields from astrophysics to electron microscopy and most notably in medical imaging. In each of these fields one would like to have a precise picture of a 2 or 3 dimensional object which cannot be obtained directly. The data which is accessible is typically some collection of averages. The problem of image reconstruction is to build an object out of the averaged data and then estimate how close the reconstruction is to the actual object. In this course we introduce the mathematical techniques used to model measurements and reconstruct images. As a simple representative case we study transmission X-ray tomography (CT). In this context we cover the basic principles of mathematical analysis, the Fourier transform, interpolation and approximation of functions, sampling theory, digital filtering and noise analysis.
Meets TTh 12:00-1:30 in DRL 4C8. See the hand-out sheet. Students with limited programming experience should let me know.
Spring 2012 Courses
Math 240: Calculus III Section 002.
Linear algebra: vectors, matrices, systems of linear equations, eigenvalues and eigenvectors. Vector calculus: functions of several variables, vector fields, line and surface integrals, Green's, Stokes' and divergence theorems. Series solutions of ordinary differential equations, Laplace transforms and systems of ordinary differential equations. Use of symbolic manipulation and graphics software.
Meets TTh
10:30-12:00 in Chem 102 with various Wednesday and Friday recitations. See the
course description
for full details. Homeworks will be posted weekly to blackboard.
Math 609/AMCS 609: Analysis.
This semester we will cover various topics from measure theory, functional
analysis and Fourier analysis as time permits. See the course description for
a little more detail.
Meets TTh 3:00-4:30 in DRL 4C8. Weekly homework available
on blackboard.
