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 2014
Tuesday 1:00-2:00
Thursday 4:30-5:30
or by appointment
I am a 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-1361697.

Research

Current CV (August 2013)
Links to Recent Papers

Recent Papers Hosted by arXiv.org, MR citations provided when available

[1308.1387] $L^p$-nondegenerate Radon-like operators with vanishing rotational curvature
[1308.1367] (w/ Y. Do ) An operator van der Corput estimate arising from oscillatory Riemann-Hilbert problems
[1212.2987] (w/ V. Sohinger and G. Staffilani) On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy
[1205.5774] Scalar oscillatory integrals in smooth spaces of homogeneous type
[1205.5773] Fractional Poincare and logarithmic Sobolev inequalities for measure spaces (MR3067789)
[1202.4088] (w/ J. Krieger and R. M. Strain) A non-local inequality and global existence (MR2914961)
[1011.5441] (w/ R. M. Strain) Global Classical Solutions of the Boltzmann Equation without Angular Cut-off (MR2784329)
[1010.0661] Uniform sublevel Radon-like inequalities (MR3023852)
[1007.1276] (w/ R. M. Strain) Sharp anisotropic ests. for the Boltzmann collision op. and its entropy production (MR2807092)
[0911.1283] On multilinear determinant functionals (MR2784813)
[0909.0875] Uniform geometric estimates for sublevel sets (MR2855039)
[0812.2589] $L^p$-improving estimates for averages on polynomial curves (MR2576685)
[0802.0428] Rank and regularity for averages over submanifolds (MR2541274)

Fall 2014 Course

Math 240: Calculus III Section 002 This course serves as an introduction to Matrix Algebra and Linear Ordinary Differential Equations. General information can be found on the MATH 240 Departmental Page.
Meets TTh 3:00-4:20 in DRL A1. See the hand-out sheet. Our section will be using Canvas and Piazza.
Lecture Slides for Chapter 2 and 3
Lecture Slides for Chapter 4 and 5
Lecture Slides for Chapter 6
Lecture Slides for Chapter 7

Spring 2014 Courses Both courses will have websites hosted by Canvas.

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 10:30-12:00 in DRL 4C6. See the hand-out sheet. Students with limited programming experience should contact me.

Math/AMCS 609: Real Analysis Construction and properties of Lebesgue measures in Euclidean space, Borel measures and convergence theorems. Elementary function spaces. Some general measure theory, including the Caratheodory construction of measures from outer measures, the Radon-Nikodym theorem, the Fubini theorem, and Hausdorff measure. Stone Weierstrass theorem. Elements of classical Harmonic analysis: the Fourier transform on basic function spaces, the Hilbert and Cauchy transforms.
Meets TTh 1:30-3:00 in DRL 3C2. See the hand-out sheet.

Fall 2013 Course

Math 360: Advanced Calculus I. A study of the foundations of the differential and integral calculus, including the real numbers and elementary topology, continuous and differentiable functions, uniform convergence of series of functions, and inverse and implicit function theorems. MATH 508-509 is a masters level version of this course.
Meets TTh 12:00-1:30 in DRL 4C6 with labs on Monday and Wednesday 6:30-8:30. See the .pdf handout for more course details.
This semester's website will be hosted by Canvas.
For those who don't have Canvas access yet, click here for the first homework (due Friday, 9/6).

This page contains some graphs of a continuous nowhere-differentiable function.

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.

Other Things

Fall 2013 Teaching

Fall 2012 Teaching

A Continuous, Nowhere Differentiable Function

Spherical Harmonics Animations

Teaching

Fall 2014
Spring 2014
Other / Archives

Seminars and Colloquia

Analysis Seminar
AMCS Colloquium
All talks this week