Department of Mathematics
University of Pennsylvania
David Rittenhouse Lab
209 South 33rd Street
Philadelphia PA 19104
Phone: (215) 898-7845
Office: DRL 3E5C
or by appointment
[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)
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).
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
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.