معرفی
Philip T. Gressman is a Professor of Mathematics at the University of Pennsylvania, affiliated with the Applied Mathematics and Computational Science (AMCS) program. His research focuses on harmonic analysis and its intersections with geometry, including geometric averaging operators, oscillatory integrals, sublevel set estimates, and Fourier restriction theory. He explores applications to PDEs such as the Boltzmann equation and Gross-Pitaevskii Hierarchy. Recent work connects Fourier restriction to geometric invariant theory, identifying symmetries in submanifolds' 'non-flatness' through affine transformations. He also investigates decoupling inequalities' links to number theory, particularly solutions of Diophantine equations.
In education, Gressman develops active learning strategies to enhance STEM inclusivity and reduce failure rates. He co-advises the Mathematics Bridge Fellowship Program and teaches advanced analysis courses (Math 5080-5090). His teaching materials emphasize intuitive proofs and computational simplicity. He produces educational tools like LaTeX question banks and in-browser mathematical plotting software. Notable creations include animations for talks (e.g., Kakeya Needle Problem) and fractal visualizations (IFS Fractal Archive).
