Paul Feehan

Paul Feehan is a Distinguished Professor of Mathematics at Rutgers, The State University of New Jersey, New Brunswick, affiliated with the Department of Mathematics. He serves as the Graduate Director and leads research in nonlinear elliptic/parabolic PDEs, geometric analysis, mathematical physics, and topology, with applications to gauge theory and four-manifold topology. His office is located in the Hill Center for Mathematical Sciences (Room 708).

Research Interests: Feehan's work spans differential geometry, Yang-Mills theory, harmonic maps, and geometric flows. Key themes include the analysis of moduli spaces, Morse-Bott theory, Lojasiewicz-Simon inequalities, and connections between Donaldson-Seiberg-Witten invariants. He frequently employs analytical methods to solve problems in low-dimensional topology and mathematical physics.

Publications: His recent articles (2013–2024) focus on gauge theory, geometric PDEs, and singularity resolution. Common topics include Yang-Mills connections, monopole cobordisms, and applications of Morse theory to geometric analysis, reflecting a consistent emphasis on bridging analysis, geometry, and topology.

Academic Leadership: Feehan co-organizes seminars including the Geometric Analysis Seminar and the Mathematical Finance/Probability/PDEs Seminar. He has co-directed conferences such as the Geometric Analysis Mini-courses and Workshop (2015–2016) and the AMS Fall Sectional Meeting Special Session (2015).