Dennis DeTurck

About

Dennis DeTurck is a Professor of Mathematics and holds the Robert A. Fox Leadership Professorship at the University of Pennsylvania. His research interests include Partial Differential Equations and Differential Geometry. He is a standing faculty member in the Department of Mathematics, contributing to the academic community through his expertise in these areas. His contact information includes his office at DRL 215-573-9036 and his email deturck@math.upenn.edu.

Research topics

• Political Science
• Geometry
• Mathematics
• Law
• Physics
• Quantum mechanics
• Surgery
• Anatomy
• Orthodontics
• Pure mathematics

Selected publications

• Electrodynamics and the Gauss linking integral on the 3-sphere and in hyperbolic 3-space

  Journal of Mathematical Physics · 2008-02-01 · 26 citations

  articleOpen access1st authorCorresponding

  In this first of two papers, we develop a steady-state version of classical electrodynamics on the 3-sphere and in hyperbolic 3-space, including an explicit formula for the vector-valued Green’s operator, an explicit formula of Biot–Savart type for the magnetic field, and a corresponding Ampere’s law contained in Maxwell’s equations. We then use this to obtain explicit integral formulas for the linking number of two disjoint closed curves in these spaces. These formulas, like their prototypes in…

  PublisherOA PDFDOI

• Linking, twisting, writing, and helicity on the 2-sphere and in hyperbolic 3-space

  Journal of Differential Geometry · 2013-05-01 · 15 citations

  articleOpen access1st authorCorresponding

  In the first paper of this series, “Electrodynamics and the Gauss Linking Integral on the 3-sphere and in Hyperbolic 3-space,” we developed a steady-state version of classical electrodynamics in these two spaces, including explicit formulas for the vector-valued Green’s operator, explicit formulas of Biot-Savart type for the magnetic field, and a corresponding Ampère’s Law contained in Maxwell’s equations, and then used these to obtain explicit integral formulas for the linking number of two dis…

  PublisherOA PDFDOI

• Influence of Geometry and Topology on Helicity

  Geophysical monograph · 2011-09-01 · 14 citations

  book-chapter

  This chapter contains sections titled: Two Fundamental Problems Hellcity and Writhing Number Relation between Helicity and Writhing Number How the Geometry of the Domain Influences Helicity Magnetic Fields and Helicity A General Point of View The Modified Biot-Savart Operator Spectral Methods Connection with the Curl Operator Explicit Computation of Energy-Minimizing Vector Fields The Isoperimetric Problem First Variation Formulas Constraints on Any Optimal Domain The Search for Optimal Domains…

  PublisherDOI

• Generalized Gauss maps and integrals for three-component links: Toward higher helicities for magnetic fields and fluid flows

  Journal of Mathematical Physics · 2013-01-01 · 12 citations

  article1st authorCorresponding

  To each three-component link in the 3-sphere we associate a generalized Gauss map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its generalized Gauss map up to homotopy. We view this as a natural extension of the familiar situation for two-component links in 3-space, where the linking number is the degree of the classical Gauss map from…

  PublisherDOI

• Pontryagin invariants and integral formulas for Milnor's triple linking number

  arXiv (Cornell University) · 2011-01-18 · 11 citations

  preprintOpen access1st authorCorresponding

  To each three-component link in the 3-sphere, we associate a geometrically natural characteristic map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its characteristic map up to homotopy. This can be viewed as a natural extension of the familiar fact that the linking number of a two-component link in 3-space is the degree of its associate…

  PublisherOA PDFDOI

Frequent coauthors

• Herman Gluck

  35 shared

• Carolyn S. Gordon

  9 shared

• John Senior

  9 shared

• Mary F. Johnson

  9 shared

• E. Roda

  Istituti Clinici Scientifici Maugeri

  9 shared

• Franco Bazzoli

  University of Bologna

  9 shared

• Jason Cantarella

  6 shared

• David L. Webb

  Dartmouth College

  6 shared

Similar researchers at University of Pennsylvania

• T. Tony Caih-93
• Ron Anafih-26
• Ian J. Barnetth-20