"I'd like to speak to you about the Calculus grade you gave my son, Finley."

I am the Robert A. Fox Leadership Professor in the School of Arts and Sciences, and a Professor of Mathematics.

Middle school math problem of the day (If you are a teacher and would like more information about these, please drop me an email at deturck@math.upenn.edu )

Mathematician Herb Wilf and I collaborated on a junior/senior-level textbook on Numerical Analysis using Maple.

Moelis Access Science

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Research

Recent preprints and publications:

• (with H. Gluck, L. Lichtenfelz, M. Merling, J Yang and Y. Wang) "Homotopy type of the group of strict contactomorphisms of the standard tight contact structure on the three-sphere" ArXiv paper arXiv:2108.08961.
• "The Mathematician's Shiva" (by Stuart Rojstaczer) book review, Notices of the American Mathematical Society 64 (2017) 1043-1045.
• (with A. Elsaify, H. Gluck, B. Grossmann, J. Hoisington, A.M. Krishnan and J. Zhang) "Making matrices better: Geometry and topology of polar and singular value decomposition", Notices of the American Mathematical Society 64 (2017) 876-886.
• (with A. Elsaify, H. Gluck, B. Grossmann, J. Hoisington, A.M. Krishnan and J. Zhang) "Making matrices better: Geometry and topology of polar and singular value decomposition", expanded version,. (PDF version (4MB)) (arXiv paper 1702.02131)
• (with H. Gluck, R. Komendarczyk, P. Melvin, H. Nuchi, C. Shonkwiler and D.S. Vela-Vick) "Generalized Gauss maps and integrals for three-component links: Toward higher helicities for magnetic fields and fluid flows, Part II" Algebraic and Geometric Topology 13 (2013) 2897-2923 ( arXiv paper 1207.1793).
• (with H. Gluck, R. Komendarczyk, P. Melvin, C. Shonkwiler. and D.S. Vela-Vick) "Generalized Gauss maps and integrals for three-component links: Toward higher helicities for magnetic fields and fluid flows J. Math. Phys. 54 (2013) 013515 ( ArXiv paper 1101.3374)
• (with H. GLuck and P. Storm) "Lipschitz minimality of Hopf fibrations and Hopf vector fields" Algebraic and Geometric Topology 13 (2013) 1369-1412 ( ArXiv paper 1009.5439)
• (with H. Gluck) "Linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space" J. Differential Geometry 94 (2013) 87-128. ( ArXiv paper 1009.3561)
• (with H. Gluck, R. Komendarczyk, P. Melvin, C. Shonkwiler and D.S. Vela-Vick) "Triple linking numbers, ambiguous Hopf invariants and integral formulas for three-component links" (ArXiv paper 0901.1612) and in Mat. comtemp. 34 (2008) 251-283.
• (with H. Gluck) "Linking integrals in the n-sphere" (ArXiv paper 0802.0320) and in Mat. comtemp. 34 (2008) 233-250.
• (with H. Gluck) "Electrodynamics and the Gauss linking integral on the 3-sphere and in hyperbolic 3-space" (ArXiv paper 0510388) and in the Journal of Mathematical Physics vol 49, 023504 (2008)
• (with H. Gluck, D. Pomerleano and D.S. Vick) "The Four-vertex Theorem and its converse", Notices AMS 54 (2007) 192-207 (ArXiv paper 0609268). A translation of this paper into Chinese appears in Mathematics in Chinese Translation 27 (2009) 313-328.
• (with S. Cappell, H. Gluck and E. Miller) "Cohomology of harmonic forms on Riemannian manifolds with boundary", Forum Math. 18 (2006) 923-931 ( PS version [137K], PDF version [119K], ArXiv paper 0508372)
• (with H. Gluck) "The Gauss linking integral on the 3-sphere and in hyperbolic 3-space" (ArXiv paper 0406276).
• "Deforming metrics in the direction of their Ricci tensors (Improved version)", in Collected Papers on Ricci Flow, HD Cao, B Chow, SC Chu and ST Yau eds, Series in Geometry and Topology 37 (2003) 163-165, International Press. (PS version (140KB), PDF version)
• (with J. Cantarella and H. Gluck) "Hodge decomposition of vector fields on bounded domains in 3-space", American Mathematical Monthly 109 (2002), 409-442. (PDF version (2.6 MB))
• (with J. Cantarella and H. Gluck) "The Biot-Savart operator for application to knot theory, fluid dynamics and plasma physics", J. Mathematical Physics 42 (2001) 876-905. ( PDF version (1.5MB))
• (with J. Cantarella and H. Gluck) "Upper Bounds for the Writhing of Knots and the Helicity of Vector Fields", in Knots, Braids, and Mapping Class Groups - Papers Dedicated to Joan S. Birman, J. Gilman, X-S. Lin and W. Menasco (eds), Studies in Advanced Mathematics AMS/International Press Studies in Advanced Mathematics 24 (2001) 1-21. (PDF version (314KB), PS version (1.7MB))
• (with J. Cantarella, H. Gluck and M. Teytel) "Isoperimetric problems for the helicity of vector fields and the Biot-Savart and curl operators" J. Mathematical Physics 41 (2000) 5615-5641. (PDF version (1.3MB))
• (with J. Cantarella, H. Gluck and M. Teytel) "The spectrum of the curl operator on spherically symmetric domains" Physics of Plasmas 7 (2000) 2766-2775 (PDF version (1.2MB))
• (with H. Goldschmidt) "Metrics with Prescribed Ricci Curvature of Constant Rank I. The Integrable Case", Advances in Mathematics 145, 1-97 (1999) (Postscript version (948k)).
• (with J. Cantarella, H. Gluck and M. Teytel) "Influence of geometry and topology on helicity", Magnetic Helicity in Space and Laboratory Plasmas, M. Brown, R. Canfield and A. Pevtsove (eds), Geophysical Monograph 111, American Geophysical Union (1999) 17-24. (PDF version (165KB), PS version (879KB))
• (with J. Cantarella and H. Gluck) "The spectrum of the curl operator on the flat torus", preprint 35 pp.
• (with H. Goldschmidt) "Aspects of prescribing Ricci curvature", in CR Geometry and Overdetermined Systems, Advanced Studies in Mathematics 25 (1997) 60-84.