"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.

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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.