


"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, a Professor of
Mathematics
and, alas, the Undergraduate Chair of the department.
Courses:
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/seniorlevel
textbook on Numerical Analysis using Maple.
Moelis Access
Science
.
.
.
My research interests are Partial Differential Equations and Differential
Geometry.
Recent preprints and publications:
 "The Mathematician's Shiva" (by Stuart Rojstaczer) book review,
Notices of the American Mathematical Society 64 (2017) 10431045.
 (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) 876886.
 (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. VelaVick) "Generalized Gauss maps and integrals
for threecomponent links: Toward higher helicities for magnetic fields and
fluid flows, Part II"
Algebraic and Geometric Topology
13 (2013) 28972923
(
arXiv paper 1207.1793).
 (with H. Gluck, R. Komendarczyk, P. Melvin, C. Shonkwiler. and D.S.
VelaVick) "Generalized Gauss maps and integrals for threecomponent
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) 13691412
( ArXiv paper 1009.5439)
 (with H. Gluck) "Linking, twisting, writhing and helicity on the
3sphere and in hyperbolic 3space" J. Differential Geometry
94 (2013) 87128.
( ArXiv paper 1009.3561)
 (with H. Gluck, R. Komendarczyk, P. Melvin, C. Shonkwiler and D.S.
VelaVick) "Triple linking numbers, ambiguous Hopf invariants and integral
formulas for threecomponent links" (ArXiv paper 0901.1612)
and in Mat. comtemp. 34 (2008) 251283.
 (with H. Gluck) "Linking
integrals in the nsphere" (ArXiv paper 0802.0320)
and in Mat. comtemp. 34 (2008) 233250.
 (with H. Gluck) "Electrodynamics and the Gauss linking integral on
the 3sphere and in hyperbolic 3space" (ArXiv paper
0510388) and in the
Journal of Mathematical Physics vol 49, 023504 (2008)
 (with H. Gluck, D.
Pomerleano and D.S. Vick) "The Fourvertex
Theorem and its converse", Notices AMS 54 (2007) 192207
(ArXiv paper
0609268). A translation of this paper into Chinese appears in
Mathematics in Chinese Translation 27 (2009) 313328.
 (with S. Cappell, H. Gluck and E. Miller) "Cohomology of harmonic
forms on Riemannian manifolds with boundary", Forum Math.
18 (2006) 923931 ( PS version [137K], PDF version [119K], ArXiv paper
0508372)
 (with H. Gluck) "The Gauss linking integral on the 3sphere and in
hyperbolic 3space" (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) 163165, International Press. (PS
version (140KB), PDF version)
 (with J. Cantarella and H. Gluck) "Hodge decomposition of vector fields on
bounded domains in 3space", American Mathematical Monthly 109
(2002), 409442. (PDF version (2.6
MB))
 (with J. Cantarella and H. Gluck) "The BiotSavart
operator for
application to knot theory, fluid dynamics and plasma physics", J.
Mathematical Physics 42 (2001) 876905. ( 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, XS. Lin and W. Menasco (eds),
Studies in Advanced Mathematics AMS/International Press
Studies in Advanced Mathematics 24 (2001) 121. (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 BiotSavart and curl operators" J.
Mathematical Physics 41 (2000) 56155641. (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) 27662775 (PDF version (1.2MB))
 (with H. Goldschmidt)
"Metrics with Prescribed Ricci
Curvature of Constant Rank I. The Integrable Case", Advances in Mathematics
145, 197 (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) 1724. (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) 6084.