DENNIS MICHAEL DETURCK

Home: 310 South 36th St RCH Box 3 Philadelphia, PA 19104-6023 (215) 417-1070

Office: Department of Mathematics University of Pennsylvania Philadelphia, PA 19104-6395 (215) 573-9036 Fax: (215) 573-4063 [email protected]

Born: July 15, 1954, in Philadelphia, PA Education: Drexel University University of Pennsylvania University of Pennsylvania Positions Held: 200920051989-

2004-07 1997-2002 1995-2002 1992-97 1985-89 1982-85 1980-82

College of Arts and Sciences University of Pennsylvania Philadelphia, PA 19104-6304 (215) 898-7867 Fax: (215) 573-2023 [email protected]

Citizenship: U.S.A.

1976 1978 1980

B.S. in Mathematics (with highest honors) M.A. in Mathematics Ph.D. in Mathematics (Thesis advisor: J.Kazdan)

Robert A. Fox Leadership Professor, University of Pennsylvania Dean, College of Arts and Sciences, University of Pennsylvania Professor of Mathematics, University of Pennsylvania (secondary appointments in the School of Engineering and Applied Science 1992-2002, and in the Graduate School of Education since 1997) Evan C Thompson Professor for Excellence in Teaching, University of Pennsylvania Chairman of Mathematics Department, University of Pennsylvania Davidson Kennedy Professor in the College, University of Pennsylvania Undergraduate Chairman of Mathematics Department, University of Pennsylvania Associate Professor, University of Pennsylvania Assistant Professor, University of Pennsylvania Courant Institute Instructor, New York University

Temporary Positions Held: 2008National Advisory Board, Cyberchase (PBS television) 1996Managing Editor, Contemporary Mathematics, AMS 2009-10 Interim Dean of College of Liberal and Professional Studies, University of Pennsylvania 2004-05 Committee of Visitors, Mathematics Department, Harvard University 1986-96 Associate Editor, American Mathematical Monthly March 1993 Visiting Professor, Université Paul Sabatier, Toulouse, France 1990-2000 Editorial Board, Studies in Advanced Mathematics, CRC Press 1989-90 Member, Institute for Advanced Study, Princeton Oct. 1985 G.A. Miller Visiting Professor, University of Illinois Spring 1984 Professore Visitatore, Università di Roma I May 1983 Visiting Member, Mathematical Sciences Research Institute (Berkeley) 1982-1993 Reviewer for Mathematical Reviews Sum. 1981 Forschunger, Mathematicsches Institute, SFB 40, Universität Bonn 1974-78 Research Assistant, IBM APL Design Group, Philadelphia, PA and (summers) Yorktown Heights, NY Principal Research Interest: Partial Differential Equations, especially nonlinear systems arising in Physics and Differential Geometry.

Honors and Awards 200920032003 2002 2001 2000 1999-2007 1998-2002 1998-99 1995-2000

1994-95 1993-94 1991 1989-92 1987-91 1985-87 1982-86, 88-92, 94-08 1981-99 1980-81 1980 1979-80 1976

National Science Foundation grant for Robert Noyce Teacher Scholarships – joint project with Graduate School of Education National Science Foundation CLT Grant (“Mathematics in America’s Cities” – joint project with Penn GSE, Rutgers, CUNY) Ira Abrams Award for Distinguished Teaching (SAS, University of Pennsylvania) MAA Deborah and Franklin Tepper Haimo Award for Distinguished Teaching EPADEL Section Distinguished Teaching Award (Mathematical Assn of America) College of General Studies Award for Distinguished Teaching National Science Foundation GK-12 Grant (Principal Investigator for "Access Science” outreach project to West Philadelphia public schools) NSF SCREMS equipment grant University of Pennsylvania Research Foundation grant. National Science Foundation Mathematics and Applications Initiative Grant (Principal Investigator and Director of Middle Atlantic Consortium for Mathematics and its Applications Throughout the Curriculum) National Science Foundation Mathematics and Applications Initiative Planning Grant National Science Foundation Calculus Grant (Large-scale Calculus revision at Penn) Lindback Award for Distinguished Teaching (University of Pennsylvania) Pew Foundation Science Research Collaboration Fellowship NATO Research Grant Sloan Foundation Fellow University of Pennsylvania Mathematics Department "Good Teaching Award" National Science Foundation Grant National Science Foundation Postdoctoral Fellow Sigma Xi Award, University of Pennsylvania Dean's Fellow, University of Pennsylvania Muchnic Foundation Award, Drexel University

Thesis Students Pei-Kun Chang, Ph.D. 1989, "An estimate on harmonic maps" Janet Talvacchia, Ph.D. 1989, "Prescribing the curvature of a principal-bundle connection" George Kamberov, Ph.D. 1990, "Differential systems with singularities" Joseph Iaia, Ph.D. 1991, "The Weyl problem for surfaces of non-negative curvature" Nets Katz, Ph.D. 1993, "Non-commutative determinants and applications" Zhenyu Zhang, Ph.D. 1993, "The best distributions on Riemannian manifolds and elastic deformations with constant principal strain invariants" Nakia Rimmer, M.A. 2000, "Integration on self-similar sets" Jason Parsley, M.A. 2001, “The Taylor problem in plasma physics” Ph.D 2004, “The Biot-Savart operator and electrodynamics on bounded subdomains of the three-sphere” Shirley Yap, M.A. 2002, “Schiffer’s problem on spherical domains” Ph.D. 2005, “Prescribing the curvature of a principal-bundle connection” Clayton Shonkweiler, Ph.D. 2009, “Poincaré duality angles on Riemannian manifolds”

University and Community Service (Ongoing) 2009200820082005200419971995-2004,061994199219921987-2000,05-

Faculty Master, Riepe College House, University of Pennsylvania Mathematical Association of America: Chair, Committee on the Status of the Profession Faculty Advisory Board, University Museum of Archaeology and Anthropology Penn Science Teachers Institute Advisory Board Netter Center for Community Partnerships Advisory Board Graduate School of Education Faculty Personnel Committee (2003-05 Chair of Tenure Review Committee for J. Remillard) Provost’s Classroom Committee (Tech Fund Chair 1996-98, Chairman, 1998-2004, 06-) Executive Committee, College of General Studies University Scholars Advisory Panel Joint Policy Board for Mathematics Public Information Resources Committee Pre-major advisor, College of Arts and Sciences

(Completed) 2010 2008 2007 2006-2009 2005-07 2004 2003-04 2003-04 2003-04 2003 2003 2002-05 2002-04 2002-03 2001-05 2001-02 2001 2000-04 2000-01 2000-02 1999 1998-2003 1998-99 1998-99 1998 1997-99 1996-99 1996-97 1995-96 1995-96 1995 1995

External Reviewer, University of Southern California Department of Mathematics National Science Foundation: Differential Geometry Panelist, CCLI Panelist External Reviewer, Temple University Department of Mathematics Cherry Hill, NJ Arts Advisory Board Mathematical Association of America: Selection of Haimo Award, Monthly editor National Science Foundation Distinguished Teaching Scholars Program Panelist College of Arts and Sciences Committee on Undergraduate Education (Chair, 2004) Search Committee for Vice Provost and Director of Libraries School of Arts and Sciences Personnel Panel National Science Foundation: GK-12 Panelist National Science Foundation: NSF/NATO Postdoctoral Fellowship Panelist American Mathematical Society Centennial Fellowship Committee Penn Middle States Accreditation Graduate Training for Teaching Committee chair Summative reviewer, Stockton State College CCLI grant Mathematical Association of America, EPADEL Section Vice President 2001-03, Section President 2003-05 (Organizer/host of Fall 2002 section meeting) (Interim) Faculty Master, Stouffer College House National Science Foundation: DUE/CCLI panelist University Council Admissions and Financial Aid Committee (Chairman, 2001-04) SAS Internal Review Committee for Music Department SAS Teaching Awards panelist National Science Foundation: VIGRE panelist PennAdvance/Caliber Distance Learning Courses Provost’s Committee on Students with Learning Disabilities Academic Consultant – Zayed University, United Arab Emirates Internal Review of Institute for Research in Cognitive Science College Quantitative Literacy Requirement Committee SIAM Education Committee American Mathematical Society: Committee to review primary print journals University Council Communications Committee National Science Foundation Information Technology in Education Committee Chair, Search Committee for Vice Provost for University Life Provost's Council on Undergraduate Education Student Information Systems Subcommittee

1994-96 College Ad Hoc Numeracy Committee 1994-95 Society for Industrial and Applied Mathematics, UME Trends Review Committee 1993-96,99-2001 University Council Student Affairs Committee (Chairman 1994-96) 1993-95 Chair, Undergraduate Science Council 1993-99 Governing Council, Eastern Pennsylvania and Delaware Section, MAA 1993-99 American Mathematical. Society: Pi Mu Epsilon Liaison Committee, Chair 1995-99 1992-2000 SAS Academic Computing Committee 1992-95 Provost's ISC Academic Computing Advisory Council 1992-2000 Penn Summer Science Academy, Mathematics Concentration Coordinator 1991-93, 99 National Science Foundation: Conference Board in the Mathematical Sciences Panel 1991 External Reviewer, Queens College Department of Mathematics 1990-91 SAS Internal Review Committee for Physics Department 1985-89,90-93 Member of Science Board of Natural Science Association (Chairman 1991-93) 1983-86 (summers) Acting Undergraduate Chairman, Mathematics Department

Publications 1.

"The equation of prescribed Ricci curvature", Bulletin Amer. Math. Soc., 3 (1980) pp. 701-704.

2.

(with D. Orth) "A derivative algorithm for APL", Proceedings, 1980 APL User's Meeting, Toronto, Canada, pp. 501-510.

3.

"Metrics with prescribed Ricci curvature", in Seminar on Differential Geometry, ed. S.T. Yau, Annals of Math. Studies 102, pp. 525-537.

4.

"Existence of metrics with prescribed Ricci curvature: Local theory", Inventiones Math., 65 (1981) pp. 179207.

5.

"The 'manifold' of Ricci curvatures" Arbeitstagung report, Universität Bonn, 1981.

6.

(with J. Kazdan) "Some regularity theorems in Riemannian geometry", Annales Scientifiques de l'Ecole Normale Superieure. 4e serie, 14 (1981) pp. 249-260.

7.

"Nonlinear Douglis-Nirenberg systems in geometry", Lecture notes, Università di Roma, 1982.

8.

(with D. Orth) "Derivatives of computer programs", IBM Technical Report, 1982.

9.

"The Cauchy problem for Lorentz metrics with prescribed Ricci curvature", Compositio Math., 48 (1983) pp. 327-349.

10. "Deforming metrics in the direction of their Ricci Tensors", J. Diff. Geom., 18 (1983) pp. 157-162. 11. (with D. Yang) "Existence of elastic deformations with prescribed principal strains and triply orthogonal systems", Duke Math. J., 51 (1984) pp. 243-260. 12. (with N. Koiso) "Uniqueness and non-existence of metrics with prescribed Ricci curvature", Ann. Inst. H. Poincare (Nonlinear Analysis), 1 (1984), pp. 351-359. 13. "Prescribing positive Ricci curvature on compact manifolds", Rendiconti Math. Sem. Torino, 43 (1985) pp. 357-369. 14. (with D. Yang) "Local existence of smooth metrics with prescribed curvature", Contemporary Math., 51 (1986) pp. 37-44 (see 15 below). 15. Editor, Nonlinear Problems in Geometry, volume 51 of Contemporary Mathematics series, American Math. Society, 1986. 16. (with C. Gordon) "Isospectral deformations I: Riemannian structures on two-step nilspaces", Comm. Pure Appl. Math., 40 (1987) pp. 367-387. 17. (with C. Gordon) "Isospectral metrics and finite Riemannian coverings", Contemporary Math., 64 (1987) pp. 79-92. 18. (with C. Gordon) "Isospectral Riemannian metrics and potentials", Bulletin AMS, 17 (1987) pp. 137-139. 19. (with G. Kamberov) "A singular problem in elasticity theory", Contemporary Math., 68 (1987), pp. 77-84. 20. "The approach to consistency in the Analytic Hierarchy Process", Math Modelling, 9 (1987) pp. 345-352.

21. (with J. Talvacchia) "Connections with prescribed curvature", Ann. Inst. Fourier, Grenoble, 34 (1987), pp. 2944. 22. "Audible and inaudible geometric properties", Rendiconti Sem. della Facolta di Scienze dell'Univ. di Cagliari, 58 (1988-Supplement): Proc. of Conference on Differential Geometry and Topology, pp. 1-26. 23. (with C. Gordon, H. Gluck and D. Webb) "You cannot hear the mass of a homology class", Comment. Math. Helv., 64 (1989) 589-617. 24. (with P. Chang) "On hearing the shape of a triangle", Proc. AMS, 105 (1989), pp. 1033-1038. 25. "Sphere and torus music", Math. Intelligencer, 11 (3) (Summer 1989), pp. 40-41 (with eight-minute soundsheet). 26. (with H. Goldschmidt) "Regularity theorems in Riemannian geometry. II: Harmonic curvature and the Weyl tensor", Forum Math. 1 (1989) 377-394. 27. (with C. Gordon) "Isospectral deformations II: Trace formulas, metrics and potentials", Comm. Pure Appl. Math., 42 (1989) 1067-1095. 28. "Local solvability for systems with extra symbol equivariance", Rendiconti Sem. Mat. Torino (1989) Fascicolo Speciale 85-94. 29. (with J. Senior, M. Johnson, F. Bazzoli and E. Roda) "In vivo kinetics of radiolucent gallstone dissolution during oral dihydroxy bile acid therapy", Gastroenterology, 99, (1990) 243-251. 30. (with H. Gluck, C. Gordon, and D. Webb) "How can a drum change shape, while sounding the same?", Differential Geometry: A symposium in honor of Manfredo do Carmo, ed. B. Lawson and K. Tenenblat, Pitman Surveys in Pure and Applied Math., 52 (1991) 111-122. 31. (with H. Goldschmidt and J. Talvacchia) "Connections with prescribed curvature and Yang-Mills currents: the semisimple case", Annales Scientifiques de l'Ecole Normale Superieure. 4e serie, 24 (1991) 57-112. 32. (with H. Gluck, C. Gordon, and D. Webb) "How can a drum change shape, while sounding the same? Part 2", Mechanics, Analysis and Geometry, 200 Years After Lagrange, ed. M. Francaviglia, North Holland Delta Series (1991) pp. 335-358. 33. (with J. Cao) "Prescribing Ricci curvature on open surfaces", Hokkaido Math. J., 20 (1991) 265-278. 34. (with H. Goldschmidt and J. Talvacchia) "Existence of connections with prescribed curvature", in Differential Geometry, Global Analysis and Topology, CMS Conference Proceedings, 12 (1991) 13-26. 35. "The Music of the Spheres", 70-minute videotape, NSF Regional Geometry Festival, 1991, Five Colleges, Inc. 36. (with H. Gluck, C. Gordon and D. Webb), "Conformal isospectral deformations", Indiana U. Math. J., 41 (1992) 99-107. 37. (with W. Ziller) "Minimal isometric immersions of spherical space forms in spheres", Comment. Math. Helv., 67 (1992) 428-458. 38. (with H. Gluck, C. Gordon and D. Webb) "The inaudible geometry of nilmanifolds", Inventiones Math., 111 (1993) 271-284.

39. (with W. Ziller) "Spherical minimal immersions of spherical space forms", Proc. Symp. Pure Math., 54 (1993) Part I, 111-120. 40. (with H. Goldschmidt and J. Talvacchia) "Existence of connections with prescribed Yang-Mills currents", Proc. Symp. Pure Math., 54 (1993) Part II, 173-182. 41. (with H. Gluck, C. Gordon and D. Webb) "The geometry of isospectral deformations", Proc. Symp. Pure Math., 54 (1993) Part III, 135-154. 42. Book review of Unsolved Problems in Geometry, (by R. Guy and K. Falconer), Math. Intelligencer, 15(1) (1993) 71-72. 43. Software review of The Geometer's Sketchpad and Cabri Géometre, College Math. J., 24 (1993), 370-376. 44. "z = (x2 + 2y2)exp(-x2 - y2)", University of Pennsylvania Almanac, 41 (No. 11, November 8, 1994) 45. (with J. Cao) "The Ricci curvature equation with rotational symmetry", American J. Math., 116 (1994) 219241. 46. (with D. Harbater) "Maple/Calculus Lab Manual for Math 140/141", 277 pp Brooks-Cole. 47. (with W. Goddard) "Maple/Calculus Lab Manual for Math 150/151", 252 pp Brooks-Cole. 48. with L. Gladney and A. Pietrovito) "Electronic textbook for Interdisciplinary Math-Phys-Chem", CD-ROM version and http://dept.physics.upenn.edu/courses/gladney/mathphys/java/Contents.html. 49. (with J. Kazdan) "Maple/Calculus Lab Manual for Math 240/241", 296pp., Brooks-Cole. 50. "Maple/Calculus Lab Manual for Math 130", pp. 141pp. Brooks-Cole. 51

(with H. Goldschmidt), "Aspects of prescribing Ricci curvature", Advanced Studies in Pure Mathematics 25 (1997) 60-84.

52

(with Tony E. Smith) "On the equivalence of stability and minimality properties of gradient systems", (preprint 30 pp).

53. (with H. Goldschmidt), "Metrics with prescribed Ricci curvature of constant rank I. The integrable case." Advances in Math.145 (1999) 1-97 54. (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. 55. "It's a secondhand sample but a trustworthy one", solicited op-ed in Philadelphia Inquirer, January 30, 2000. 56. (with H. Beavers) "Shall We Dance? - Team Teaching and the Harmony of Collaboration", University of Pennsylvania Almanac 46 (No. 30, April 25, 2000). 57. (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. 58. (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.

59. (with J. Cantarella and H. Gluck) “Upper bounds for the writhing of knots and the helicity of vector fields” , in Proceedings of the Conference in Honor of the 70th birthday of Joan Birman, J. Gilman, X-S Lin and W. Menasco (eds), International Press, AMS/IP Series on Advanced Mathematics 24 (2001) 1-21. 60. “Mathematical Thinking through Web Programming in a Liberal Arts Course” Journal of Online Mathematics and its Applications, 1 (2001) 61. (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. 62. (with J. Cantarella and H. Gluck) “Vector fields and the topology of domains in 3-space” American Mathematical Monthly 109 (2002) 409-442. 63. (with H. Wilf) “Lecture notes on Numerical Analysis”, electronic textbook at http://www.math.upenn.edu/%7Ewilf/DeturckWilf.pdf 64. "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. 65. (with H. Gluck) “The Gauss linking integral on the three-sphere and in hyperbolic space” (preprint 40 pp, arXiv article math.GT/0406276) 66. (with S. Cappell, H. Gluck and E. Miller) “Cohomology of harmonic forms on Riemannian manifolds with boundary” Forum Math. 18 (2006) 923-931 (arXiv article math.GT/0508372). 67. "How Can I Help?", University of Pennsylvania Almanac 52 (No. 17, January 10, 2006). 68. (with H. Gluck, D. Pomerleano and D.S. Vick) “The Four-vertex Theorem and its converse” Notices AMS 54 (2007) 192-207 (arXiv article math.GT/0609268). 69. (with H. Gluck) “Electrodynamics and the Gauss Linking Integral on the 3-sphere and in hyperbolic space” (preprint 90 pp, arXiv article math.GT/0510388), J. Math. Phys. 49 (2008) 023504. 70. (with H. Gluck) “Linking integrals in the n-sphere” (arXiv article arXiv.0802.0320), Mat. Cont. 34 (2008) 233250. 71. (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 article 0901.1612), Mat. Cont. 34 (2008) 251-283. 72. Translation of item 68 into Chinese, in “Mathematics in Chinese Translation” 27 (2009) 313-328 73. (with H. Gluck) "Linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space" (arXiv article 1009.3561). 74. (with H. GLuck and P. Storm) "Lipschitz minimality of Hopf fibrations and Hopf vector fields" (arXiv article 1009.5439) 75. (with H. Goldschmidt), “Metrics with prescribed Ricci curvature of constant rank II. The non-integrable case.” (preprint 50 pp). 76. (with J. Cantarella and H. Gluck) “The principal eigenvalue of the curl operator on the flat torus” (preprint 33 pp).

77. (with J. Cantarella and H. Gluck) “Hodge decomposition of vector fields on bounded domains in 3-space, II” (preprint 36 pp) 78. (with H. Goldschmidt and S. Yap) “Connections and curvature for non-semi-simple structure groups” (preprint 22 pp) 79. (with H. Gluck) “Invariant forms and linking integrals on Sn and Hn” (preprint 35 pp) 80. (with H. Gluck, M. Lewandowski and S. Sabo) “Linking, twisting and writhing in Rn” (preprint 25 pp) 81. (with H. Gluck, L. He and M. Klein) “Linking, twisting and writhing in S2 × R and H2 × R” (preprint 35 pp) 82. (with H. Gluck, R. Komendarczyk, P. Melvin, C. Shonkwiler and D.S. Vela-Vick) "Pontryagin invariants and integral formulas for Milnor’s triple linking numbers" (preprint 56 pp)