B.S., M.S., Massachusetts Institute of Technology, 1960

Diplôme d'Études Supérieures, Université de Paris, 1962

Ph.D., Princeton University, 1966

- Instructor, University of California, Berkeley, 1965-1967
- Lecturer, University of California, Berkeley, 1967-1968
- Assistant Professor, SUNY at Stony Brook, 1968-1970
- Participant in National Academy of Sciences - Soviet Academy Exchange, Steklov Institute, Moscow, Spring term - 1969
- Associate Professor, SUNY at Stony Brook, 1970-1974
- Member, Institute for Advanced Study, 1971-1972
- Professor, SUNY at Stony Brook, 1974-present
- Visiting Professor, PUC-Rio de Janeiro, Fall, 1975
- Visiting Professor, Université Paris VII, 1977-1978
- Visiting Professor, Scuola Normale Superiore, Pisa, Fall, 1985
- Visitor, Deutsches Elektronen-Synchrotron (DESY), Hamburg, March, 1986
- Visiting Professor, University of Rome "La Sapienza," Spring, 1986
- Head Coach, Summer Institute, Geometry Center, University of Minnesota, Summers 1992-1995
- Visiting Professor, Summer School, Universidade Federal de Pernambuco, Recife, January 1996
- Co-Chair, Mathematics Department, SUNY at Stony Brook 1996-97
- Chair, 1997-2000
- Acting Director, Mathematics Secondary Teacher Preparation Program 2000-2002
- Visiting Fellow, Yale University, Spring 2002
- Co-director, Mathematics Secondary Teacher Preparation Program 2002
- Associate Dean for Curriculum, College of Arts and Sciences 2003-2006
- Mathematics Executive Officer, Simons Center for Geometry and Physics 2008
- Director, Mathematics Secondary Teacher Preparation Program 2009-2010
- Interim Chair, Department of Art 2010-2011

- Turning a surface inside-out, Sc. Am., 214, No. 5 (1966), 112-120.
- Submersions of open manifolds, Topology 6 (1967), 171-206.
- Foliations on open manifolds, Comm. Math. Helv. 43 (1968), 204-211.
- Foliations on open manifolds, II, Comm. Math. Helv. 44 (1969), 367-370.
- Smooth maps transverse to a foliation, Bull. A.M.S. 76 (1970), 792-797.
- Smooth maps of constant rank. Bull. A.M.S. 80 (1974), 513-517.
- Geometry of leaves (with D. Sullivan), Topology 20 (1981), 209-218.
- The Euler cycle of a foliation (with D. Stone), J. Diff. Geom., 15 (1980), 39-50.
- Characteristic numbers of U(1)-valued lattice gauge fields, Ann. Phys., 161 (1985), 399-422.
- A reliable topological algorithm for the topological charge of SU(2) lattice gauge fields (with G. Lasher and D. Stone), Quark Confinement and Liberation, World Scientific (1985).
- Lattice gauge fields, principal bundles and the calculation of topological charge (with D. Stone), Commun. Math. Phys., 103 (1986), 599-636.
- Lattice gauge fields and Chern-Weil theory (with D. Stone), in Proceedings, (1985) Georgia Topology Conference, C. McCrory and T. Shifrin, eds. Lecture Notes in Pure and Applied Math., 105 Marcel Dekker, Inc., New York, (1987), 211-231.
- Lattice gauge fields and topology (with D. Stone) in Lattice Gauge Theory '86, H. Satz, I. Harrity and J. Potvin, eds., Plenum, New York, (1987).
- Computation of characteristic classes of lattice gauge fields (with D. Stone), Commun. Math. Physics. 131 (1990) 255-282
- An Algorithm for the detection of Abelian monopoles in SU(2)-valued Lattice gauge - Higgs systems (with D. Stone), Commun. Math. Physics. 137 (1991) 231-247
- A Topological Chern-Weil theory (with D. Stone), Memoirs of the Amer. Math. Soc. 105 #504, 79 pages, September 1993
- The Chern-Simons character of a lattice gauge field (with D. Stone), in Louis Kauffman and Randy Baadhio, (eds.), "Quantum Topology," World Scientific 1993, 244-291 Abstract. Full text (PostScript).
- Self-intersection of curves on the punctured torus (with Moira Chas), Experimental Mathematics 19 (2010) 129-148
- Self-intersection of curves in the doubly-punctured plane (with Moira Chas) Experimental Mathematics, 21:1 (2012), 26-37
- Almost simple geodesics on the triply punctured sphere (with Moira Chas and Curtis McMullen) to appear in
*Mathematische Zeitschrift*(arXiv posting).

- Topology (Entry in Encyclopedia Americana) (1970).
- Geometry's amazing new uses,
*Search*8 (1978), 28-35. - Fiber Bundles and Quantum Theory (with H. Bernstein),
*Scientific Am.*245, No.1 (1981), 122-137. Translated in*Uspekhi Fizicheskikh Nauk*136, 665-692 (1982) - Review of "Geometric Theory of Foliations" by C. Camacho and A.
Lins Neto,
*Amer. Math. Monthly*96 (1989) 71-76 - Topology of Labryrinths, in M. Emmer (ed.)
*L'occhio di Horus: itinerari nell'imaginario mathematico,*Istituto della Enciclopedia Italiana, Roma (1989) - The topology of Roman mosaic mazes,
*Leonardo*25 (1992) 321-329 (reprinted in Michele Emmer, (ed.),*The Visual Mind: Art and Mathematics,*MIT Press 1993, 65-73) Abstract. - Editor, What's New in Mathematics (on AMS web-page :
http://www.ams.org) 2/1999 - 2/2002;

Math in the Media (monthly column) 2/1999 -

Contributor to Feature Column 2/2002 - - Review of "The invention of Infinity" by J. V. Field,
*Notices of the Amer. Math. Soc*47,1 (2000) 46-50 - Review of "Fragments of Infinity" by Ivars Peterson,
*Notices of the Amer. Math. Soc*49,10 (2002) - Il romanzo della contabilità in partita doppia
[The romance of double-entry bookkeeping], in
*Matematica e Cultura 2003*(M. Emmer, ed.) Springer-Verlag Italia 2003 - Meander mazes on polysphericons, in
*The Visual Mind II*(Michele Emmer, ed.) MIT Press 2005 - Review of "Shadows of Reality" by Tony Robbin,
*Notices of the Amer. Math. Soc.*54,4 (2007) 506-510 - Simmetrie fronte-retro in manufatti tessili del periodo pre-Inca
[Front-back symmetries in Pre-Incan textiles],
in
*Matematica e Cultura 2007*(M. Emmer, ed.) Springer-Verlag Italia 2007 - Sphere eversion sketches exhibited at the Walker Art Center, Minneapolis; an item in the show: "The Quick and the Dead", April-Sept. 2009
- Il canto delle maree [The song of the tides], in
*Matematica e Cultura 2011*(M. Emmer, ed.) Springer-Verlag Italia 2011 - Review of "Galileo's Muse: Renaissance Mathematics and the Arts" by
Mark A. Peterson,
*Notices of the Amer. Math. Soc.*Nov. 2012, 1435-1442 - Fragments of Three Tablets from Ur III Nippur with Drawings of Labyrinths (with Jöran Friberg), Chapter 14 in Jöran Friberg and Farouk N. Al-Rawi,
*New Mathematical Cuneiform Texts*, Springer 2017 - The sound of topology: two-dimensional manifolds in Bach (with Eric L.
Altschuler),
*The Musical Times*, Winter 2015, 57-64 - A new type of classical labyrinth, from Mesopotamia (with Jöran Friberg), in
*Imagine Maths 5*(M. Emmer. ed.), UMI, Unione Matematica Italiana, Bologna & IVSLA, Istituto Veneto di Scienze, Lettere e Arti, Venice 2016 - Seventeen years of "Math in the Media" on the American Mathematical
Society website, in
*Imagine Maths 5*(M. Emmer. ed.), UMI, Unione Matematica Italiana, Bologna & IVSLA, Istituto Veneto di Scienze, Lettere e Arti, Venice 2016 - The numbers behind Plimpton 322,
*N. A. B. U. (Notices Assyriologiques Brèves et Utilitaires)*2017/3, #84. For background, etc. see the arXiv posting, October 2015. - Colored strip patterns and front-back symmetry in warp-faced pre-Colombian textiles,
*Leonardo*Just Accepted publication July 31, 2018. https://doi.org/10.1162/leon_a_01691