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, 1974-2019
- 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
- Professor Emeritus, Stony Brook University, 2019-

- 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)
*Mathematische Zeitschrift***291**(2019) 1175-1196 (arXiv posting). - Impossible configurations for geodesics on negatively-curved surfaces,
to appear in
*Israel J. of Math.*(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***53**304-308 2020 - Colored figurative tilings in pre-Incan textiles,
*to appear*