Educational Background

PhD, University of Utah
AB, MA, University of California, Berkeley

Research Interests

Low-dimensional topology, knot theory, computer applications to topology

Selected Publications

A new polynomial invariant of knots and links, with D. Freyd, W.B.R. Lickorish, K. Millett, A. Ocneanu, and P. Yetter, Bull. Amer. Math. Soc. 12 no. 2 (1985), 239–246.

A formula for Casson’s invariant, Trans. Amer. Math. Soc. 297 no. 2 (1986), 547–562.

The first 1,701,936 knots国产偷拍视频, with Morwen Thistlethwaite and Jeff Weeks, Math. Intelligencer 20, no. 4 (1998) 33–48. 

A formula for the A-polynomial of twist knots, with Patrick Shanahan, J. Knot Theory and Ramifications, 13, no. 2 (2004) 193–209.

Sampling Lissajous and Fourier knots国产偷拍视频, with A. Boocher, G. Daigle, and W. Zhang, J. Experimental Math. 18, no. 4, (2009), 481–497, .

Epimorphisms and Boundary Slopes of 2-Bridge Knots国产偷拍视频, with P. Shanahan, Algebraic and Geometric Topology 10, (2010), 1221–1244, .

Links with finite n-quandles, with Patrick D.Shanahan, Algebraic and Geometric Topology, 17, (2017), 2807-2823, .

Triple-crossing number and moves on triple-crossing link diagrams 国产偷拍视频, with Colin Adams and Martin Palmer, .

Recent Conference Presentations and Invited Talks

Lissajous, Fourier, and Chebyshev knots国产偷拍视频, Topology and Computers, Tokyo Institute of Technology, Japan, September 8–10, 2010.

Epimorphisms and boundary slopes of 2-bridge knots,  with P. Shanahan, Topology and Computers, Tokyo Institute of Technology, Japan, September 8-10, 2010.

Twisted Alexander Polynomials, MAA Invited Paper Session on Knot Theory Untangled, Rolland Trapp organizer,  Joint Mathematics Meetings, Boston, January 6, 2012.

Links with finite n-quandles, with P. Shanahan, AMS meeting #1110, University of Nevada, Las Vegas, Las Vegas, NV April 18-19, 2015.

Alexander polynomials of 2-bridge links, AMS meeting #1117, University of Georgia, Athens, GA, March, 5-6, 2016.

Links with finite n-quandles国产偷拍视频, with P. Shanahan, Knots in Hellas, Olympia, Greece, July 21, 2016.

Diagrammatic moves on 3-diagrams, with C. Adams and M. Palmer, AMS meeting #1128, Washington State University, Pullman, WA,  April 22-23, 2017.

Charles Newton Little: America’s First Knot Theorist, with J. Przytycki, Special Session on the History of Mathematics, Joint Mathematics Meeting, San Diego, CA, January 12, 2018.

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