Professor of Mathematics
With Pitzer Since: 1989
Field Group: Mathematics
Campus Address: Bernard 205
Office Hours: Mondays 11:00 a.m. – 12:00 p.m.; Wednesdays 11:00 a.m. – 12:00 p.m.; Fridays 1:00 p.m. – 2:00 p.m.
PhD, University of Utah
AB, MA, University of California, Berkeley
Low-dimensional topology, knot theory, computer applications to topology
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, with Morwen Thistlethwaite and Jeff Weeks, Math. Intelligencer 20, no. 4 (1998) 33–48. [pdf]
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, with A. Boocher, G. Daigle, and W. Zhang, J. Experimental Math. 18, no. 4, (2009), 481–497, arXiv:0707.4210.
Epimorphisms and Boundary Slopes of 2-Bridge Knots, with P. Shanahan, Algebraic and Geometric Topology 10, (2010), 1221–1244, arXiv:0708.3590.
Links with finite n-quandles, with Patrick D. Shanahan, to appear in Algebraic and Geometric Topology, arXiv:1606.08324.
Triple-crossing number and moves on triple-crossing link diagrams , with Colin Adams and Martin Palmer, arXiv:1706.09333.
Recent Conference Presentations and Invited Talks
Lissajous, Fourier, and Chebyshev knots, 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, 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.