Jim Hoste, Professor of Mathematics

Jim Hoste

Flora Sanborn Pitzer Professor Emeritus of Mathematics

With Pitzer Since: 1989
Field Group: Mathematics
Email: [email protected]

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, 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, Algebraic and Geometric Topology, 17, (2017), 2807-2823, 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.

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.

Additional Information

Personal Website

Page last updated on December 4, 2023