Formely trained as point-set toplogist under A.V. Arhangelskii at Ohio University, in order to include undergraduates in my research I transitioned to knot theory with the help of Colin Adams of Williams College. This has included work on knots and links in straight-edge embeddings of spatial graphs as well as knot mosaics. Recently, I have used 3D printing to help better understsnd knot mosaics as depicted in the image above. With Colin Adams, I created and hosted the UnKnot Conference.
Selected publications
- Knot Mosaic Tabulation, (with H.J. Lee, J. Paat ‘11, and A. Peiffer ’16) Involve: A journal of mathematics, to appear.
- An infinite family of knots whose mosaic number is realized in non-reduced projections, (with undergrads Joe Paat and Erica Evans) J. Knot Theory Ramifications 22 (2013) no. 7, 11 pp.
- Linking in Straight-edge embeddings of K7, (with undergrad Pam Arbisi) J. Knot Theory Ramifications, 19 (2010), no. 11, 1431-1447.
- When graph theory meets knot theory, (with Joel Foisy)Communicating mathematics, 67-85, Contemporary Mathematics 479 Amer. Math. Soc., Providence, RI, 2009.
- From Molecules to the Universe: An Introduction to Topology, (with Erica Flapan et al.), contributed Chapters 4 and 11, AMS Student Mathematical Library series, 2015.
- On alpha-normal and beta-normal spaces, (with A.V. Arhangelskii)Comment. Math. Univ. Carolin. 42 (2001), no. 3, 507-519.
- Hereditarily alpha-normal spaces and infinite products, (with Dennis K. Burke) Topology Proc. 25, (2000), Summer, 291-299.