Gordon Williams

Gordon Williams

2009  |  Professor of Mathematics
University of Washington 2002, PhD
CH 306D   |  907-474-2756
giwilliams@alaska.edu

I’m a discrete geometer, which means that I study geometric objects (shapes) that are described in terms of their distinct component parts. For example, a cube can be thought of as being made up of a collection of eight vertices, 12 edges, and six square faces. Most of my research is focused on questions about the role of symmetry in investigating the structure of discrete geometric objects. For example, it’s been known since antiquity that there are only five 3-dimensional solids that are regular, and we know them as the Platonic solids, but the story becomes much more interesting once we drop requirements like convexity, or consider the possibilities available in other dimensions or geometric spaces, or require less stringent amounts of symmetry than regularity. Important applications of this kind of discrete geometry arise in areas including microbiology and crystallography, and have inspired a lot of creative activity and analytical tools in the arts.

Highlighted works:

  1. Berman, I. Kovacs, and G. Williams. On the flag graphs of regular abstract polytopes: Hamiltonicity and Cayley index. Disc. Math., 343(1):1–16, January 2020.
  2. W. Berman, G. G. Chappell, C. Hartman, J. Faudree, J. Gimbel, and G. I. Williams. On graphs with proper connection number 2. Theory and Applications of Graphs, 8(2):Article 2, 2021.
  3. Monson, D. Pellicer, and G. I. Williams. Mixing and monodromy of abstract polytopes. Trans. of the AMS, 366:2651–2681, 2014.
  4. Pellicer and G. I. Williams. Pyramids over regular 3-tori. SIAM J. Discrete Math., 32(1):249– 265, January 2018.
  5. Schulte, P. Soberon, and G. I. Williams. Prescribing symmetries and automorphisms for polytopes. In Polytopes and Discrete Geometry, Contemporary Mathematics, volume 764 of Contemp. Math., pages 221–233, Providence, RI, 2021. Amer. Math. Soc.