Research

I love interesting mathematics in many areas, but my research focus is combinatorics. In particular, I like applying algebraic or analytic methods to combinatorial problems.

Some publications:

  • On the cone of weighted graphs generated by triangles (with K. Garaschuk)
  • Fractional triangle decompositions of dense 3-partite graphs (with F.C. Bowditch)
  • Thickly-resolvable block designs (with Alan C.H. Ling and Amanda Malloch)
  • Mutually orthogonal latin squares with large holes (with C.M. van Bommel)
  • Pairwise balanced designs covered by bounded flats (with N. Benson)
  • Generalized laminar families and certain forbidden matrices
  • Pairwise balanced designs of dimension three (with J. Niezen)
  • A three-factor product construction for mutually orthogonal latin squares (with A.C.H. Ling)
  • Pairwise balanced designs with prescribed minimum dimension (with A.C.H. Ling)
  • Semidefinite programming for permutation codes (with M. Bogaerts)
  • Nonexistence results for tight block designs (with J.A. Short-Gershman)
  • Fractional edge-decompositions of dense graphs and related eigenvalues
  • other articles on MathReviews (library credentials required)
  • an updated version of my doctoral thesis

    Recent talks:

    I like using a chalkboard when possible, although a talk with slides can sometimes add visual value. (This is not a bad test for whether to use slides at all, in my view). Here are slides from my recent talks.

  • Designs covered by small subdesigns (2015 CMS Summer meeting)
  • A survey of permutation codes (2016 CUMC)

    Computer code/data files:

  • Small latin square intersections: int-ls-data.gz
  • Destructing tight designs with small 'beta': tightsearch.c
  • Incomplete list of 'triangulation cone' facets on 9 vertices: facets-tri9.txt

    Conferences/Workshops:

  • I attended the 2017 CanaDAM conference in Toronto.
  • I attended Combinatorics 2016 in Maratea, Italy.
  • I attended the Fields Conference on algebraic combinatorics in June 2014, celebrating the research of one of my mentors, Chris Godsil.
  • I attended the Shanghai Conference on Algebraic Combinatorics in August 2012.
  • I was co-organizer of BIRS workshop 08w5098 on Combinatorial Design Theory in 2008.