## 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.