My research is in the structure of finite groups, especially
around a prime p. I tend to think most about fusion systems
and their associated homotopy theory and homological algebra,
geometries and subgroup complexes of finite groups, and modular
representation theory.
Extensions of the Benson-Solomon fusion systems
(arXiv),
with Ellen Henke submitted, 14pp.
Fusion systems with some sporadic
J-components (arXiv), with Julianne Rainbolt J. Algebra (to appear), 14pp.
Control of fixed points and existence and uniqueness
of centric linking systems (doi,
postprint),
with George Glauberman Invent. Math.206 (2016), no.2, 441-484.
A characterization of the 2-fusion system of
L_{4}(q)
(doi,
arXiv),
J. Algebra428 (2015), 315-356.
The Thompson-Lyons transfer lemma for fusion systems
(doi,
arXiv),
Bull. Lond. Math. Soc. (2014) 46 (6): 1276-1282
Weak closure and Oliver's
p-group conjecture (doi, arXiv), with David J.
Green.
Israel J. Math.197 (2013), no. 1, 497-507.
2-subnormal quadratic offenders and Oliver's p-group
conjecture (doi, arXiv)
Proc. Edin. Math. Soc.56 (2013), 211-222.
Analogues of Goldschmidt's thesis for fusion systems (doi, arXiv), with Sejong Park J. Algebra324 (2010), 3487-3493.