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 (doi,
arXiv), with Julianne Rainbolt J. Algebra489 (2017), 165-178.
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.