Philip Hackney, PhD, joined the Department of Mathematics at the University of Louisiana at Lafayette as an assistant professor in August 2018. He earned his PhD in Mathematics in 2010 from Purdue University, having previously earned an MS in Mathematics from Purdue University in 2006. Before beginning at Purdue, Philip earned a BS in Computer Science - Mathematics from Central Michigan University.
Just before moving to Louisiana, Philip spent a year and a half at the Centre of Australian Category Theory, at Macquarie University in Sydney, Australia. Prior to that, he held posts at Max-Planck-Institut für Mathematik, Universität Osnabrück, Stockholms universitet, and the University of California, Riverside.
Dr. Hackney's research interests lie within the fields of higher category theory, algebraic topology, and operad theory. His recent work is centered on the abstract homotopy theory (in the sense of Quillen model categories) of generalized operads. In the most basic setting, operads are algebraic gadgets which parametrize other types of algebras. This allows us to consider, say, the collection of all associative algebras (or all commutative algebras, all Lie algebras, etc) in much the same way as we consider the collection of all modules over a fixed ring R. Understanding the relationship between various operads (for example between the "associative operad" and the "commutative operad") can give information analogous to the information about categories of modules provided by a ring homomorphism (the latter is actually a very special case of the former).
Recent work of Dr. Hackney is largely focused on various homotopical generalizations of this concept, and of other related concepts.