research is in the area of algebraic topology, specifically
questions involving localization and model categories. My work has
applications to the theory of algebras over operads, equivariant
homotopy theory, and motivic homotopy theory. In the near future I plan
to do more work developing
the theory of Bousfield localization, to better understand the various
model structures which arise in equivariant homotopy theory, and to
investigations into motivic homotopy theory. I am also interested in
creating a stronger bridge between infinity categories and model
categories, and in particular in determining whether methods from the
former can be applied to the latter. For more details, please see:
have also done research in computer science and discrete mathematics,
as a part of my master's in Computer Science under the
My thesis problem applied methods of discrete mathematics and
probability theory to settle a conjecture involving autonomous agents
moving on a graph. I've put aside computer science for the time being
but may return to it to resolve out-standing questions or to advise a
project. I am also an active contributor to MathOverflow.
Projects (see long research statement for details)
- Monoidal Bousfield Localization and Algebras Over Operads, 2014. Also available as arXiv 1404.5197.
Structures on Commutative Monoids in General Model Categories, 2014. Also available as arXiv 1403.6759.
- An Alternative Approach to Equivariant Stable Homotopy Theory (with Mark Hovey), 2013. Also available as arxiv 1312.3846.
of Infinite Graphs with Random Local Orientations, Wesleyan University Library,
2012. Available digitally through WesScholar,
or as arxiv
- White Paper Research Report
(title is classified), Internal
NSA Journal, Division R6, 2010.
- An Overview of Schema Theory,
Expository Paper, 2009. Also available as arxiv 1401.2651.
Investigation into the
Structure of Digroups
A. Magyar, K. Prifogle, and W. Young), Proceedings of the Wabash Summer
Institute in Algebra,
Ideas for Undergraduate Research
- Encoding Equivariant Commutativity via Operads (with Javier Gutiérrez), in final revisions.
- Localization and Cellularization for Motivic Symmetric Spectra (with Carles Casacuberta), being written up.
- A short note on smallness and topological monoids, being written up.
- The Random
Basic Walk on Infinite Graphs, in final revisions.
an undergraduate I was lucky to be part of two REUs, so I firmly
in the value of summer research for undergraduates. I maintain a list
of projects on which I would be happy to collaborate with
undergraduates and early graduate students in mathematics or computer
science. If you're interested in seeing this list please email me.