Interests

As an undergraduate I was lucky to be part of two REUs, so I firmly believe 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.

My 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 make further 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:

I have also done research in computer science and discrete mathematics, as a part of my master's in Computer Science under the supervision of Danny Krizanc. 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.

Publications/Preprints- Monoidal Bousfield Localization and Algebras Over Operads, 2014. Also available as arXiv 1404.5197.
- Model 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.
- Traversals of Infinite Graphs with Random Local Orientations, Wesleyan University Library, 2012. Available digitally through WesScholar, or as arxiv 1308.1041.
- 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.
- An Investigation into the Structure of Digroups (with A. Magyar, K. Prifogle, and W. Young), Proceedings of the Wabash Summer Institute in Algebra, 2007.

- 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.

As an undergraduate I was lucky to be part of two REUs, so I firmly believe 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.