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.


Ongoing Projects (see long research statement for details)

Ideas for Undergraduate Research

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.