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Interests

My primary 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 (colored) 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. My PhD thesis was supervised by Mark Hovey, and my coauthors in homotopy theory have included Michael Batanin, Donald Yau, Javier Gutierrez, Gabriel Valenzuela, Boris Chorny, and Carles Casacuberta.

I have also done research in computer science and discrete mathematics. Under the supervision of Danny Krizanc, my Master's thesis settled a conjecture involving autonomous agents moving on a graph. At Denison, I supervised an undergraduate research project resulting in a paper (with Jessica Tang) about the structure of social network graphs.

I have begun to dabble in statistics, with two papers so far focusing on statistical pedagogy. I have also supervised undergraduate research projects in statistics related to spatial econometrics, genomic modeling, and R package development.

I have done work in Economics, with my co-author Olga Nicoara, to create a game theoretic model for the collective action problem in revolutions, with a particular focus on the rebellion in Ukraine.

I am also an active contributor to MathOverflow.

Publications/Preprints

Ongoing Projects

Research I have supervised

Grants

Ideas for Undergraduate Research

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

To Denison students: I will happily take on research students in applied statistics at any time, ideally during the semester. For pure mathematics or computer science, my research interests tend towards the abstract. Thus, research with me will likely best serve students interested in graduate school. For such students, the best time to do research with me is during the summer after your sophomore year, or as an independent study in your junior or senior year. The summer after your junior year would be best spent at an REU, to best position yourself for applying to graduate school.