My research is in equivariant homotopy theory. More specifically, I study the commutative and homological algebra of Mackey functors and (incomplete) Tambara functors. I am also interested in trace methods and algebraic K-Theory. My advisor is Inna Zakharevich.

Research Statement (Last updated 31 October 2021)

Papers and Preprints

  • Free incomplete Tambara functors are almost never flat. With Mike Hill and J.D. Quigley. Preprint 2021. To appear in International Mathematical Research Notices. [arXiv]

Talks

  • UCLA Topology Seminar. November 2021.

  • Rochester Topology Seminar. October 2021.

  • Johns Hopkins Topology Seminar. October 2021.

  • Free incomplete Tambara functors are almost never flat. GROOT Summer Seminar. May 2021. [YouTube]

  • Topological Hochschild Homology of \(\mathbb Z\) and \(\mathcal O_K\) as Thom Spectra. Arizona Winter School, University of Arizona, March 2019. Project group presentation. [Slides]

  • Why is Algebraic K-theory Hard? NYRGMC, Syracuse University, March 2018. Expository Talk.

  • Stable Homotopy Theory and Algebra over Spheres. BUGCAT, Binghamton University, October 2017. Expository Talk. [Notes]

  • An Eckmann-Hilton Argument for 2-categories. Young Topologists' Meeting, KTH Royal Institute of Technology, Stockholm, Sweden, July 2017.

Undergraduate Papers

  • Newman's conjecture in function fields. With Alan Chang, Stephen J. Miller, Tomer Reiter, Joseph Stahl, and Dylan Yott. Journal of Number Theory 157, 2015. (Undergrad Publication) [arXiv] [Published Version]

  • Constructing families of moderate-rank elliptic curves over number fields. With Stephen J. Miller, Tomer Reiter, Joseph Stahl, and Dylan Yott. Minnesota Journal of Undergraduate Mathematics 2, 2017. (Undergrad Publication) [arXiv] [Published Version]

  • Walk-modularity and community structure in networks. With Anthony Harkin and Amy Strosser. Network Science 3, 2015. (Undergrad Publication) [arXiv] [Published Version]

Undergraduate Talks