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
- Newman's Conjecture for function field L-functions. Conférence de Théorie des Nombres Québec-Maine, September 2014 and Joint Mathematics Meetings, January 2015. [Slides]
- A Family of rank six elliptic curves over number fields. Young Mathematician's Conference, August 2014 and Joint Mathematics Meetings, January 2015. [Slides]
- Community detection in graphs based on a generalization of modularity. Joint Mathematics Meetings, January 2014, and Young Mathematician's Conference, August 2013. [Slides]