Research

I study a certain kind of degenerate projective spaces called Mustafin varieties. In particular, I study a degenerate version of projective geometry arising from Mustafin varieties. For example, Mustafin variety analogues of cubic surfaces and Grassmannians. I am also interested in classifying modular compactifications of the moduli space of genus \(g\) curves with \(n\) marked points. One of my primary tools is the use of combinatorics and tropical geometry.

Current Projects

• Degenerations of projective spaces and their subvarieties (Thesis project)

  Mustafin varieties are a form of degenerate projective spaces. I study their subvarieties and how these subvarieties behave similarly to projective varieties.

• Modular Compactifications of \(\mathcal{M}_{2,n}\)

  \(\mathcal{M}_{2,n}\) is the moduli space of genus \(2\) curves with \(n\) marked points. This is a joint project with Ari Atkins, Sebastian Bozlee, Yanxin Li, Adrian Neff, and Jonathan Wise. We study compactifications of \(\mathcal{M}_{2,n}\) via admissible covers and tropical geometry.

Papers

• S. Bozlee, B. Kuo, A. Neff, A classification of modular compactifications of the space of pointed elliptic surves by Gorenstein curves, Algebra and Number Theory Vol. 17 (2023), No. 1, 127-163 arxiv:2105

Seminars Organized

• CU Boulder graduate student seminar on Category Theory (Fall 2022)

Talks

• "An arithmetic count of lines on a smooth cubic surface" at the CU Boulder algebraic geometry seminar. (2023)
• Lightning talk at the Front Range Number Theory Day. (2023)
• "Modular compactifications of genus one curves part I" at the CU boulder algebraic geometry seminar. The first of two talks given jointly with Adrian Neff. (2022)