# Research

My research is in algebraic geometry and combinatorics, especially algebraic curves and Young tableaux. I am particularly interested in Brill-Noether theory, which studies the variety of ways that a chosen curve is realized in projective space. I also study analogous questions in the setting of tropical geometry, and the relation between these persepctives via non-Archimedean analytic geometry. My publications are listed below.

## Papers

*Relative Richardson Varieties*(with M. Chan). Preprint. arXiv*Combinatorial relations on skew Schur and skew stable Grothendieck polynomials*(with M. Chan). To appear in Algebraic Combinatorics. arXiv*The Gieseker-Petri theorem and imposed ramification*(with M. Chan and B. Osserman). Bulletin of the London Mathematical Society 51:6 (2019) 945-960. arXiv*Euler characteristics of Brill-Noether varieties*(with M. Chan). Transactions of the AMS 374:3 (2021) 1513-1533. arXiv*Weierstrass semigroups on Castelnuovo curves*. To appear in Journal of Algebra. arXiv*On non-primitive Weierstrass points*. Algebra and Number Theory 12 (2018), no. 8, 1923-1947. arXiv*Brill-Noether varieties of k-gonal curves*. Advances in Mathematics 312 (2017) 46-63. arXiv. A video of me speaking about this result is here.*Special divisors on marked chains of cycles*. Journal of Combinatorial Theory, Series A 150 (2017) 182-207. arXiv*Genera of Brill-Noether curves and staircase paths in Young tableaux*(with M. Chan, A. López Martín, and M. Teixidor i Bigas). Trans. Amer. Math. Soc. 370 (2018) 3405-3439. arXiv*Bitangents of tropical plane quartic curves*(with M. Baker, Y. Len, R. Morrison, and Q. Ren). Mathematische Zeitschrift 282:3 (2016) 1017-1031. arXiv*On linear series with negative Brill-Noether number.*Unpublished manuscript. arXiv*Graph reductions, binary rank, and pivots in gene assembly.*Discrete Applied Mathematics 159:17 (2011) 2117-2134. arXiv

## Exposition

*Tropical Curves*. pdf- This is my minor thesis from graduate school. It is an introduction to tropical curves, with an emphasis on how they are analogous to algebraic curves, both formally and informally.
- The minor thesis is part of the Harvard graduate program in which students must rapidly learn (in three weeks) a subject outside of their research and write an expository paper about it. This was a very useful exercise for me, and in fact tropical curves later became an important part of my research!
- Because this paper was created on a short deadline, it is not particularly polished, and (for example) has hand-drawn diagrams. Nonetheless, I am happy to make it available online for anyone who might benefit from it.