Student research

To get an idea of the type of maths I do, below are past projects that I supervised as part of the Georgia Tech REU program and the Fields Undergraduate Summer Research Program. Broadly speaking, my research is in tropical geometry, a relatively new area concerned with interactions between algebraic geometry and combinatorics. The topics that show up in my work include (but are not limited to) graphs, polytopes, chip-firing games, Brill-Noether theory, enumerative geometry, toric varieties, matroids, and non-archimedean geometry.

If you are interested in doing a PhD with me (or joint with another member of the school), please get in touch. I will not respond to generic emails, so please demonstrate that you have read my website, and that we have some mathematical interests in common.

Past projects

  • Brill-Noether theory of Prym varieties, with Steven Creech, Caelan Ritter, and Derek Wu (summer 2019), published in International Maths Research Notices. A fruitful observation in tropical geometry suggests that geometric invariants of curves may be translated to a game played on the vertices of a graph, known as the chip-firing game (you can play the game on this website if you wish). In this project, we used the chip-firing game and Young tableaux to study cycles in Prym varieties, an important abelian group associated with double covers of curves.

  • Bitangents of non-smooth tropical quartics, with Heejong Lee (summer 2017), published in Portugaliae Mathematica. In a celebrated piece of 19th century geometry, Plücker showed that every plane quartic curve has 28 lines that are tangent to it at two points. In this project we proved a combinatorial analogue of this classical result: every tropical plane quartic (the combinatorial analogue of a classical quartic) admits 7 bitangent lines.