[PLACEHOLDER: research_statement] Broadly, my interests lie in algebraic geometry: the geometry of solution sets of polynomial equations, studied through the language of schemes and sheaves. I am drawn to the classical end of the subject — concrete varieties, intersection-theoretic counts, and theorems whose statements would have made sense to Cayley or Salmon, even when the modern proofs are very different.

A particular fascination is the configuration of the twenty-seven lines on a smooth cubic surface, and more generally the way that small finite invariants — character tables, Weyl groups, marked configurations — arise from the geometry of low-dimensional varieties.

Currently reading

  • Hartshorne, Algebraic Geometry, Chapters IIIII.
  • Eisenbud and Harris, 3264 and All That: Intersection Theory in Algebraic Geometry.
  • Vakil, The Rising Sea: Foundations of Algebraic Geometry (used as a parallel text).

Projects

No standalone research projects to report yet. Working notes appear under notes; I expect this section to gain content over the first year of the BSc.

In progress

  • [PLACEHOLDER: in-progress item — exposition of the Schläfli double-six.]
  • [PLACEHOLDER: in-progress item.]

I am a first-generation student at the start of my undergraduate studies. Anything described here as “in progress” should be read accordingly. Corrections are very welcome — see contact.