Research

I am currently interested in wall-crossings in the moduli of weighted stable marked moduli spaces of cubic surfaces and their KSBA compactifications. The work of studying cubic surfaces is a very deep and rich field in algebraic geometry dating back to the work of Cayley and Salmon in the 1800s. Since then there has been a lot of work studying its moduli space and compactifications.

"Algebraic geometry starts with cubic polynomial equations. Everything of smaller degree, like linear maps or quadratic forms, belongs to the realm of linear algebra."

-Daniel Huybrechts

Research

Moduli of (b,c)-weighted stable marked cubic surfaces
- arXiv preprint coming soon!
- Poster
  - Supplement: Extra fiber descriptions

Talks

CU Boulder AG Seminar 2024: Moduli of weighted stable marked cubic surfaces (see below)
CU Boulder AG Seminar 2024: Classification of algebraic surfaces and MMP (see below)
CU Boulder GSS 2024: Hodge theory and the Hodge decomposition
CU Boulder GSS 2024: Linear systems, blow-ups, and cubic surfaces
Math For All 2024: How to blow-up curves (Beamer)
Oral Exam Talk: Log-canonical singularities
CU Boulder GSS 2023: An illustrated introduction to blow-ups
CU Boulder: Quick talk on Serre's GAGA
CU Boulder GSS 2022: A friendly introduction to algebraic geometry

Notes

Undergraduate writing

Senior thesis: Finding polynomials that generate the ideal of the rational normal curve in affine and projective space
- Advisor: Bianca Viray
Proof of the Riemann open mapping theorem from scratch
Introduction to fuzzy set theory and applications