Notes and Talks

The following is a collection of notes and talks I have written throughout my academic career.

Talks

Research Talks

• Ohio State University Algebraic Geometry Seminar 2026: The log MMP for the moduli space of cubic surfaces with a marked line

• UC Irvine Algebraic Geometry Seminar 2026: KSBA moduli spaces of cubic surfaces with a marked line

• AMS 2026 Spring Central Sectional Meeting: Moduli of (b, c)-weighted stable marked cubic surfaces (20-min talk)

• Annual New York State Regional Graduate Mathematics Conference: Moduli of cubic surfaces with a marked line (20-min talk) 

• WAGS Spring 2026: Moduli of (b, c)-weighted stable marked cubic surfaces (5-min talk)

• CSU FRAGMENT Seminar 2026: Moduli of (b, c)-weighted stable marked cubic surfaces

• CU Boulder AG Seminar 2025: Moduli of (b, c)-weighted stable marked cubic surfaces

Expository Talks

• CU Boulder AG Seminar 2026: Hodge theory and the Hodge decomposition

• CU Boulder GSS 2025: What even is a moduli space?

• CU Boulder AG Seminar 2025: Moduli of K3 surfaces and its compactifications (see below)

• 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

• 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

• Examples of Hodge structures and polarizations

• Moduli of K3 surfaces and its compactifications (SRI 2025 Bootcamp)

• Moduli of weighted stable marked cubic surfaces

• Notes on root systems (WIP)

• Classification of algebraic surfaces and the minimal model program

• Log-canonical singularities

• Examples of blow-up computations and classifying singularities

• Introduction to Serre's GAGA

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