Research

Current interests

My work is in the intersection of algebraic geometry, computer vision and multi-view geometry (sometimes called algebraic vision). You can read a detailed research statement here. A list of citations is available here. 

Lately I've been thinking about Carlsson-Weinshall duality, camera resectioning, and compactifications of the moduli space parametrizing pairs of (possibly concentric) pinhole cameras.

Below are some illustrations from a talk I gave in 2020.

Preprints

• "Algebra and geometry of camera resectioning" (with Erin Connelly and Tim Duff, 2023. Submitted to Journal of Algebra.)

Publications

• "Squarefree divisor complexes of certain numerical semigroup elements" (REU paper with Jackson Autry, Paige Graves, Christopher O'Neill, Vadim Ponomarenko, Samuel Yih, published 2021)

In Preparation

• "The essential variety revisited" (with Ben Antieau, Max Lieblich, Lucas Van Meter, Bianca Viray)

• "A compactification for the moduli of camera pairs" (Ph.D. thesis, exp. 2024)

Notes

• "An algebraic approach to multiview geometry" - a mostly expository writeup from my general exam (Sp22).

Relevant coursework

• A Short Course on Alterations; Spring 2021

  • • "Smoothness, semi-stability and alterations," de Jong

    • "Families of curves and alterations," de Jong

• Stacks and Moduli; Winter 2021

• Resolution of Singularities; Autumn 2020

  • • Lectures on Resolution of Singularities, Kollár

• Intersection Theory; Spring 2020

  • • 3264 and all that, Eisenbud & Harris

    • Intersection theory, Fulton

• Algebraic Geometry; Autumn 2019 - Spring 2020

  • •  Algebraic Geometry (Ch. II-III), Hartshorne (Wi20 -  Sp20)

    •  Algebraic Varieties, Kempf (Au19)

    • The Rising Sea, Vakil (Wi20 - Sp20)

• Arithmetic of Elliptic Curves (Ch. I-III, V), Silverman; Winter 2020

• Number Fields (Ch. 1-4), Marcus; Autumn 2019

• Topology and Geometry of Manifolds, Autumn 2019

  • • Introduction to Topological Manifolds, Lee

• Graduate Algebra; Autumn 2018 - Spring 2019

  • • Algebra, Lang

    • Abstract Algebra, Dummit & Foote

    • Linear Representations of Finite Groups (§1), Serre

    • Commutative Algebra, Atiyah & Macdonald

Previous projects

As an undergraduate, I was part of various research projects involving 

• combinatorics of numerical semigroups (SDSU REU 2017)

• vertex operator algebras (Sac State undergrad research project 2017 - 18).