About me

I am a fifth-year Ph.D. student working with Christine Berkesch.
My résumé is here, and here are some recent updates:

• Fall 2022: AMS sectional meetings in El Paso, Texas and Salt Lake City, Utah.
• Aug. 2022: A short resolution of the diagonal for smooth projective toric varieties of Picard rank 2.
• July 2022: Minischool in Ann Arbor, Michigan.
• June 2022: PASCA in Guanajuato, Mexico.
• Oct. 2021: Characterizing Multigraded Regularity on Products of Projective Spaces.
• Spring 2021: Combinatorial Algebraic Geometry semester program at ICERM.

Research

My interests lie in the neighborhood of algebraic geometry, commutative algebra, and intersection theory. Roughly speaking, I’m interested in using derived tools to translate the book Geometry of Syzygies to the toric setting. Here are some things I’ve recently read about:

• Secondary Fan of Toric Varieties and Truncations of modules over the Cox ring
• Beilinson monads and the (toric) Bernstein–Gelfand–Gelfand correspondence
• Fourier–Mukai Transforms and Exceptional Collections
• Horrocks Splitting Criterion and Tate Resolutions
• Derived Category of Simplicial Toric Varieties
• Toric Vector Bundles and Virtual Resolutions
• Mori Dream Spaces and GKM Varieties
• Losev–Manin Moduli Spaces

I passed my oral exam on June 16th, 2021. Here are my exam materials.

Activities

If you’d like to join or contribute to any of these activities, feel free to get in touch.

GradMoCCA ☕

With Caitlyn and Connor, we organized a graduate student conference here in Minneapolis.

Directed Reading Program

The Directed Reading Program is a graduate student-run program that provides undergraduates with the opportunity to work closely with mathematics graduate students in an independent reading project.

Student Commutative Algebra Meeting

• Spring 2022: Research Meetings
• Fall   2021: Research Meetings
• Spring 2021: Student talks and pre-talks for the adult seminar
• Fall   2020: On hiatus
• Spring 2020: Introductory topics and $D$-Modules
• Fall   2019: Boij-Söderberg theory

Macaulay2

A main aspect of my research involves developing and implementing algorithms to study explicit examples in algebraic geometry and commutative algebra. Here are some of the packages I’ve contributed to:

• FGLM
• LocalRings
• Saturation
• Truncations
• VirtualResolutions
• NormalToricVarieties

Always happy to chat about Macaulay2 and learn how others use it in research.

Personal

I’m a fan of fermented foods, volcanoes, sewing & mending, anti-racism, poetry, and bouldering.
I also like radio astronomy, gerrymandering, cryptography, and privacy as a human right.