About me

I am a sixth-year graduate student working with Christine Berkesch.
This year I am on the job market and supported by the Doctoral Dissertation Fellowship at UMN. My CV is here and my job statements are available upon request.

Recent updates/plans:

• Apr. 2024: organizing session at AMS meeting in Milwaukee with Maya and Ola.
• Jan. 2024: Joint Math Meetings in San Francisco, CA.
• Oct. 2023: AMS sectional meeting in Omaha, Nebraska.
• Sep. 2023: Syzygies and mirror symmetry at AIM.
• Aug. 2022: Bounds on Multigraded Regularity.
• Aug. 2022: A short resolution of the diagonal for bigraded smooth proj. toric varieties. (To appear in Algebra & Number Theory)

Research

My research area is multigraded commutative algebra, particularly in the setting of toric geometry. Roughly speaking, I’m interested in using derived categories to translate the book Geometry of Syzygies to the toric setting and beyond.

Things I’ve recently thought about:

• GIT fan and truncations of modules over Cox rings
• Tate resolutions and the (toric) BGG correspondence
• $F$-thickness of del Pezzo surfaces and other Mori dream spaces
• Fourier–Mukai transforms and exceptional collections in derived categories
• Beilinson monads and homological mirror symmetry
• Horrocks splitting criterion and virtual resolutions
• $K$-equivalence and $D$-equivalence

Activities

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

April 2024: AMS Sectional in Milwaukee‍

With Maya and Ola, we’re planning a session on nonstandard & multigraded commutative algebra.

June 2023: M2Week 🧑‍💻

With Ayah, Christine, Tim, and Mike, we organized a Macaulay2 workshop and mini-school.

May 2022: GradMoCCA ☕

With Christine, Caitlyn, and Connor, we held a graduate student conference in Minneapolis.

Directed Reading Program

The Directed Reading Program is a graduate student-run program that matches undergraduates with mathematics graduate students in independent reading projects followed by presentations.

New: read about the DRP in the School of Mathematics Critical Points newsletter!

Macaulay2 Development

A main aspect of my research involves developing and implementing algorithms to study explicit examples in algebraic geometry and commutative algebra. Some 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.

Old News

Travel, papers, et cetera:

• Sep. 2023: Macaulay2 workshop at AIM.
• July 2023: SIAM AAG23 in Eindhoven, NL.
• July 2023: GAeL XXX in Warwick, UK.
• June 2023: Derived Categories MRC.
• May 2023: TA at MSRI/CMND summer school.
• Apr. 2023: CA+ Conference in Minneapolis, Minnesota.
• Apr. 2023: Syzygies and Regularity graduate workshop in Chicago, Illinois.
• Mar. 2023: AMS sectional meeting in Atlanta, Georgia.
• Dec. 2022: Graduate Workshop on Birational Geometry at SCGP, New York.
• Fall 2022: AMS sectional meetings in El Paso, Texas and Salt Lake City, Utah.
• Fall 2022: WAGS in Riverside, California.
• July 2022: Derived Minischool in Ann Arbor, Michigan.
• June 2022: PASCA summer school in Guanajuato, Mexico.
• Oct. 2021: Characterizing Multigraded Regularity on Products of Projective Spaces.
• June 2021: I passed my oral exam on June 16th. Here are my exam materials.
• Spring 2021: ICERM’s Combinatorial Algebraic Geometry program (virtual).
• Nov. 2020: Blog post on the AMS Capital Currents Blog.
• Dec. 2019: Blog post on the AMS Grad Blog.

Personal

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