Mahrud Sayrafi @ School of Mathematics, UMN
- PhD Candidate
- 557 Vincent Hall
206 Church St SE
Minneapolis, MN 55455
- mahrud [at] umn.edu
- Pronouns: He/Him
I am a fifth-year graduate student working with Christine Berkesch.
My résumé is here, and here are some recent updates:
- Jun. 2023: M2Week 🧑💻
- Apr. 2023: CA+ in Minneapolis.
- Apr. 2023: Syzygies and Regularity: graduate workshop in Chicago.
- Mar. 2023: AMS sectional meeting in Atlanta, Georgia.
- Aug. 2022: Bounds on Multigraded Regularity.
- Aug. 2022: A short resolution of the diagonal for sm. proj. toric varieties of Picard rank 2.
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
- Weak factorization of toric varieties and positivity
- 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.
If you’d like to join or contribute to any of these activities, feel free to get in touch.
June 2023: M2Week 🧑💻
With Ayah, Tim, and Mike, we are organizing a Macaulay2 workshop and graduate mini-school.
May 2022: 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 2023: (informal) Research Meetings
- Fall 2022: (informal) Research Meetings
- 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
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.
- Dec. 2022: Graduate Workshop on Birational Geometry at SCGP.
- Fall 2022: AMS sectional meetings in El Paso, Texas and Salt Lake City, Utah.
- Fall 2022: WAGS in UC Riverside.
- Aug. 2022: MAGGC in Chicago, Illinois.
- 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: 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.
I’m a fan of fermented foods, volcanoes, sewing & mending, anti-racism, poetry, and bouldering.
I also like radio astronomy, anti-gerrymandering, cryptography, and privacy as a human right.