Mahrud Sayrafi @ School of Mathematics, UMN
June 2021: I passed my oral exam on June 16th. Here are my exam materials.
Spring 2021: I participated in ICERM’s Combinatorial Algebraic Geometry program.
My interests lie in the neighborhood of algebraic geometry, commutative algebra, and intersection theory. Here are some things I’ve recently read about:
- Losev–Manin Moduli Spaces
- Toric Minimal Model Program
- Mori Dream Spaces and GKM Varieties
- Derived Category of Simplicial Toric Varieties
- Multigraded Castelnuovo–Mumford Regularity and Truncation
- Beilinson monads and the Bernstein–Gelfand–Gelfand correspondence
- Fourier–Mukai Transforms and Exceptional Collections
- Horrocks Splitting Criterion and Tate Resolutions
- Toric Vector Bundles and Virtual Resolutions
- Hilbert Schemes and Generic Ideals
- Linkage and Residual Intersections
- $D$-Modules and Hodge Ideals
If you’d like to join or contribute to any of these activities, feel free to get in touch.
- 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
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.
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:
Always happy to chat about Macaulay2 and learn how others use it in research.
I’m a fan of all sorts of fermented foods, volcanoes, sewing, anti-racist activism, poetry, and bouldering.