Curriculum Vitae
| Mahrud Sayrafi |
|
McMaster University Britton Postdoctoral Fellow
Research Group: Combinatorial Algebraic Geometry
Fields Institute for Research in Mathematical Sciences Postdoctoral Fellow
Thematic Program: Commutative Algebra and Applications
Max Planck Institute for Mathematics in the Sciences Postdoctoral Fellow
Research Group: Nonlinear Algebra
University of Minnesota, Twin Cities Advisor: Christine Berkesch
Thesis: Diagonalization, Direct Summands, and Resolutions of the Diagonal
University of California, Berkeley (with Honors) Advisor: David Eisenbud
Thesis: Local Computations in Macaulay2
Math in Moscow (semester abroad at the Independent University of Moscow)
NSF Workshop Grant DMS-2302476 for M2Week
Co-PI and organizer for the Macaulay2 Workshop & Mini-school in Minneapolis, MN.
NSF Workshop Grant DMS-2206872 for GradMoCCA
Co-PI and organizer for the Graduate Meeting on Combinatorial Commutative Algebra.
“A short resolution of diagonal for smooth projective toric varieties of Picard rank 2”
M. K. Brown. Algebra & Number Theory 18-10 (2024), 1923-1943.
“The virtual resolutions package for Macaulay2”
A. Almousa, J. Bruce, and M. C. Loper. J. of Software for Algebra & Geometry 10 (2020),
51–60.
“What is the optimal way to prepare a Bell state using measurement and feedback?”
L. Martin and K. B. Whaley. Quantum Sci. & Technol. 2 (2017), no. 4.
“Connection Matrices in Macaulay2” arXiv:2504.01362
P. Görlach, J. Koefler, A.-L. Sattelberger, H. Schroeder, N. Weiss, F. Zaffalon. Submitted.
“Splitting of vector bundles on toric varieties”
Submitted. arXiv:2412.19793
“Computing Direct Sum Decompositions”
D. Mallory. Submitted. arXiv:2412.19799
“Bounds on multigraded regularity”
J. Bruce, and L. Cranton Heller. Submitted. arXiv:2208.11115
“Characterizing multigraded regularity and virtual resolutions on products of projective spaces”
J. Bruce, and L. Cranton Heller. Submitted. arXiv:2110.10705
Conferences
Effective Methods in Algebraic Geometry, MPI MiS, Leipzig, Germany
Spring Western AMS Sectional Meeting, San Francisco State University
Joint Math Meetings, San Francisco, California
Fall Central AMS Sectional Meeting, Creighton University, Omaha
SIAM Applied Algebraic Geometry Conference, Eindhoven University, the Netherlands
Géométrie Algébrique en Liberté, University of Warwick, UK
CA+ Conference, University of Minnesota, Twin Cities
Spring Southeastern AMS Sectional Meeting, Georgia Tech, Atlanta
Fall Western AMS Sectional Meeting, University of Utah, Salt Lake City
Fall Central AMS Sectional Meeting, University of Texas, El Paso
Macaulay2 Conference, Cleveland State University
Spring Central AMS Sectional Meeting, University of Cincinnati (virtual)
SIAM Applied Algebraic Geometry Conference, Universität Bern, Switzerland
Joint Mathematics Meetings, San Diego, California
Seminars
University of Edinburgh, Hodge Institute, EDGE Geometry Seminar
UC Berkeley, Commutative Algebra and Algebraic Geometry Seminar
University of Michigan, Ann Arbor, Commutative Algebra Seminar
University of Notre Dame, Algebraic Geometry and Commutative Algebra Seminar
University of Nebraska - Lincoln, Commutative Algebra Seminar
University of Illinois, Chicago, Commutative Algebra Seminar
ICERM semester in Combinatorial Algebraic Geometry, Grad/Postdoc Seminar (virtual)
Posters
Group actions, combinatorics, and Fano varieties, Universität Innsbruck, Austria
Syzygies and Hilbert Schemes, Jagiellonian University, Kraków, Poland
Connections Workshop: Commutative Algebra, SLMath, Berkeley
Western Algebraic Geometry Symposium, Washington University in St. Louis
MSRI/SLMath Summer School in Commutative Algebra, University of Notre Dame
Western Algebraic Geometry Symposium, UC Riverside
Pan-American School in Commutative Algebra, CIMAT, Mexico
SIAM Applied Algebraic Geometry Conference, Georgia Tech, Atlanta
School of Mathematics, University of Minnesota, Twin Cities
MATH 1272: instructor of record for Calculus II (class of approx. 100 students).
MATH 8253: graded homework for Algebraic Geometry (graduate course).
MATH 1272: instructor of record for Calculus II (class of approx. 90 students).
MATH 2243: TA for Linear Algebra & Differential Equations (six sections total).
MATH 1271: TA for Calculus I (two sections total).
REU: mentored P. Cranford, A. Peng, and V. Srinivasan towards arXiv:2106.12667.
DRP: mentored five undergraduate students in weekly reading projects.
Department of Mathematics, UC Berkeley
Math113: graded homework for Abstract Algebra.
Math116: graded homework and assisted the instructor for Mathematical Cryptography.
MathCenter, Irvine Valley College
Tutored lower-div courses including linear algebra, differential equations, and discrete math.
Developed curriculum for computer science-based problem-solving using Python.
Macaulay2 in the Sciences Workshop
Three-day workshop on computational algebra with 45 participants in Leipzig, Germany.
Macaulay2 Workshop & Mini-school
Weeklong event in computational commutative algebra bringing 70 researchers to Minneapolis.
Graduate Meeting on Combinatorial Commutative Algebra
Weekend graduate event with 12 speakers bringing 70 students and postdocs to Minneapolis.
Directed Reading Program, University of Minnesota, Co-founder and co-organizer
Matched over 250 undergraduate and graduate students in guided mathematics reading projects.
Student Commutative Algebra Meeting, University of Minnesota, Co-organizer
Held a weekly meetup of friendly neighborhood commutative algebra students.
Graduate Student Combinatorics Conference, Session Chair
Chairedthe session on Combinatorial Algebraic Geometry.
Pauline Sperry Undergraduate Lecture Series, UC Berkeley, Organizer
Inaugurated an annual lecture aimed at providing a role model for marginalized students in math.
Referee Work:
Journal of Pure and Applied Algebra, Journal of Software for Algebra and Geometry
Vincent Hall Thespians, University of Minnesota, Performer
Helped with first-time teaching assistant orientation through situational comedy.
Minnesota Project in Mathematics, Counselor
Helped with workshops and mentored two undergraduate projects during the week-long program.
AMS Graduate Student Blog, Staff Writer
Wrote about finding community through mathematical art and history.
Girls Who Code @ Cloudflare, Workshop Leader
Instilled an appreciation for mathematics in high school girls using elliptic cryptography puzzles.
Mathematics Undergraduate Student Association, UC Berkeley, President
Helped build an inclusive and diverse community among undergraduate math students at Berkeley.
Berkeley mini Math Tournament, Grader and Lecturer
Instilled an appreciation for knot theory in advanced elementary and middle school students.
Mathematical Sciences Research Institute, Macaulay2 Developer (see below)
Cloudflare, Inc. Cryptography Engineering Intern
Launched multiple products involving Tor, Keyless SSL, and distributed randomness
generation.
Proton Research, Inc. Cryptography Research and Development Intern
Added support for elliptic curve cryptography in OpenPGP.js.
Syzygies and mirror symmetry, American Institute of Mathematics, Pasadena, California Topics: resolutions of the diagonal for toric varieties, homological mirror symmetry
Géométrie Algébrique en Liberté, University of Warwick, UK
Topics: Mori Dream Spaces and quiver GIT, klt singularities, the geometry of curves
MRC Derived Categories, Arithmetic and Geometry, AMS
Topics: Frobenius pushforwards and F-thickness of the blowup Bl5P2
MSRI/SLMath Summer School in Commutative Algebra, University of Notre Dame
TA for mini-course on the geometry of nonstandard syzygies by Daniel Erman
RTG Workshop on Birational Complexity, SCGP, Stony Brook University
Topics: rationality, curves in algebraic varieties, the Cremona group, measures of irrationality
Pan-American School in Commutative Algebra, CIMAT, Mexico
Topics: positive characteristic methods, toric varieties, DG algebras, modules of differentials
Combinatorial Algebraic Geometry, ICERM
Topics: Schubert varieties, toric varieties, tropical varieties, cluster algebras and varieties
RTG Summer School in Commutative Algebra, University of Utah
Topics: limits in positive characteristic, symbolic powers, differential operators, and syzygies.
Geometry of Redistricting Workshop, University of San Francisco
Topics: gerrymandering, voting rights, discrete geometry and graph theory
Macaulay2 Internals
I have contributed to various internal components of Macaulay2, including the engine,
interpreter, core mathematical routines, and documentation. I have also contributed to the
following packages:
DirectSummands: for decomposing modules and coherent sheaves, with D. Mallory.
Varieties: for computations involving projective varieties, including complexes of coherent sheaves and their morphisms, with D. Mallory, R. Ramkumar, G. Smith, K. VandeBogert.
NormalToricVarieties: added support for pullbacks of coherent sheaves over toric maps,
and computations on the Cox ring of toric varieties whose class group has torsion.
Truncations: added support for truncations of modules with respect to arbitrary cones,
for instance on simplicial toric varieties where the nef and effective cones differ.
Saturation: improved and added to core routines for computing annihilators, saturations,
and quotients of ideals and modules, with J. Chen and M. Stillman.
FGLM: for computing Gröbner bases of zero-dimensional ideals, with D. Peifer.
VirtualResolutions: see paper above, with A. Almousa, J. Bruce, and M. Loper.
LocalRings: for symbolic computations over local rings, with M. Stillman.
Memberships:
AMS, SIAM Activity Group on Algebraic Geometry.
Programming:
Proficient in Macaulay2, C/C++, Python, and Node.js.
Experienced in Go, Rust, SageMath, and IDL.
Familiar with Julia, Mathematica, MATLAB, and Haskell.
Institute for Quantum Computing, University of Waterloo
Topics: quantum error correcting codes from algebraic curves under John Watrous.
Berkeley Quantum Information and Computation Center, UC Berkeley
Topics: control theory & entanglement generation under Leigh Martin and Birgitta
Whaley.
Institute for Quantum Information and Matter, Caltech
Topics: quantum game theory and semi-definite optimization under Thomas Vidick.
Jet Propulsion Laboratory, NASA
Topics: secure multiparty computation and secret sharing systems under Ed Chow.