Research | Colorful Algebra

Research

Interests: Algebra, Algebraic Geometry, Number Theory, Computational Mathematics

Articles that I've written, or had a part in writing:

  1. Refined index obstructions for Brauer classes on an abelian variety
    2. May 26, 2026
  2. An algorithmic reduction to canonical forms for vector bundles on anisotropic conics
    3. joint with Diego Yépez.
    April 19, 2026
  3. A looming of phantoms
    4. joint with Kimoi Kemboi, Daniel Krashen, Tianle Liu, Yeqin Liu, Svetlana Makarova, Alexander Perry, Antonios-Alexandros Robotis, and Sridhar Venkatesh.
    Advances in Mathematics. November 10, 2025
  4. On deformations of Azumaya algebras with quadratic pair
    5. joint with Cameron Ruether.
    April 3, 2025
  5. Elliptic curves and their principal homogeneous spaces: splitting Severi--Brauer varieties
    6. joint with Nick Rekuski.
    January 18, 2024
  6. On the algebraizability of formal deformations in K-cohomology
    7. September 1, 2024
  7. The period and index of a generic geometrically elliptic normal curve
    8. Journal of Algebra. September 1, 2024
  8. Pro-representability of K^M-cohomology in weight 3 generalizing a result of Bloch
    9. Annals of K-theory. January 19, 2023
  9. On the Chow groups of a biquaternion Severi--Brauer variety
    10. Pacific Journal of Mathematics. October 17, 2022
  10. Algebraic connective K-theory of a Severi--Brauer variety with prescribed reduced behavior
    11. Documenta Mathematica. April 23, 2021
  11. A universal coefficient theorem with applications to torsion in Chow groups of Severi--Brauer varieties
    12. New York Journal of Mathematics. April 29, 2020
  12. Codimension 2 cycles on Severi-Brauer varieties and decomposability
    13. (Corrections.) October 14, 2020
    Manuscripta Mathematica. June 23, 2020
  13. A^1-homotopy equivalences and a theorem of Whitehead
    14. Homology, Homotopy, and Applications. July 2, 2020
  14. Universal additive Chern classes and a GRR-type theorem
    15. Journal of Algebra. June 4, 2020
  15. Functorality of the gamma filtration and computations for some twisted flag varieties
    16. Annals of K-theory. August 21, 2019
  16. On the K-theory coniveau epimorphism for products of Severi-Brauer varieties
    17. joint with Nikita Karpenko.
    Annals of K-theory. October 19, 2018
  17. The coniveau filtration on K_1 for some Severi-Brauer varieties
    18. Canadian Mathematical Bulletin. October 9, 2018
  18. Six variations on a theme: almost planar graphs
    19. joint with Max Lipton, Thomas W. Mattman, Mike Pierce, Samantha Robinson, Jeremy Thomas, Ilan Weinschelbaum.
    Involve. August 5, 2016

Some additional things that I've written, that aren't inteded for publication:

  1. A factorization algorithm based on Cohn's irreducibility criterion
    2. March 16, 2026
  2. Rational equivalence classes on Severi--Brauer varieties
    3. July 16, 2021
  3. The arithmetic genus of a complete intersection curve
    4. May 11, 2020
  4. The genera of smooth curves in a projective variety
    5. December 12, 2019
  5. A degree bound on the genus of a projective curve
    6. October 3, 2021