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Research

My research interests lie at the intersection of noncommutative algebra and algebraic geometry. I am particularly interested in the study of

  • the Brauer group,
  • Clifford algebras,
  • unramified cohomology groups, and
  • rationality questions.

ArXiv: Click here for my preprints on ArXiv

ORCID: 0000-0003-4484-956X

Publications

  1. Tensor products of cyclic algebras of degree 4 and their Kummer subspaces. joint with Adam Chapman. Comm. Algebra 45 (2017), no. 3, 1218–1226. 16K20 (05C38 12J20)
    publisher’s version ArXiv version
  2. Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation. joint with Hongdi Huang, Van C. Nguyen, Kent B. Vashaw, Padmini Veerapen, and Xingting Wang. Transform. Groups (2022) 16S37 (16S80 16T05 16W50 17B37)
    publisher’s version ArXiv version
  3. Symbol length in Brauer groups of elliptic curves. joint with Mateo Attanasio, Caroline Choi, and Andrei Mandelshtam. Proc. Amer. Math. Soc. 151 (2023), pp. 5031-5046. 11G05 (14H52 14F22)
    publisher’s version ArXiv version
  4. Prime torsion in the Brauer group of an elliptic curve. Trans. Amer. Math. Soc. 377 (2024), no. 4, pp. 2413-2437.
    publisher’s version ArXiv version
  5. A cogroupoid associated to preregular forms. joint with Hongdi Huang, Van C. Nguyen, Kent B. Vashaw, Padmini Veerapen, and Xingting Wang. J. Noncommut. Geom. (2024), pp. 1-31.
    publisher’s version ArXiv version
  6. Twisting Manin’s universal quantum groups and comodule algebras. joint with Hongdi Huang, Van C. Nguyen, Kent B. Vashaw, Padmini Veerapen, and Xingting Wang. Adv. Math. 445 (2024) 109651.
    publisher’s version ArXiv version

Preprints

  • A moduli interpretation of untwisted binary cubic forms. joint with Rajesh Kulkarni. arXiv:2103.16691
    (2021)
  • Period-index in top cohomology over semiglobal fields. joint with Sarah Dijols, Raman Parimala, and Ramdorai Sujatha. arXiv:2312.03934 (2023)
  • Towards a refinement of the Bloch-Kato conjecture. joint with Sunil K. Chebolu, Ján Mináč, Cihan Okay, and Andrew Schultz. arXiv:2405.13223 (2024)

Recorded Talks

  • A video of my talk at the BIRS workshop “Noncommutative Geometry and Noncommutative Invariant Theory” in September 2022 on “Twisting comodule algebras and preregular forms” is available here.
  • A video of my talk at the BIRS workshop “Arithmetic aspects of algebraic groups” in June 2022 on “Symbol Length in Brauer Groups of Elliptic Curves” is available here.
  • A video of my talk at the online BIRS workshop “Arithmetic aspects of algebraic groups” in September 2020 on “The Generic Clifford Algebra and its Brauer Class” is available here.
  • A video of my talk for the Junior Mathematicians Research Archive in September 2020 on “Prime Torsion in the Brauer Group of an Elliptic Curve” is available here. 
  • A video of my talk at the Simons Conference on Rationality in July 2020 on “The Brauer Group of Elliptic Curves” is available here.
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