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

- 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 - 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 - 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 - Prime torsion in the Brauer group of an elliptic curve. Trans. Amer. Math. Soc. (forthcoming)

ArXiv version - A cogroupoid associated to preregular forms. joint with Hongdi Huang, Van C. Nguyen, Kent B. Vashaw, Padmini Veerapen, and Xingting Wang. J. Noncommut. Geom. (forthcoming)

ArXiv version

## Preprints

- A moduli interpretation of untwisted binary cubic forms. joint with Rajesh Kulkarni. arXiv:2103.16691

(2021) - Twisting Manin’s universal quantum groups and comodule algebras. joint with Hongdi Huang, Van C. Nguyen, Kent B. Vashaw, Padmini Veerapen, and Xingting Wang. arXiv:2209.11621 (2022)

ArXiv version

## 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.