Research Areas

Commutative algebra, algebraic geometry

Research Interests

• Algebraic vector bundles/projective modules

• Algebraic K-theory/Hermitian K-theory

• Motivic homotopy theory/motivic cohomology

• Affine algebraic geometry/complex algebraic geometry

• Clifford algebras/Spin groups

In preparation

• A motivic approach to efficient generation of projective modules (with Aravind Asok, Morgan Opie and Brian Shin)

Preprints

• On algebraic vector bundles of rank 2 over smooth affine fourfolds (submitted) (with Thomas Brazelton and Morgan Opie) [arXiv]

• A symplectic version of Suslin's n!-theorem (submitted) [arXiv]

• Motivic cohomology of cyclic coverings (submitted and revised following a positive referee report) [arXiv]

Publications

• The generalized Vaserstein symbol revisited, accepted for publication in Homology, Homotopy and Applications [arXiv]

• A note on Suslin matrices and Clifford algebras, accepted for publication in Homology, Homotopy and Applications [arXiv]

• Some remarks on Spin-orbits of unit vectors, Journal of Pure and Applied Algebra (2025), Volume 229, Issue 1, 107802 [arXiv]

• Symplectic orbits of unimodular rows, Journal of Algebra (2024), Volume 646, 478-493  [arXiv]

• Cancellation of vector bundles of rank 3 with trivial Chern classes on smooth affine fourfolds, Journal of Pure and Applied Algebra (2022), Volume 226, Issue 9, 107038  [arXiv]

• The cancellation of projective modules of rank 2 with a trivial determinant, Algebra & Number Theory 15 (2021), no. 1, 109-140  [arXiv]

• A generalized Vaserstein symbol, Annals of K-Theory 4 (2019), no. 4, 671-706  [arXiv]