My research interests lie broadly in algebra, focusing on the intersection with algebraic and arithmetic geometry and algebraic number theory.
I am in particular interested in the local aspects and the local-global principles of algebraic objects, as well as their obstructions in the following directions:
- Patching for arithmetic curves and local-global principles.
- The arithmetic of algebraic stacks with applications to number theory.
- Topics that are broadly related to algebraic groups, such as invariant theory, differetial Galois theory and toric varieties.
Publications and Preprints
- The étale Brauer-Manin obstruction for classifying stacks. Joint with Ajneet Dhillon, Nicole Lemire and Jonanthan Martin. Manuscript in preparation.
- The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations. Joint with Juanita Duque-Rosero, Christopher Keyes, Andrew Kobin, Manami Roy, and Soumya Sankar. 41 pages. 2025 Preprint available at arXiv:2509.13248.
- Patching for étale algebras and the period-index problem for higher degree Galois cohomology groups over Hensel semi-global fields. 25 pages. Submitted. 2023 Preprint available at arXiv:2310.20119.
- Cohomology for Picard-Vessiot theory. Joint with Man Cheung Tsui. Journal of Algebra,vol 658 (2024) 49-72. Also available at arXiv:2308.03025.
- Arithmetic invariant theory of reductive groups. Communications in Algebra, vol 53(11) 4749--4765 (2025). Also available at arXiv:2212.12863.