Research Intererst:
Witt vectors of Associative rings: For any commutative ring R, there is an associated Witt ring W(R). It is a very useful tool in number theory and arithmetic geometry. For non-commutative rings, there are many interesting ways to build Witt vectors. Then one can ask: are these different ways somehow the same? Can we find a universal way to define the Witt functor? Currently, I'm investigating the differences and similarities between two constructions of Witt vectors for associative rings. One of them is given by Lars Hesselholt and the other by Cuntz-Deninger. Though they may look different in appearance, both agree with the classical definition of Witt vectors when restricted to commutative rings.
Rational points on varieties: I’m also interested in studying rational points on varieties, as not all varieties satisfy Hasse’s local-global principle. Manin came up with a cohomological obstruction, now called the “Brauer–Manin obstruction.” It has been conjectured that for projective, geometrically integral, rationally connected varieties defined over number fields, this is the only obstruction to the Hasse principle. I study the Brauer–Manin obstruction and related problems of rational points on varieties. I am also interested in studying low-degree points on curves and their Galois groups.
Publications:
Supriya Pisolkar and Biswanath Samanta, A universal group-theoretic characterisation of p-typical Witt vectors, Journal of Algebra, 677, Pages 1-12, 2025, (journal version).
Preprints:
M. Biswas, D. C. Ramachandran, and B. Samanta, “Pullback Method with Applications to Severi-Brauer Fibrations,” arXiv preprint arXiv:2410.15125, 2024. (Submitted)
A universal group-theoretic characterisation of p-typical Witt vectors of non-commutative rings, (with Dr. Supriya Pisolkar) (Pre-print)