Motivated by Waring’s problem in number theory and Kaplansky’s conjecture in algebra, various generalizations of these problems have been studied over different algebraic objects. Analogous questions have been asked in group theory, often framed as the study of images of word maps on groups.
The focus is on studying generalized polynomials over algebras, including associative and non-associative algebras. Understanding these structures provides a foundation for exploring other classes of algebras, which present additional challenges and opportunities for research.
Publications:
Surjectivity of polynomial maps on matrices, European Journal of Mathematics 11, 62, 2025. (with Saikat Panja and Anupam Singh)
Images of polynomial maps with constants, Mathematika 11, 3 2025. (with Saikat Panja and Anupam Singh)
Polynomial maps with constants on split octonion algebras, Communications in Algebra, 2025. (with Saikat Panja and Anupam Singh)