I am a researcher in the field of mathematics, specializing in abstract algebraic structures and their topological applications. I completed my Bachelor of Science in Mathematics from Seth Anandaram Jaipuria College under the University of Calcutta, followed by a Master of Science in Mathematics from Jadavpur University. Currently, I am pursuing my Ph.D. under the joint supervision of Sujit Kumar Sardar and Abhishek Mukherjee.
My primary research interests lie at the intersection of advanced algebra and topology, with particular emphasis on algebras, fields, knots, and graphs. My current doctoral work investigates the properties and applications of racks and quandles. These specialized algebraic structures are equipped with binary operations that closely reflect the Reidemeister moves used in the manipulation of knot diagrams. While they play an important role in constructing knot invariants, I also study them as independent algebraic objects with rich internal structure.
A central theme of my recent research concerns quandles, which capture the essential properties of conjugation in groups. My work focuses on developing simpler and computable topological invariants obtained by counting homomorphisms from a fundamental knot quandle into a fixed finite quandle. I also study racks, which generalize quandles by relaxing the idempotency condition, thereby providing algebraic models for twisted ribbons and related topological phenomena.
More specifically, my recent investigations analyze the structural properties of quandles arising naturally from rings and modules. Alongside my theoretical research, I also maintain a strong interest in technical computation and mathematical visualization frameworks.
Beyond my research activities, I am deeply interested in teaching.. I am eager to facilitate students in developing a strong and intuitive understanding of mathematics by encouraging curiosity, logical reasoning, and active problem-solving. I strive to create a supportive learning environment in which students feel comfortable engaging with abstract concepts and exploring mathematical ideas independently.
