My research lies at the intersection of algebraic topology, homological algebra, and non-associative algebraic structures, focusing on homological and categorical methods applied to algebraic structures arising in low-dimensional topology. My current and developing interests include:

• Algebraic Topology of Non-associative Structures: Studying the homology and homotopy types of algebraic structures such as racks, quandles, and generalized Legendrian racks, and exploring their relationships with homotopy invariants.

• Generalized Homological Frameworks: Applying categorical and homological algebra techniques to relate quandle cohomology with Hochschild and Quillen cohomology, and developing unified frameworks for the (co)homology of algebraic structures.

• Structural and Geometric Invariants: Investigating structural and geometric properties of quandles and related structures such as residual finiteness using tools from 3-manifold theory and geometric group theory (Bounded cohomology), with applications to knot theory.

• Connections with Broader Algebraic Structures: Exploring connections with Hopf algebras, quantum groups, and set-theoretic solutions to the Yang-Baxter equation, aiming to understand how topological and homological methods can inform the structure of these objects.

Additionally, I am eager to expand my expertise in areas closely related to the project, including homotopy theory, group (co)homology, and geometric group theory.