Algebra is the discipline of pure mathematics that is concerned with the study of the abstract properties of a set, once this is endowed with one or more operations that respect certain rules (axioms) ...

Algebraic Structures and Combinatorial Geometry represent an increasingly interwoven field that harnesses the rigour of algebra with the spatial intuition of geometry. At its core, the study explores ...

Algebraic structures, ranging from groups and rings to modules and fields, constitute the foundation of modern mathematics. Among these, Hopf algebras have emerged as pivotal constructions that ...

My primary research interests are in algebra and combinatorics. In particular, I work within the realm of combinatorial representation theory, attempting to connect combinatorial objects (such as ...

After previously discussing permutations, Dr. James McCaffrey of Microsoft Research uses step-by-step examples and full code presentations to explore combinations. A zero-based mathematical (n, k) ...

Let K[x,y] be the polynomial algebra in two variables over a field K of characteristic 0. A subalgebra Rof K[x,y] is called a retract if there is an idempotent homomorphism (a retraction, or ...

I arrived in the US in 2006, as a Visiting Assistant Professor at the University of Notre Dame. Before then, I was a Ph.D. student at Queen's University, Canada, a postdoc at the University of Genova, ...