Marzullo, Adriano
Dr. Adriano Marzullo
Research experience
Ph.D.
Research projects
Much of my research is in a field called “commutative algebra”, and I also carry out research in arithmetic combinatorics.
In number theory we study we study structures that are closed under addition and multiplication – such as all multiples of a prime number, or polynomials with integer coefficients. These structures are called commutative rings (“commutative ” means axb = bxa).
Commutative rings also arise when we study geometry of curves from an algebraic point of view. The language and ideas of commutative rings provides common way of dealing with problems in number theory and algebraic geometry which, at first glance, seem to be quite different subjects.
Betti numbers, named for Enrico Betti, were originally used to count the number of holes of various dimensions in topological spaces. It might be hard to imagine a 5-dimensional hole, but the Betti numbers can be defined to count such strange things. Since then, they have been generalized in algebraic ways in many other contexts.
Some articles:
- Marzullo, A., & Chapman, J. (2015). On rapid generation OF SL2 (Zq). Online Journal of Analytic Combinatorics, 10.
- Marzullo, A. (2013). On the perodicity of the first Betti number of the semigroup rings under translations. Journal of the Ramanujan Mathematical Society, 28(2), 195-212.