My research involves that area of Algebra where Ring Theory, Commutative Algebra and Algebraic Geometry overlap. The main focus is the Brauer group of a commutative ring, which classifies the Azumaya algebras. The rings that arise are rings of functions defined on algebraic varieties. This study employs many methods from all areas of Algebra. There are essential connections with the theory of separable algebras, Morita theory, the theory of faithfully flat descent, Galois theory, cohomology, derivations, differentials, reflexive lattices, maximal orders and class groups.
"The Brauer group of an affine double plane associated to a hyperelliptic curve", Comm. Algebra, vol. 45, pp. 1416--1442, 2017.
(with D. M. Harmon), "The Relative Brauer Group and Generalized Cross Products for a Cyclic Covering of Affine Space", J. Pure Appl. Algebra, vol. 218, pp. 721--730, 2014.
(with D. M. Harmon), "The Brauer Group of an Affine Rational Surface with a Non-rational Singularity", J. Algebra, vol. 388, pp. 107--140, 2013.
"The Relative Brauer Group and Generalized Cyclic Crossed Products for a Ramified Covering", J. Algebra, vol. 450, pp. 1--58, 2016.
"Separable Algebras", An algebra book containing an introduction to the theory of separable algebras, including a rigorous treatment of Azumaya algebras, henselization, and
Galois theory. To be published by The American Mathematical Society in the Graduate Studies in Mathematics series.
Being a mathematical fanatic, I never stop working. I'm doing math 24 hours a day, 7 days a week.
Lighthouse, Pompano Beach Inlet
When I am not grading papers, I enjoy playing my guitar.