Disclaimer: This page is severely outdated. For an overview of my research, please visit
my Papers section. One day soon, I will have the time to write something coherent and current about
my research interests.
My main area of specialization is Computational
Commutative Algebra and algebraic geometry with emphasis
on their applications. I have
done research in the following subjects:
This area proposes computational commutative algebra as a tool
in experimental design, discrete probability, and statistical modeling.
In my Ph. D. thesis, I studied a particular statistical model known as
Bayesian network from the point of view of computational
algebraic geometry. My contributions to this subject are:
You can check the following links to know more about algebraic statistics:
I am interested in the fascinating interplay between combinatorics and commutative algebra.
In particular, I am very interested in monomial ideals and toric ideals.
I have worked on
cellular resolutions of monomial ideals. To know more about
the subject, you can check
the book Combinatorial Commutative
Algebra written by Ezra Miller and Bernd Sturmfels.
I am currently working with Mike Falk on
certain resolutions of monomial ideals arising from hyperplane
arrangements. I gave a
talk that contains
some of the results in our work.
(with Mike Falk).
Minimal Cohen-Macaulay deformations of matroid ideals. In progress.
- Toric Ideals
- Gröbner bases
- Primary Decomposition: During the Fall 2002, I was a "visiting
student" in the Mathematics Department at the University of Genova in
Italy. Everything started having dinner at
Olivier's restaurant in New
Lorenzo Robbiano in September of 2001. Then he invited me to work
with the wonderful
CoCoA team. We are in
the process of implementing a library to perform primary decomposition
of polynomial ideals in the new version of CoCoA.
- Sequential Dynamical Systems