Research Interests.

Broadly speaking, my mathematical interests are in Commutative Algebra and its interactions with Algebraic Geometry and Combinatorics. Here is a concise list of problems/research areas:

• Interpolation problems and symbolic powers of ideals: a few of my recent papers are on this topic, for which I have a growing interest.
• Structure theorems for special classes of ideals: Several of my papers are dedicated to explicitly described the structure of special classes of ideals, and their numerical characters (Betti numbers, multiplicity, projective dimension, …)
• Projective dimension and Stillman’s conjecture: 6 of my papers are dedicated either to the  problem of finding sharp upper bounds in Stillman’s conjecture, or development of tools to attack this problem.
• Combinatorial Commutative Algebra: 3 of my papers formulas or bounds for projective dimension, regularity and arithmetical rank of monomial ideals.
• Koszul (commutative) algebras: I have a paper on this very interesting topic, but I suspect that I may be working more in this direction.
• Conormal modules and infinite resolutions: currently two of my papers are dedicated to the conormal module.
• Linkage, residual intersections, j-multiplicity, and Sally’s conjecture: although I have used linkage in most papers that I have worked on, I have realized that so far I have only written one paper on Liaison Theory. I have written also one paper on j-multiplicity and Sally’s conjecture.

For a fairly updated list of research papers I have authored, see my papers.

At the link, you will find my CV.