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Sam Huckaba
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Professor and Dean College of Arts and Sciences
Ph.D., Purdue University, USA, 1986

Detailed description of research

Commutative Algebra
Generally, I study the powers of ideals in Noetherian graded or local rings. More specifically, I seek to understand associated graded rings and Rees algebras of ideals in local rings (usually Cohen-Macaulay local rings, often regular local rings). These objects belong to a class of "blowup algebras" that arise in the algebraic realization of the blowing up process used in desingularization. In particular, much of my work involves predicting arithmetic properties of these rings, such as normality, Cohen-Macaulayness, smoothness, etc. Part of my research also involves Hilbert-Samuel polynomials of zero-dimensional ideals. Those are used to give a modern definition of multiplicity, and also play a role in predicting depth properties of blowup algebras. I am also interested in applications to other areas, not just within commutative algebra but also outside (e.g. algebraic geometry, combinatorics, cryptography).

I have a continuing interest in understanding existing cryptosystems and exploring possibilities for using elements of commutative algebra to create new systems.