My research interests are in
commutative algebra, finite abelian groups, combinatorics and number theory. In
particular, I am very interested in problems concerning factorization of
elements in integral domains and monoids and problems concerning integer-valued
polynomials. You can find a complete list of my publications on my
VITA. You can find a list of my publications with
here. Here are some recent titles which are either preprints or "to
appear" and can be downloaded as pdf files (* denotes an undergraduate
Shifts of generators and Delta sets of numerical monoids,
(with N. Kaplan, T. Lemburg*, A. Niles* and C. Zlogar*) to appear in the
J. Commutative Algebra.
- Elements in a numerical semigroup with factorizations of the
same length,(with P. A. Garca-Sanchez and D. Llena and J. Marshall*) to
appear in Canad. Math. Bull.
Elasticity in generalized arithmetical
congruence monoids, (with D.
Steinberg*) to appear in
An algorithm to compute omega-primality
in a numerical monoid,
(with D. F. Anderson, N. Kaplan
and D. Torkornoo*) to appear in Semigroup Forum.
(with W. W. Smith) to appear in Period. Math. Hungar.
A closer look at non-unique factorization via atomic
decay and strong atoms, (with U. Krause) submitted.
A tale of two sequences: a
friendly introduction to the theory of non-unique factorizations,
Some Invited Talks
Factorization Theory: The Basics," Keynote Address at the MAA-PREP Workshop The
Art of Factorization in Multiplicative Structures, May 2007.
"Numerical Monoids are Totally Cool!"
Address at the Univeristy of Tennessee Undergraduate Mathematics Conference,
April 2007 and Mathematics on the Northern Plains, North Dakota State
University, April 2008.
Introduction to the Theory of Non-Unique Factorizations,"
Algebra Colloquium, Texas A&M University, November 2008.
- "A tale
of Two Sequences, A Friendly Introduction to the Theory of Non-Unique
Factorizations," Sam Houston State University
Mathematics Colloquium, December 2008.
- "On the Delta Set of a Krull Domain with
Infinite Cyclic Divisor Class Group,"
Special Session on Commutative Rings at the Annual AMS-MAA Meeting in
Washington, DC, January 2009.
- "Basic Factorization Theory" and "Factorization in Int(Z),"Immerse
Program Algebra Lectures, June 2009.
"Elastic Properties of Some Semirings Defined by
Positive Systems," Special Session on Commutative Rings, a
Tribute to Jim Brewer, at the Sectional AMS Meeting in Boca Raton, Florida,
Sets of Numerical Monoids: A Progress Report," Iberian Meeting on
Numerical Semigroups - Granada 2010, Granada, Spain, February 2010.
All-Divisor Sets," (algebra version)
Special Session on Commutative Rings at the Sectional AMS Meeting in
Minneapolis, Minnesota, April 2010.
All-Divisor Sets," (number theory version) 8th Annual Combinatorics and
Additive Number Theory Conference (CANT), CUNY, New York, May 2010.
"A Tale of Two Sequences: A Friendly Introduction to
the Theory of Non-Unique Factorizations," Amherst College,
Amherst, Massachusetts, October 2010.
"Factoring Integer-Valued Polynomials: A Survey with
Open Problems," Third Integer-Valued Polynomial Encounter,
Marseille, France, November/
Some Mathematical Links of