| Research Interests
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
undergraduates
here. Here are some recent titles which are either preprints or "to
appear" and can be downloaded as pdf files (* denotes an undergraduate
co-author).
-
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
Results Math.
-
An algorithm to compute omega-primality
in a numerical monoid,
(with D. F. Anderson, N. Kaplan
and D. Torkornoo*) to appear in Semigroup Forum.
-
Erdös-Zaks
all-divisor sets,
(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,
submitted.
Slides from
Some Invited Talks
- "Why
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!"
Keynote
Address at the Univeristy of Tennessee Undergraduate Mathematics Conference,
April 2007 and Mathematics on the Northern Plains, North Dakota State
University, April 2008.
- "An
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,
October 2009.
- "Delta
Sets of Numerical Monoids: A Progress Report," Iberian Meeting on
Numerical Semigroups - Granada 2010, Granada, Spain, February 2010.
- "Erdös-Zaks
All-Divisor Sets," (algebra version)
Special Session on Commutative Rings at the Sectional AMS Meeting in
Minneapolis, Minnesota, April 2010.
- "Erdös-Zaks
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/
December 2010.
Some Mathematical Links of
Interest:
|
Slides from Author's Talks at AMS Special Session on Arithmetic and Ideal Theory of Integral Domains and Monoids at the San Diego JMM, January 2013