| 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. García-Sánchez and D. Llena and J. Marshall*) to
appear in Canad. Math.
Bull.
- How
far is an element from being prime? (with D.F. Anderson) to appear
in J. Algebra Appl.
- A
note on the sum of the quotient and remainder in the division algorithm,"
(with D. F. Anderson and W. W.
Smith) to appear in Elem. Math.
- Delta sets of numerical monoids using non-minimal sets of
generators," (with G. Daigle*, R.
Hoyer* and N. Kaplan) to appear in Comm. Algebra.
-
On the delta set and catenary
degree of Krull Monoids with non-cyclic divisor class group," (with P. Baginski, R.
Rodriguez*, G. Schaefer and Y. She*) to appear in J. Pure Appl.
Algebra.
- Elasticity in generalized arithmetical
congruence monoids," (with D.
Steinberg*) submitted.
-
A note on cancellation properties of semistar operations,"
(with R. Matsuda)
submitted.
-
An
algorithm to compute omega-primality in a numerical monoid,"
(with D. F. Anderson, N.
Kaplan and D. Torkornoo*) submitted.
-
On the delta
set of a 3-generated numerical monoid,"
(with A. Malyshev* and D.
Steinberg*)
submitted.
Slides from
Recent 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.
Some Research Links
of Interest:
Where are they now? A
list of my former Undergraduate Research Students and their present
locations.
Website for
the MAA PREP Workshop "The Art of Factorization in Multiplicative
Structures" at Trinity University May 21-25, 2007
Focus Article on "The Art of Factorization in
Multiplicative Structures" (December
2007)
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