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My
research interested are primarily in
noncommutative algebra and algebraic geometry. In particular,
I study associated primes and tosion thoery. I have
classified
the associated primes of skew-polynomial modules over Ore extensions of
the
form $R[x;\sigma]$, where $\sigma$ is a surjective endomorphism of the
base
ring
$R$. My dissertation expands this result to generalized Weyl
algebras. Past work has also included representations of
generalized Weyl
algebras, $R[u,d; \sigma, q]$. I am currently working on
fundamental results on the structures of Leavitt path algebras (LPAs)
built over arbitrary associative rings--including iterated LPAs.

#### Publications:

*Associated Primes over Ore
Extensions*, J. Algebra, 286(1),
2005.
A .pdf is available here.

*The genus level of a group*, (with M. Arbo, K.
Benkowski, B. Coate, C. Peterson & A. Wootton)
Involve, 2 (3),
2009.
A .pdf is available here.

Simple Modules Over Generalized Weyl Algebras and Their Associated Primes, Comm. in Algebra, 40(9), 3224-3235. A .pdf eprint is available here. (There are 50 copies available; if you cannot access an eprint, please contact me for a copy. HN)

#### Professional Talks/ Seminars:

*Leavitt path algebras over arbitrary unital rings,* 1073rd
AMS meeting: Noncommutative Algebra, September 2011.

Torsion-theoretic representations of generalized Weyl algebras,
1041th AMS
Meeting: Noncommutative Algebra and Geometry, October 2008.

Associated primes over generalized Weyl algebras, II,
1024th AMS
Meeting: Noncommutative Algebra, March 2007.

Associated primes over generalized Weyl algebras, I,PNWMAA
Meeting: Junior Faculty Reserach, June 2006*.*

Associated Primes over Generalized Weyl Rings, 1012thAMS
Meeting:
Special Session on Regular Algebras and Projective Geometry,
November 2005.

Games, Graphs and other Tricks, Pacific University Mathematics Colloqium, April 2005

*Associated Primes over Ore
Extensions, *Joint AMS/MAA
Meetings:
Number Theory III Contributed Paper Session, January 2005.

*Prime Numbers, Prime Ideals,
and Associated primes, *Linfield
College, Science Colloquium, Oct, 2004.

*Generalizations of Primes in
Noncommutative Algebra, *University
of Portland, Mathematics Colloquium, Oct. 6th, 2004.

*Torsion Theories, *University
of Oregon, Ring Theory Seminar,
May 25th, 2004.

*Associated Primes over Ore
Extensions I, *University of
Oregon,
Ring Theory Seminar, Feb. 10th, 2004.

*Associated primes over
Skew-Polynomial Rings II, *University
of
Oregon, Ring Theory Seminar, Nov. 18th, 2003.

*Some Theorems on Cubic Plane
Curves, *University of Oregon,
Ring
Theory Seminar, May 27th, 2003.

*Associated Primes over
Skew-Polynomial Rings, *University
of
Oregon, Ring Theory Seminar, Nov 5th, 2002.

*Linking Prime Ideals, *University
of Oregon, Ring Theory
Seminar, May 21st, 2002.

*Goldie Rings and the Three
Bears, *University of Oregon,
Ring
Theory Seminar, April 30th, 2002.

*A Festival of Prime Ideals, *University
of Oregon, Ring Theory
Seminar, Nov. 6th, 2001.

Simple Modules Over Generalized Weyl Algebras and Their Associated Primes, Comm. in Algebra, 40(9), 3224-3235. A .pdf eprint is available here. (There are 50 copies available; if you cannot access an eprint, please contact me for a copy. HN)

Torsion-theoretic representations of generalized Weyl algebras,

Associated primes over generalized Weyl algebras, II,

Associated primes over generalized Weyl algebras, I,

Associated Primes over Generalized Weyl Rings, 1012th

Games, Graphs and other Tricks, Pacific University Mathematics Colloqium, April 2005