Research
Published articles
9. Quantum projective planes as certain graded twisted tensor products, (with A. Conner), Journal of Algebra, 620(2023), 293-343, https://doi.org/10.1016/j.jalgebra.2022.11.033
8. Classification, Koszulity and Artin-Schelter regularity of certain graded twisted tensor products , (with A. Conner), Journal of Noncommutative Geometry (2021), DOI: 10.4171/JNCG/395
7. Graded Coherence of Certain Extensions of Graded Algebras, Communications in Algebra (2020), published online June 12, 2020, https://doi.org/10.1080/00927872.2020.1775844
6. The Koszul property for graded twisted tensor products , (with A. Conner), Journal of Algebra, 513 (2018), 50-90 .
5. Some non-Koszul algebras from rational homotopy theory (with A. Conner), The Bulletin of the London Mathematical Society, Volume 47, Issue 3 (June 2015), 473-482.
4. A-infinity algebra structures associated to K2 algebras , (with A. Conner), Journal of Algebra, 337 (2011), no. 1, 63-81.
3. Fat point modules over generalized Laurent polynomial rings , Journal of Algebra, 313 (2007), no. 2, 657-671.
2. Generalized Laurent polynomial rings as quantum projective 3-spaces , (with T. Cassidy, B. Shelton), Journal of Algebra, 303 (2006), no. 1, 358-372.
1. Representation theory of two families of quantum projective 3-spaces , (with B. Shelton), Journal of Algebra, 295 (2006), no. 1, 141-156.
In preparation or submitted articles
1. Artin-Schelter Regular Algebras from Dual Reflection Groups (with Ellen Kirkman, Frank Moore, Kent Vashaw), in preparation.
2. Algebras Associated to Inverse Systems of Schemes with Applications (with Andrew Conner), in preparation.
Thesis
The noncommutative algebraic geometry of quantum projective spaces , University of Oregon, 2003, (Advisor: Brad Shelton).
Presentations, conferences and workshops
Frobenius Extensions in Noncommutative Invariant Theory, AMS-MAA Joint Mathematics Meeting, Special Session on Homological Techniques in Noncommutative Algebra, January 2024. (slides)
Frobenius extensions, Artin-Schelter regular algebras and Azumaya loci, AMS Spring Western Sectional Meeting, California State University, Fresno, CA, May 2023. (slides)
A certain 4-dimensional Artin-Schelter regular algebra from noncommutative invariant theory, Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, University of Washington, June 2022. (slides)
Global section rings and certain twisted tensor products, AMS-MAA Joint Mathematics Meeting, January 2021. (slides)
Graded coherence and noncommutative geometry of certain twisted tensor products, AMS Fall Southeastern Sectional Meeting, University of Florida, Gainesville, FL, November 2019.
The Koszul property for graded twisted tensor products, AMS Spring Western Sectional Meeting, Portland State University, Portland, OR, April 2018. (slides)
Quadraticity and Koszulity for graded twisted tensor products, AMS Fall Western Sectional Meeting, University of North Texas, Denton, TX, September 2017. (slides)
Special Session on New Developments in Noncommutative Algebra, AMS Spring Western Sectional Meeting, University of Nevada, Las Vegas, April 2015.
Some non-Koszul algebras from rational homotopy theory, AMS Fall Western Sectional Meeting, San Francisco State University, San Francisco, CA, October 2014. (slides)
The cohomology of the "group of loops", AMS Sectional Meeting, Wake Forest University, Winston-Salem, NC, September 2011. (slides)
K2 algebras and A-infinity structures, AMS Sectional Meeting, UC Riverside, Riverside, CA, November 2009. (slides)
Point modules over a Z^2-graded quantum projective 3-space, AMS Sectional Meeting, Davidson College, Davidson, NC, March 2007. (slides)
Noncommutative algebraic geometry workshop, School of Mathematical Sciences, Fudan University, Shanghai, China, September 2006.
Special Session on Regular algebras and noncommutative projective geometry, AMS Sectional Meeting, University of Oregon, November 2005.
Representation theory of a class of quantum projective 3-spaces, AMS/MAA Joint Mathematics Meeting, Atlanta, GA, January 2005.
AMS Sectional Meeting, University of North Carolina, October 2003.
The geometry of a generic quantum projective 3-space, AMS/MAA Joint Mathematics Meeting, Baltimore, MD, January 2003.
Talks
Pascal's Mystic Hexagon, Cal Poly Humboldt, September 2022. (slides)
A Brief Introduction to Elliptic Curves, Humboldt State University, September 2018. (slides)
Bézout's Theorem: A Tale of Two Curves, Humboldt State University, November 2017. (slides)
Dividing a Square into Triangles: Combinatorial Topology meets the 2-adic Absolute Value, CSU Chico, Math Colloquium, October 2017. (slides)
Dividing a Square into Triangles: Combinatorial Topology meets the 2-adic Absolute Value, Humboldt State University, April 2017.
Bézout's Theorem: A Tale of Two Curves, Saint Mary's College of California, April 2015.
The Fundamental Group, Braids and Circles, Humboldt State University, April 2014. (slides)
An Introduction to Koszul Algebras, Sonoma State University, November 2013. (slides)
Some non-Koszul algebras I met on sabbatical, Humboldt State University, February 2013. (slides)
Some non-Koszul algebras I met on sabbatical, Wake Forest University, December 2012.
Why certain integrals are "impossible", Sonoma State University, March 2009.
Bézout's Theorem: A Tale of Two Curves, Seattle University, February 2006.
Constructions of algebras and a new family of quantum projective 3-spaces, Humboldt State University, February 2006.
Fat point modules over a generalized Laurent polynomial ring, AMS Sectional Meeting, University of Oregon, November 2005.
Artin-Schelter regular algebras and noncommutative geometry, Bucknell University, April 2003.
The mystery of the missing points, Sonoma State University, March 2003.
Representation theory of quivers and Hall algebras, AMS Summer Session, University of Washington, August 1996.