## Research

On this page are links to papers, preprints, and slides from talks I've given. You can also find all of my preprints on arXiv.

I work in an area of mathematics called *noncommutative algebra*, specifically in *noncommutative algebraic geometry*, and *noncommutative invariant theory*. If you'd like to learn more about some of those topics, I can recommend the following:

- An Invitation to Noncommutative Algebra by Chelsea Walton
- Invariant Theory of Artin-Schelter Regular Algebras: A survey by Ellen Kirkman
- An Introduction to Noncommutative Projective Geometry by Daniel Rogalski.

I also enjoy thinking about certain problems in combinatorics (in particular, about capsets in **F**_{3}^{n}). It turns out that the card game SET is related to these affine geometric spaces. To learn more:

*The Joy of SET* by Liz McMahon, Gary Gordon, Hannah Gordon, and Rebecca Gordon.

My Erdős number is 3 (via two paths: *Michael Tait→Fan Chung→Paul Erdős* and *Thang Pham→Arie Bialostocki→Paul Erdős*).

In a past life, I did some research in neuroscience. Those papers can be found at the bottom of this page.

*noncommutative algebra*, specifically in

*noncommutative algebraic geometry*, and

*noncommutative invariant theory*. If you'd like to learn more about some of those topics, I can recommend the following:

**F**

_{3}

^{n}). It turns out that the card game SET is related to these affine geometric spaces. To learn more:

*The Joy of SET*by Liz McMahon, Gary Gordon, Hannah Gordon, and Rebecca Gordon.*Michael Tait→Fan Chung→Paul Erdős*and

*Thang Pham→Arie Bialostocki→Paul Erdős*).

### Publications

#####
Sidon sets and 2-caps in **F**_{3}^{n}

with Yixuan (Alice) Huang and Michael Tait.

*Involve, a Journal of Mathematics*. (To appear).

Alice is a Wake Forest undergraduate who was awarded a Wake Forest Research Fellowship to work with me during the summer of 2018. She presented a poster at Wake Forest's Undergraduate Research Day.
arXiv
Journal

C++ code
Auslander's Theorem for permutation actions on noncommutative algebras

with Jason Gaddis, Ellen Kirkman, and W. Frank Moore.

*Proceedings of the American Mathematical Society* 147, no. 5, 1881–1896. (2019).
arXiv
Journal
Discriminants of Taft algebra smash products and applications

with Jason Gaddis and Daniel Yee.

*Algebras and Representation Theory*. (To appear).
arXiv
Journal
The noncommutative schemes of generalized Weyl algebras.

*Journal of Algebra* 506, 322–349. (2018).
arXiv
Journal
The Picard group of the graded module category of a generalized Weyl algebra.

*Journal of Algebra* 493, 89–134. (2018).
arXiv
Journal
A structure theorem for product sets in extra special groups

with Thang Pham, Michael Tait, and Le Anh Vinh.

*Journal of Number Theory* 184, 461–472. (2018).
arXiv
Journal
Partitions of *AG*(4,3) into maximal caps

with Michael Follett, Kyle Kalail, Elizabeth McMahon, and Catherine Pelland.

*Discrete Mathematics* 337, 1–8. (2014).
arXiv
Journal
The graded module category of a generalized Weyl algebra. Ph.D. thesis, University of California, San Diego (2016).
pdf
eScholarship

**F**_{3}^{n}with Yixuan (Alice) Huang and Michael Tait.

*Involve, a Journal of Mathematics*. (To appear).Alice is a Wake Forest undergraduate who was awarded a Wake Forest Research Fellowship to work with me during the summer of 2018. She presented a poster at Wake Forest's Undergraduate Research Day.

C++ code

with Jason Gaddis, Ellen Kirkman, and W. Frank Moore.

*Proceedings of the American Mathematical Society*147, no. 5, 1881–1896. (2019).with Jason Gaddis and Daniel Yee.

*Algebras and Representation Theory*. (To appear).*Journal of Algebra*506, 322–349. (2018).*Journal of Algebra*493, 89–134. (2018).with Thang Pham, Michael Tait, and Le Anh Vinh.

*Journal of Number Theory*184, 461–472. (2018).*AG*(4,3) into maximal capswith Michael Follett, Kyle Kalail, Elizabeth McMahon, and Catherine Pelland.

*Discrete Mathematics*337, 1–8. (2014).### Preprints

#####
Simple **Z**-graded domains of Gelfand-Kirillov dimension two

with Luigi Ferraro and Jason Gaddis.
arXiv
Three infinite families of reflection Hopf algebras

with Luigi Ferraro, Ellen Kirkman, and W. Frank Moore.
arXiv
Fixed rings of generalized Weyl algebras

with Jason Gaddis.
arXiv

**Z**-graded domains of Gelfand-Kirillov dimension twowith Luigi Ferraro and Jason Gaddis.

with Luigi Ferraro, Ellen Kirkman, and W. Frank Moore.

with Jason Gaddis.

### Invited Talks

#####
"The card game SET, finite affine geometry, and combinatorial number theory"

Portland State University Colloquium, Portland, OR, May 2019
Slides
"A translation principle for generalized Weyl algebras"

AMS Central/Western Sectional Meeting, Honolulu, HI, March 2019
Abstract
Slides
"**Z**-graded noncommutative algebraic geometry"

University of Washington Algebra/Algebraic Geometry Seminar, Seattle, WA, February 2018
Slides
"Simple **Z**-graded domains of Gelfand-Kirillov dimension 2"

AMS-MAA Joint Mathematics Meetings, San Diego, CA, January 2018
Abstract
Slides
"**Z**-graded noncommutative algebraic geometry"

Miami University Colloquium, Oxford, OH, November 2017
Slides
"Noncommutative invariant theory and Auslander's Theorem"

Miami University Algebra Seminar, Oxford, OH, November 2017
Slides
"Discriminants of Taft algebra smash products and applications"

AMS Central Sectional Meeting, Denton, TX, September 2017
Abstract
Slides
"Auslander's Theorem for permutation actions on noncommutative algebras"

AMS Western Sectional Meeting, Pullman, WA, April 2017
Abstract
Slides
"The noncommutative schemes of generalized Weyl algebras"

AMS Western Sectional Meeting, Denver, CO, October 2016
Abstract
Slides
"The noncommutative schemes of generalized Weyl algebras"

AMS Eastern Sectional Meeting, Brunswick, ME, September 2016
Abstract
Slides
"The category of graded modules of a generalized Weyl algebra"

AMS Central Sectional Meeting, East Lansing, MI, March 2015
Abstract
Slides

Portland State University Colloquium, Portland, OR, May 2019

AMS Central/Western Sectional Meeting, Honolulu, HI, March 2019

**Z**-graded noncommutative algebraic geometry"University of Washington Algebra/Algebraic Geometry Seminar, Seattle, WA, February 2018

**Z**-graded domains of Gelfand-Kirillov dimension 2"AMS-MAA Joint Mathematics Meetings, San Diego, CA, January 2018

**Z**-graded noncommutative algebraic geometry"Miami University Colloquium, Oxford, OH, November 2017

Miami University Algebra Seminar, Oxford, OH, November 2017

AMS Central Sectional Meeting, Denton, TX, September 2017

AMS Western Sectional Meeting, Pullman, WA, April 2017

AMS Western Sectional Meeting, Denver, CO, October 2016

AMS Eastern Sectional Meeting, Brunswick, ME, September 2016

AMS Central Sectional Meeting, East Lansing, MI, March 2015

### Other Talks

#####
"SET and *AG*(4,3)"

Wake Forest Combinatorics Seminar, Winston-Salem, NC, October 2016
Slides
"Categories of graded modules: What they are and what you can do with them"

GradSWANTAG III, La Jolla, CA, May 2016
"The graded module category of a generalized Weyl algebra"

UC San Diego Final Defense, La Jolla, CA, May 2016
Abstract
Slides
"The category of graded modules of a generalized Weyl algebra"

AMS-MAA Joint Mathematics Meetings, Seattle, WA, January 2016
Abstract
Slides
"**Z**-graded noncommutative projective geometry"

UC San Diego Algebra Seminar, La Jolla, CA, November 2015
Abstract
Slides

Pre-talk
"What is noncommutative algebraic geometry?"

UC San Diego Graduate Algebraic Geometry Seminar, La Jolla, CA, August 2015
Slides
"A (gentle) introduction to Hopf algebras"

UC San Diego Informal Noncommutative Algebra Seminar, La Jolla, CA, June 2015
"SET and *AG*(4,3)"

UC San Diego Food For Thought Seminar, La Jolla, CA, February 2015
Abstract
Slides
"Graded modules over generalized Weyl algebras"

UC San Diego Advancement to Candidacy, La Jolla, CA, December 2014
Slides
"SET and disjoint complete caps in *AG*(4,3)"

AMS-MAA Joint Mathematics Meetings, New Orleans, LA, January 2011
Abstract

*AG*(4,3)"Wake Forest Combinatorics Seminar, Winston-Salem, NC, October 2016

GradSWANTAG III, La Jolla, CA, May 2016

UC San Diego Final Defense, La Jolla, CA, May 2016

AMS-MAA Joint Mathematics Meetings, Seattle, WA, January 2016

**Z**-graded noncommutative projective geometry"UC San Diego Algebra Seminar, La Jolla, CA, November 2015

Pre-talk

UC San Diego Graduate Algebraic Geometry Seminar, La Jolla, CA, August 2015

UC San Diego Informal Noncommutative Algebra Seminar, La Jolla, CA, June 2015

*AG*(4,3)"UC San Diego Food For Thought Seminar, La Jolla, CA, February 2015

UC San Diego Advancement to Candidacy, La Jolla, CA, December 2014

*AG*(4,3)"AMS-MAA Joint Mathematics Meetings, New Orleans, LA, January 2011

### Non-math Publications

#####
Appelbaum, L.G., Boehler, C.N., Davis, L.A., **Won, R.J.**, Woldorff, M.G. (2014). "The dynamics
of proactive and reactive cognitive control processes in the human brain". *Journal of Cognitive
Neuroscience*. 26(5), 1021–1038.
PubMed
Journal
Appelbaum, L.G., Boehler, C.N., **Won, R.J.**, Davis, L.A., Woldorff, M.G. (2012). "Strategic
Allocation of Attention Reduces Temporally Predictable Stimulus Conflict". *Journal of Cognitive Neuroscience*. 24(9), 1834–1848.
PubMed
Journal

**Won, R.J.**, Woldorff, M.G. (2014). "The dynamics of proactive and reactive cognitive control processes in the human brain".*Journal of Cognitive Neuroscience*. 26(5), 1021–1038.**Won, R.J.**, Davis, L.A., Woldorff, M.G. (2012). "Strategic Allocation of Attention Reduces Temporally Predictable Stimulus Conflict".*Journal of Cognitive Neuroscience*. 24(9), 1834–1848.