## Publications and Preprints

"Artin-Schelter regular algebras", survey article to appear in Contemporary Mathematics. Preliminary version available at www.arxiv.org, arXiv:2307.03174.

(With Sue Sierra and Toby Stafford), "Ring-theoretic blowing down II: birational transformations", to appear in Journal of Noncommutative Geometry. Preliminary version available at www.arxiv.org, arXiv:2107.01991.

(with Rob Won and James Zhang), "A proof of the Brown--Goodearl Conjecture for weak Hopf algebras",
Algebra Number Theory **15** (2021) no. 4, 971--997.
Preliminary version available at www.arxiv.org, arXiv:1912.11922.

(with Jason Gaddis), "Quivers supporting twisted Calabi-Yau algebras",
J. Pure Appl. Algebra **225** (2021), no. 9, Paper No. 106645, 33 pp.
Preliminary version available at www.arxiv.org, arXiv:1809.10222.

"Stably noetherian algebras of polynomial growth", Alg. Rep. Theory,
**24** (2021), no. 2, 519--540.
Preliminary version available at www.arxiv.org, arXiv:1810.05769.

(with Manny Reyes), "Graded twisted Calabi-Yau algebras are generalized Artin-Schelter regular",
Nagoya Math. J., **245** (2022), 100--153.
Preliminary version available at www.arxiv.org, arXiv:1807.10249.

(with S. Sierra and J. T. Stafford), "Noncommutative minimal surfaces", Adv. Math, **369**
(2020), 107151, 48 pp.
Preliminary version available at www.arxiv.org, arXiv:1807.09889.

(with Manny Reyes), "Growth of graded twisted Calabi-Yau algebras",
J. Algebra **539** (2019), 201–-259.
Preliminary version available at www.arxiv.org, arXiv:1808.10538.

"Well-closed subschemes of noncommutative schemes",
Theory Appl. Categ. **34** (2019), Paper No. 14, 375–-404.
Preliminary version available at www.arxiv.org, arXiv:1707.07052.

(with G. Bellamy, T. Schedler, J. T. Stafford, and M. Wemyss), "Noncommutative algebraic geometry", Mathematical Sciences Research Institute Publications 64, Cambridge University Press, Cambridge, 2016. Preliminary version of Rogalski's chapter available at www.arxiv.org, arXiv:1403.3065.

(with S. Sierra and J. T. Stafford), "Ring-theoretic blowing down: I",
J. Noncommut. Geom. **11** (2017), no. 4, 1465–-1520.
Available at www.arxiv.org, arXiv:1603.08128.

(with M. Reyes and J. J Zhang), "Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras",
Trans. Amer. Math. Soc. **369** (2017), no. 1, 309--340.
Preliminary version available at www.arxiv.org, arXiv:1408.0536.

(with J. Bell), "Z-graded simple rings",
Trans. Amer. Math. Soc. **368** (2016), no. 6, 4461--4496.
Preliminary version available at www.arxiv.org, arXiv:1310.5406.

(with S. Sierra and J. T. Stafford), "Classifying orders in the Sklyanin algebra",
Algebra Number Theory **9** (2015),
no. 9, 2055--2119. Preliminary version available at www.arxiv.org, arXiv:1308.2213.

(with S. Sierra and J. T. Stafford), "Noncommutative blowups of elliptic algebras", Algebr. Represent. Theory **18**, (2015), no. 2, 491--529.
Preliminary version available at www.arxiv.org, arXiv:1308.2216.

(with M. Reyes and J. J Zhang), "Skew Calabi-Yau algebras and homological identities", Adv. Math. **264**, (2014), 308--354.
Preliminary version available at www.arxiv.org, arXiv:1302.0437.

(with S. Sierra and J. T. Stafford), "Algebras in which every subalgebra is noetherian", Proc. Amer. Math. Soc. **142**, (2014), no. 9, 2983--2990.
Preliminary version available at www.arxiv.org, arXiv:1112.3869.

(with J. Bell), "Free subalgebras of division rings over uncountable fields", Math Z. **277**, (2014), no. 1-2, 591--609.
Preliminary version available at www.arxiv.org, arXiv:1112.0041.

(with J. Bell), "Free subalgebras of quotient rings of Ore extensions", Algebra Number Theory **6**, (2012), no. 7, 1349--1368.
Preliminary version available at www.arxiv.org, arXiv:1101.5829.

(with S. Sierra), "Some projective surfaces of GK-dimension 4", Compositio Math., **148**, (2012), no. 4, 1195--1237.
Preliminary version available at www.arxiv.org, arXiv:1101.0737.

(with J. J. Zhang), "Regular algebras of dimension 4 with 3 generators", New trends in noncommutative algebra, Contemp. Math., **562**, (2012), 221--241.
Preliminary version available at www.arxiv.org, arXiv:1101.1998.

####
We wrote some Maple programs which were used in the calculations in the preceding paper. We
make these programs freely available here; click on the following link:

Maple programs for "Regular algebras of dimension 4 with 3 generators"

"Blowup subalgebras of the Sklyanin algebra". Adv. Math., **226**, (2011), no. 2, 1433--1473. Preliminary version
available at www.arxiv.org, arXiv:0912.2304.

(with J. Bell and S. J. Sierra), "The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings", Israel J. Math.**180** (2010), no. 1, 461--507. Preliminary version available at www.arxiv.org, arXiv:0812.3355.

"GK-dimension of birationally commutative surfaces", Trans. Amer. Math. Soc. **361** (2009), no. 11, 5921--5945. Preliminary version available at
www.arxiv.org, arXiv:0707.3643.

(with J. T. Stafford), "Naive noncommutative blowups at zero-dimensional schemes", J. Algebra **318** (2007), no.
2, 794--833. Preliminary version available at www.arxiv.org, arXiv:math/0612658.

(with J.T. Stafford), "Naive noncommutative blowups at zero-dimensional schemes: An Appendix". This is a brief (unpublished) appendix to the preceding paper containing full proofs of a few of the more peripheral results. pdf

(with J. T. Stafford), "A Class of Noncommutative Projective Surfaces", Proc. Lond. Math. Soc. **99** (2009), no. 1, 100--144.
Preliminary version available at www.arxiv.org, arXiv:math/0612657.

(with J. J. Zhang), "Canonical Maps to Twisted Rings'', Math. Z. **259** (2008), no. 2, 433--455.
Preliminary version available at www.arxiv.org, arXiv:math/0409405.

(with Z. Reichstein and J. J. Zhang), "Projectively Simple Rings'', Adv. Math, **203** (2006), no. 2, 365-407. Preliminary version available at
www.arxiv.org, arXiv:math/0401098.

(with D.S. Keeler and J. T. Stafford), "Naive Noncommutative Blowing up'', Duke Math J. **126** (2005),
no. 3, 491-546. Preliminary version available at www.arxiv.org, arXiv:math/0306244.

"Idealizer Rings and Noncommutative Projective Geometry,'' J. Algebra **279** (2004),
no. 2, 791-809. Preliminary version available at www.arxiv.org, arXiv:math/0305002.

"Generic Noncommutative Surfaces,'' Adv. Math **184** (2004), no.2, 289-341. Preliminary version
available at www.arxiv.org, arxiv:math/0203180.

"Examples of Generic Noncommutative Surfaces", University of Michigan PhD thesis. This contains more background and some extra results not included in the paper "Generic Noncommutative Surfaces" above. pdf