Office phone: (858) 534-4421

(Webpage will appear shortly before Fall quarter starts. Please contact me if you have questions about the course.)

Spring 2014: Math 103b (Modern Algebra II)

Winter 2014: Math 142a (Introduction to Analysis I)

Winter 2014: Math 201a (Topics in Algebra: Lie Algebras)

Fall 2012: Math 200a (Graduate Algebra)

Fall 2012: Math 103a (Applied Modern Algebra)

Spring 2012: Math 200c (Graduate Algebra)

Winter 2012: Math 200b (Graduate Algebra)

Winter 2012: Math 207a (Topics in algebra: an introduction to noncommutative rings)

Fall 2011: Math 200a (Graduate Algebra)

Spring 2011: Math 200c (Graduate Algebra)

Spring 2011: Math 207c (Topics in algebra: representations of quivers)

Winter 2011: Math 200b (Graduate Algebra)

Spring 2010: Math 20c (Multivariable calculus)

Winter 2010: Math 109 (Mathematical Reasoning)

Winter 2010: Math 100b (Abstract Algebra II)

Fall 2009: Math 100a (Abstract Algebra I)

Spring 2009: Math 201b (Polynomial Identity Algebras)

Spring 2009: math 200b (Graduate Algebra)

Winter 2009: Math 20b (Integral Calculus)

Fall 2008: Math 200a (Graduate Algebra)

Winter 2008: Math 20d (Differential Equations)

Winter 2008: Math 103b (Applied Modern Algebra II)

Fall 2007: Math 20b (Integral Calculus)

Fall 2007: Math 103a (Applied Modern Algebra I)

Spring 2007: Math 207b (The representation theory of quivers) course handout

Winter 2007: Math 207a (An introduction to Noncommutative Projective Geometry).

Winter 2007: Math 109 (Mathematical Reasoning)

Fall 2006: Math 103a (Applied Modern Algebra I)

Spring 2006: Math 109 (Mathematical Reasoning)

Winter 2006: Math 103b (Applied Modern Algebra II)

Fall 2005: Math 103a (Applied Modern Algebra I)

(with M. Reyes and J. J Zhang), "Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras", preprint. Available at www.arxiv.org, arXiv:1408.0536.

(with J. Bell), "Z-graded simple rings", preprint. To appear in Trans. Amer. Math. Soc. Available at www.arxiv.org, arXiv:1310.5406.

(with S. Sierra and J. T. Stafford), "Classifying orders in the Sklyanin algebra", preprint. Available at www.arxiv.org, arXiv:1308.2213

(with S. Sierra and J. T. Stafford), "Noncommutative blowups of elliptic algebras", preprint. Available at www.arxiv.org, arXiv:1308.2216.

(with M. Reyes and J. J Zhang), "Skew Calabi-Yau algebras and homological identities", preprint. To appear in Adv. Math. Available at www.arxiv.org, arXiv:1302.0437.

(with S. Sierra and J. T. Stafford), "Algebras in which every subalgebra is noetherian", preprint. To appear in Proceedings of the AMS. Available at www.arxiv.org, arXiv:1112.3869.

(with J. Bell), "Free subalgebras of division rings over uncountable fields", preprint. 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.

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. dvi , 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. dvi , pdf

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