Office phone: (858) 534-4421

Math 100a (Abstract Algebra I)

Webpages and syllabi for these courses will be available shortly before the fall quarter begins. If you have any urgent questions about the courses before then, please send me an e-mail.

Winter 2015: Math 200b (Graduate Algebra II)

Winter 2015: Math 109 (Mathematical Reasoning)

Fall 2014: Math 200a (Graduate Algebra I)

Spring 2014: Math 142b (Introduction to Analysis II)

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. To appear in Trans. Amer. Math. Soc. 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", 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.

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

UCSD Algebra Seminar

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