Daniel Rogalski

Associate Professor of Mathematics

5131 Applied Physics and Mathematics Building (AP&M)
Office phone: (858) 534-4421
drogalsk "at" math.ucsd.edu

Conferences

I organize the Southern California Algebra Conference (SCAC), which is a twice-yearly one-day algebra meeting, usually at UCLA. Please contact me if you would like to be on the mailing list. The last meeting was April 18, 2011. For more information, please visit the conference web page:

SCAC website

Teaching

Winter 2012:

Math 200b (Graduate Algebra)
Math 207a (Topics in algebra: an introduction to noncommutative rings)


Past quarters:

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)

Research

My research is about noncommutative ring theory and noncommutative projective geometry. Here is a list of preprints and publications.

(with J. Bell), "Free subalgebras of quotient rings of Ore extensions", preprint. Available at www.arxiv.org, arXiv:1101.5829.

(with S. Sierra), "Some projective surfaces of GK-dimension 4", preprint. Available at www.arxiv.org, arXiv:1101.0737.

(with J. J. Zhang), "Regular algebras of dimension 4 with 3 generators", preprint. To appear in Contemporary Mathematics. 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", to appear in Adv. Math. Also 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. Also available at www.arxiv.org, arXiv:0812.3355.

"GK-dimension of birationally commutative surfaces", Trans. Amer. Math. Soc. 361 (2009), no. 11, 5921--5945. Also 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. Also 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. Also 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. Also 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. Also 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. Also available at www.arxiv.org, arXiv:math/0306244.

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

"Generic Noncommutative Surfaces,'' Adv. Math 184 (2004), no.2, 289-341. Also 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

CV

Here is an (outdated) copy of my cv if you are interested.