Daniel Rogalski

Associate Professor of Mathematics

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


Teaching

Spring 2014:

Math 142b (Introduction to Analysis II)

Math 103b (Modern Algebra II)


Past quarters:

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)

Lecture Notes

I wrote lecture notes, together with exercises, for a series of five lectures on noncommutative projective geometry which I gave at the MSRI graduate workshop in Berkeley in June 20 12. There is now a revised version as of March 2014 which replaces the version that was posted here (but is still not the final version):

MSRI course notes on noncommutative projective geometry

Any comments are welcome.


Research

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

(with J. Bell), "Z-graded simple rings", preprint. 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. 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. To appear in Math. Z. 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. 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


UCSD Algebra Seminar

The UCSD algebra seminar meets sporadically in the winter and spring quarters. Check the seminar listings on the math department home page.

Conferences

I organize the Southern California Algebra Conference (SCAC), which is a one-day algebra meeting at UCLA. Please contact me if you would like to be on the mailing list. The last meeting was on April 27, 2013. For more information, please visit the conference web page:

SCAC website


CV

Here is a (not necessarily current) copy of my cv if you are interested.

Advice on applying for research jobs

I wrote the following document for a panel aimed at graduate students weighing whether they might want a career as an academic research mathematician. It also contains advice about the specifics of the job application process. I don't claim to have any unique point of view on this, but some people have told me they found this document helpful.
Advice on research jobs