Daniel Rogalski

Associate Professor of Mathematics

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

UCSD Algebra Seminar

The UCSD Algebra seminar will meet certain Mondays in the fall 2014 and winter 2015 quarters. I maintain a webpage for the seminar here:


UCSD Algebra Seminar

The seminar will also appear in the list of all seminars for a given week on the UCSD Math department home page.

Teaching

Spring 2015:

Math 200c (Graduate Algebra III)




Past quarters:

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)

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

These notes are planned to be published as a book together with the lecture notes of the other courses at the workshop; further details TBA. Any comments on the notes are welcome.


Research

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

(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", preprint. To appear in Algebras and Rep. Theory. 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.

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


Conferences

In the past I have organized the Southern California Algebra Conference (SCAC), a one-day algebra meeting at UCLA. The last meeting was on April 27, 2013. For more information, please visit the conference web page:

SCAC website


CV

Here is a (current as of August 2014) 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