Daniel Rogalski

Associate Professor of Mathematics

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

Teaching


Winter 2010:

Math 100b (Abstract Algebra II)

Math 109 (Mathematical Reasoning)


Past quarters:

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.

"Blowup subalgebras of the Sklyanin algebra", preprint. Available at www.arxiv.org, arXiv:0912.2304.

(with J. Bell and S. J. Sierra), "The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings", preprint. Available at www.arxiv.org, arXiv:0812.3355.

"GK-dimension of birationally commutative surfaces", preprint, to appear in Transactions of the AMS. 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 This is a brief (unpublished) appendix to the preceding paper containing full proofs of a few of the more peripheral results.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", preprint, to appear in Proceedings of the LMS. 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 a copy of my cv if you are interested.