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Research
I conduct research in the fields of
algebraic topology
and algebra.
I've written a brief description (PDF file)
of some of my work; this is taken from a document (intended for a somewhat
general audience) that I wrote in 2001. Note that it focuses on my research,
and does not attempt to give a general overview of algebraic topology or stable
homotopy theory.
Slides from lectures
Papers and preprints
(These are listed with the most recent papers first, more or less.)
 30. Invariant theory for quantum Weyl
algebras under finite group action,
joint with S. Ceken, Y. Wang, J. J. Zhang, preprint
arXiv 1501.07881 (15 pages).
 Read the abstract.
 29. The discriminant criterion and automorphism
groups of quantized algebras,
joint with S. Ceken, Y. Wang, J. J. Zhang,
Advances in Mathematics 286 (2015), 754801
 Read the abstract
or until December 25,
download
the paper.
 28. The discriminant controls automorphism groups of noncommutative algebras,
joint with S. Ceken, Y. Wang, J. J. Zhang,
Advances in Mathematics 269 (2015), 551–584
 Read the abstract.
 27. Commutators in the Steenrod algebra,
joint with J. J. Zhang,
New York J. Math. 19 (2013), 2337
 Read the abstract, or
go to the article.
 26. The Bousfield lattice for truncated polynomial
algebras, joint with W. G. Dwyer, in Homology,
Homotopy, and Applications 10(1) (2008),
413436.
 Read the abstract, or
go to the
article
at the HHA website.
 25. The problem session, joint with Carles
Broto, Nguyen H V Hung, Nicholas J Kuhn, Stewart Priddy and
Nobuaki Yagita, in Geometry and Topology Monographs
11 (2007), 435441
 Go to the
article
at the Geometry and Topology website.
 24. Koszul equivalences in Ainfinity algebras,
joint with D.M. Lu, Q.S. Wu and J. J. Zhang,
New York J. Math. 14 (2008), 325378.
 Read the abstract or
go to the
article
at the New York Journal website.
 23. Ainfinity structure on Extalgebras,
joint with D.M. Lu, Q.S. Wu and J. J. Zhang, Journal of Pure
and Applied Algebra 213 (2009), 20172037.
 Read the abstract.
 22. A user's guide to the Bockstein spectral
sequence, preprint (2005), 7 pages.
 Read the abstract, or
download a dvi file or a
pdf file.
 21. The Lambda algebra and Sq^{0}, in
Geometry and Topology Monographs 11 (2007), 201216.
 Read the abstract, or
go to the
article
at the Geometry and Topology website.
 20. Some quotient Hopf algebras of the dual
Steenrod algebra, Trans. Amer. Math. Soc.
358 (2006), 671685.
 Read the abstract, or
download either a dvi file or a
pdf file.
 19. Regular algebras of dimension 4 and their
A_{oo}Extalgebras,
joint with D.M. Lu, Q.S. Wu and J. J. Zhang, Duke
Mathematical Journal 137 (2007), 537584.
 Read the abstract.
 18. A_{oo}algebras for ring theorists,
joint with D.M. Lu, Q.S. Wu and J. J. Zhang,
Algebra Colloquium 11 (2004), 91128.
 Read the abstract.
 17. There is no paper 17 at the moment.

 16. Stably thick subcategories of modules over Hopf
algebras,
joint with Mark Hovey, Math. Proc. Cambridge
Philos. Soc. 130 (2001) 441474.
 Read the abstract.
 15. Galois theory of thick subcategories in modular representation theory,
joint with Mark Hovey, J. Algebra
230 (2000), 713729.
 Read the abstract
 14. Ohkawa's theorem: there is a set of Bousfield classes,
joint with Bill Dwyer, Proc. Amer. Math. Soc.
129 (2001), 881886.
 Read the abstract or
or go the
issue of the Proceedings containing this article (at the AMS website).
 13. Stable homotopy over the Steenrod algebra,
Memoirs of the American Mathematical Society, volume
151, number 716 (2001).
 Read the abstract.
There is also a list of errata: dvi
file or pdf file.
 12. Vanishing lines in generalized Adams spectral sequences are generic,
joint with Mike Hopkins and Jeff Smith, Geometry and
Topology 3 (1999), 155165.
 Read the abstract or go
to the Geometry and Topology link to the paper.
 11. The structure of the Bousfield lattice, joint
with Mark Hovey, Homotopy invariant algebraic
structures (J.P. Meyer, J. Morava, and W. S. Wilson,
eds.), Contemp. Math., 239 (1999), 175196.
 Read the abstract.
 10. Quillen stratification for the Steenrod algebra,
Annals of Mathematics 149 (1999), 421449.
 Read the abstract or go
to the link to the paper at the Mathematics ArXiv.
There is also a list of errata: dvi
file or pdf file.
 9. Support varieties for the Steenrod algebra,
joint with Dan Nakano, Mathematische Zeitschrift
227 (1998), 663684.
 Read the abstract
or go to the article.
(at the SpringerVerlag website).
 8. Axiomatic stable homotopy theory, joint with
Mark Hovey and Neil P. Strickland, Memoirs of the American
Mathematical Society, volume 128, number 610 (1997).
 Read the abstract.
 7. A note on the cohomology of finitedimensional cocommutative Hopf algebras,
Journal of Algebra 188 (1997), 203215.
 Read the abstract.
 6. Nilpotence for modules over the mod 2 Steenrod algebra II,
Duke Mathematical Journal 82 (1996), 209226.
 Read the abstract.
 5. Nilpotence for modules over the mod 2 Steenrod algebra I,
Duke Mathematical Journal 82 (1996), 195208.
 Read the abstract.
 4. The chromatic filtration and the Steenrod algebra,
Topology and Representation Theory (E. Friedlander and
M. E. Mahowald, eds.), Contemp. Math. 158 (1994),
187201.
 Read the abstract.
 3. Self maps of spectra, a theorem of J. Smith, and Margolis' killing construction,
joint with Hal Sadofsky, Mathematische Zeitschrift
215 (1994), 477490.
 Read the abstract.
 2. A nilpotence theorem for modules over the mod 2 Steenrod algebra,
joint with Michael J. Hopkins, Topology 32
(1993), 751756.
 Read the abstract.
 1. Selfmaps of modules over the Steenrod algebra,
Journal of Pure and Applied Algebra 79
(1992), 281291.
 Read the abstract.
Notes:
 I no longer own the copyright on most of the published papers. So
for each of those, you will have to satisfy yourself with an abstract
and a pointer to its physical location. If you want copies,
email me and
I'll try to send you a reprint.
 For each of the unpublished papers, there is a link a pdf
file, which you can view onscreen or
download and print. If you have any problems doing these things,
email me and
I'll try to send you a preprint.
