SOME EXPOSITORY MANUSCRIPTS

Below are links for .pdf files of some expository manuscripts. The author's research in manuscripts on this site was all conducted while the author was partially supported by grants from the National Science Foundation. The current grant is DMS-1902116 and the two most recent previous grants were DMS-1401384 and DMS-0901145. The preprint versions posted here may not be identical with published versions.


Finiteness properties and numerical behavior of local cohomology Communications in Algebra, 47 (2019) 1-11. [In honor of Gennady Lyubeznik]


Homological conjectures and lim Cohen-Macaulay sequences , in Homological and Computational Methods in Commutative Algebra, Springer INdAM Series 20, Springer, 2017, pp. 181-197. [In honor of Winfried Bruns]


Cohen-Macaulay varieties, geometric complexes and combinatorics, in The Mathematical Legacy of Richard P. Stanley, AMS, Providence, R.I., 2016, 203-229.


Slides from a talk Ideals generated by quadratic polynomials given at the Midwest Commutative Algebra and Geometry Conference at Purdue on May 24, 2011


A composite version of the Lecture Notes for Math 711, Fall 2007 entitled Foundations of Tight Closure Theory, 276 pages.


An edited version of the slides used for a talk entitled Intersection Theorems at a conference in honor of the sixtieth birthday of Paul C. Roberts held at Snowbird, Utah, May 18-19, 2006.


An extended version of a talk Homological conjectues, old and new at a conference in honor of Phil Griffith at the University of Illinois, Urbana, September 16-18, 2005; to appear in the Illinois J. of Math.


An edited version of the file used for the transparencies for a talk entiteld Thirteen Open Questions in Commutative Algebra at a conference in honor of the sixty-fifth birthday of Joseph Lipman held at Purdue University, July, 2004.


A written version of three expository lectures given in September, 2002, as part of the Introductory Program for the year in Commutative Algebra at MSRI. Tight closure theory and characteristic p methods.  The paper, with an Appendix by Graham J. Leuschke, has appeared in Trends in Commutative Algebra, MSRI Pubications 51, Cambridge University Press, Cambridge, England, 2004, pp. 181-210.


Notes from a two lecture introduction to Grobner bases  given in the Student Combinatorics Seminar, September, 2003.


The text of a book review   of Multiplicities and Chern classes in local algebra by Paul C. Roberts (the review appeared in the Bulletin (New Series) of the Amer. Math. Soc. 38 (2001), pp. 83-92).


An exposition of Gabber's proof   of nonnegativity of intersection multiplicities using De Jong's results on alterations (an expansion of an article by Berthelot, but with some differences in the argument).


Why characteristic p is better   (text used to prepare transparencies for an invited address at the annual A.M.S. meeting in Baltimore on January 8, 1998).


The notion of tight closure in equal characteristic zero   (in Proc. of the CBMS Conference on Tight Closure and Its Applications Fargo, North Dakota, July, 1995), Appendix to the notes on the main lectures by Craig Huneke, C.B.M.S. Regional Conference Series, A.M.S., Providence, R.I., 1996.


The text of a book review   of Cohen-Macaulay rings by Winfried Bruns and Jurgen Herzog, containing an exposition, intended for readers with very modest background, of some material in this area (the review appeared in the Bulletin (New Series) of the Amer. Math. Soc. 32 (1995), pp. 265-275).


Tight closure in equal characteristic, big Cohen-Macaulay algebras, and solid closure   (in Commutative Algebra: Syzygies, Multiplicities and Birational Algebra, Contemp. Math. 159, Amer. Math. Soc., Providence, R. I., 1994, 173-196).