University of Michigan
530 Church Street
Ann Arbor, MI 48109-1043 USA
Office: Room 3078 East Hall
Office Phone: (734) 764-4924
To leave messages: (734) 764-0335
Department FAX: (734) 763-0937
Title: Jack E. McLaughlin Distinguished University Professor of Mathematics
The author's research papers on this site as well as the exposition in the lecture notes from advanced graduate courses were all
prepared while the author was partially supported by grants from the National Science Foundation. The current grant is
DMS-1401384 and the previous grant was DMS-0901145.
Research profile ·
Expository mss. ·
Research mss. ·
Web Pages for Courses
Some other sites
Some recent manuscripts:
Strength conditions, small subalgebras, and Stillman bounds
in dimension ≤ 4
(with T. Ananyan), preprint.
The Eisenbud-Green-Harris conjecture for defect two quadratic ideals}
(with S. Güntürkün), preprint.
Small subalgebras of polynomial rings and
Stillman's conjecture (with T. Ananyan), preprint.
Finiteness properties and numerical behavior of local cohomology to appear, Communications in Algebra.
[In honor of G. Lyubeznik. Primarily expository.]
Content of local cohomology,
parameter ideals, and robust algebras (with W. Zhang), Trans. Amer. Math. Soc. 370 (2018), 7789-7814.
Continuous closure, natural closure, and axes closure,
(with N. Epstein), Trans. Amer. Math. Soc. 370 (2018), 3315-3362.
On the support of local cohomology via Frobenius (with L. Núñez-Betancourt), Math. Res. Letters. Vol. 24 (2017), pp. 401-420.
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. Primarily expository.]
Cohen-Macaulay varieties, geometric complexes and combinatorics, in The Mathematical Legacy of Richard P. Stanley, AMS, Providence, R.I., 2016,
Math 615, Winter 2019
Math 614, Fall 2017
Math 615, Winter 2017 Math 615, Winter 2016 Math 614, Fall 2015
Math 615, Winter 2015
Math 615, Winter 2014
Math 614, Fall 2013
Math 614, Fall 2012
Math 615, Winter 2012
Math 615, Winter 2011
Math 614, Fall 2010
Math 615, Winter 2010
Math 614, Fall 2008
Math 711, Fall 2007
Math 615, Winter 2007
Math 711, Fall 2006
Math 711, Fall 2005 - Commutative Algebra Seminar, Winter 2006
Math 711, Fall 2004
Math 615, Winter 2004
Math 614, Fall 2003
Tight Closure Lectures (Math 715 F2002, Seminar
VIGRE Algebra QR Review Material:
Jan. '04 sol'ns
May '04 sol'ns
Sept. '04 sol'ns
Jan. '05 sol'ns
Going bats? No, just the Fermat surface x3 + y3 = z3.