MEL HOCHSTER
Address:

Mathematics Department
University of Michigan
East Hall
530 Church Street
Ann Arbor, MI 481091043 USA

Email:
hochster@umich.edu
Office: Room 3078 East Hall
Office Phone: (734) 7644924
To leave messages: (734) 7640335
Department FAX: (734) 7630937

Title: Jack E. McLaughlin Distinguished University Professor of Mathematics
The author's research and expository papers on this site as well as 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 DMS1902116 and the two most recent previous grants were DMS1401384 and DMS0901145.
Research profile ·
Bibliography
·
CV ·
Ph.D. students
Expository mss. ·
Research mss. ·
Web Pages for Courses
Some other sites
ADVANCE and
STRIDE
at UM
Some recent manuscripts:
Tight closure in equal characteristic 0 and open questions in all characteristics, slides for a talk at the ICTP Graduate Course on Tight Closure of Ideals and Its Applications, given July 25, 2022.
Frobenius splitting, strong Fregularity, and small CohenMacaulay modules
(with Y.Yao), preprint, February, 2022.
A Jacobian criterion for nonsingularity in mixed characteristic
(with J. Jeffries), preprint, June, 2021.
Frational signature and drops in the HilbertKunz multiplicity
(with Y. Yao), Algebra & Number Theory, to appear.
Extensions of primes, flatness, and intersection flatness
(with J. Jeffries), in "Commutative Algebra: 150 years with Roger and Sylvia Wiegand," Contemporary Mathematics Volume 773 , 2021, 6381.
The mathematical contributions of Craig Huneke
(with B. Ulrich), J. Algebra 571 (2021) 114. [Expository]
Faithfulness of top local cohomology modules in domains
(with J. Jeffries), Math. Res. Letters 27 (2020) 17551765
The EisenbudGreenHarris conjecture for defect two quadratic ideals
(with S. Güntürkün), Math. Res. Lett. Math. 27 (2020) 13411365.
Universal lex approximations of extended Hilbert functions and Hamilton numbers
(with T. Ananyan), Journal of Algebra 560 (2020) 10531074.
Strength conditions, small subalgebras, and Stillman bounds
in dimension ≤ 4
(with T. Ananyan), Trans. of the Amer. Math. Soc. 373 (2020), 47574806;
Corrigendum , 374 (2021), 83078308.
Small subalgebras of polynomial rings and
Stillman's conjecture (with T. Ananyan), Journal of the Amer. Math. Soc. 33 (2019) 291309.
Finiteness properties and numerical behavior of local cohomology Communications in Algebra,
47 (2019) 111. [In honor of Gennady Lyubeznik. Primarily expository.]
Content of local cohomology,
parameter ideals, and robust algebras (with W. Zhang), Trans. Amer. Math. Soc. 370 (2018), 77897814.
Continuous closure, natural closure, and axes closure,
(with N. Epstein), Trans. Amer. Math. Soc. 370 (2018), 33153362.
On the support of local cohomology via Frobenius (with L. NúñezBetancourt), Math. Res. Letters. Vol. 24 (2017), pp. 401420.
Homological conjectures and lim CohenMacaulay sequences
, in Homological and Computational Methods in Commutative Algebra, Springer INdAM Series 20, Springer, 2017, pp. 181197. [In honor of Winfried Bruns. Primarily expository.]
CohenMacaulay varieties, geometric complexes and combinatorics, in The Mathematical Legacy of Richard P. Stanley, AMS, Providence, R.I., 2016,
203229.
Math 615, Winter 2022
Math 614, Fall 2020
Math 615, Winter 2020
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: Foundations of Tight Closure Theory
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
W2003)
VIGRE Algebra QR Review Material:
Fall 2002
Fall 2003
Jan. '04 sol'ns
May '04 sol'ns
Sept. '04 sol'ns
Jan. '05 sol'ns
Going bats? No, just the Fermat surface x^{3} + y^{3} = z^{3}.