MEL HOCHSTER

Address:     
Mathematics Department
University of Michigan
East Hall
530 Church Street
Ann Arbor, MI 48109-1043 USA     
E-mail:     hochster@umich.edu
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 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 DMS-1902116 and the two most recent previous grants were DMS-1401384 and DMS-0901145.

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 F-regularity, and small Cohen-Macaulay modules (with Y.Yao), preprint, February, 2022.
A Jacobian criterion for nonsingularity in mixed characteristic (with J. Jeffries), preprint, June, 2021.
F-rational signature and drops in the Hilbert-Kunz 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, 63-81.
The mathematical contributions of Craig Huneke (with B. Ulrich), J. Algebra 571 (2021) 1-14. [Expository]
Faithfulness of top local cohomology modules in domains (with J. Jeffries), Math. Res. Letters 27 (2020) 1755-1765
The Eisenbud-Green-Harris conjecture for defect two quadratic ideals (with S. Güntürkün), Math. Res. Lett. Math. 27 (2020) 1341--1365.
Universal lex approximations of extended Hilbert functions and Hamilton numbers (with T. Ananyan), Journal of Algebra 560 (2020) 1053-1074.
Strength conditions, small subalgebras, and Stillman bounds in dimension ≤ 4 (with T. Ananyan), Trans. of the Amer. Math. Soc. 373 (2020), 4757-4806; Corrigendum , 374 (2021), 8307-8308.
Small subalgebras of polynomial rings and Stillman's conjecture (with T. Ananyan), Journal of the Amer. Math. Soc. 33 (2019) 291-309.
Finiteness properties and numerical behavior of local cohomology Communications in Algebra, 47 (2019) 1-11. [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), 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, 203-229.

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

A3

Going bats? No, just the Fermat surface x3 + y3 = z3.