**Abstract:**

This is a writeup of the help session that I led at MSRI in September 2003 after Mel Hochster’s lectures on tight closure.

**Notes:**

This isn’t really a proper paper. It’s a reworked version of the notes that I used when I ran a help session at the Introductory Workshop that MSRI had at the beginning of the 2002-2003 Special Year in Commutative Algebra. The workshop consisted of series of lectures by Mel Hochster, Mark Haiman, Dave Benson, Rob Lazarsfeld, David Eisenbud, and Bernard Teissier, and each of them had a “helper”, who gave a single help session. The idea of the help session was that senior mathematicians were not allowed, and participation from the younger participants was explicitly encouraged. I was Mel Hochster’s “helper”, and rambled on for an hour about how hard it is to compute examples in tight closure. I’ve never worked in tight closure, so it was a fun session to prepare and a very hard paper to write.

**Bibtex code:**

@incollection {MR2132652, AUTHOR = {Hochster, Melvin}, TITLE = {Tight closure theory and characteristic {$p$} methods}, BOOKTITLE = {Trends in commutative algebra}, SERIES = {Math. Sci. Res. Inst. Publ.}, VOLUME = {51}, PAGES = {181–210}, NOTE = {With an appendix by Graham J. Leuschke}, PUBLISHER = {Cambridge Univ. Press}, ADDRESS = {Cambridge}, YEAR = {2004}, MRCLASS = {13A35}, MRNUMBER = {MR2132652}, }