Stanley-Reisner theory is a useful and beautiful area of mathematics involving elements of combinatorics, commutative algebra and topology (in no particular order). The goal of this seminar is to learn about the theory of Stanley-Reisner rings and complexes from the ground up, at a level accessible to graduate students.

Two sources for Stanley-Reisner theory are:

- R. Stanley,
__Combinatorics and Commutative Algebra__(Birkhauser) - W. Bruns and J. Herzog,
__Cohen-Macaulay Rings__(Cambridge)

All talks are on Thursdays, 11:15 AM - 12:05 PM, in 315 Lind Hall.

**17 October**

Speaker: Vic Reiner

"Introduction and motivation for Stanley-Reisner rings"

Scribe notes by Jeremy Martin:
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**24 October**

Speaker: Vic Reiner

"Introduction and motivation for Stanley-Reisner rings, II"

Scribe notes by Ning Jia:
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**31 October**

Speaker: Vic Reiner

"Introduction and motivation for Stanley-Reisner rings, III"

Scribe notes by John Hall:
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**7 November**

Speaker: Jeremy Martin

"Introduction to Gröbner bases, I"

Speaker's notes:
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**14 November**

Speaker: Jeremy Martin

"Introduction to Gröbner bases, II"

Speaker's notes:
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**21 November**

Speaker: Vic Reiner

"Free resolutions of Stanley-Reisner rings"

Scribe notes by Sandra Di Rocco (LaTeX'ed by Jeremy Martin):
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**28 November**

No seminar - Thanksgiving

**5 December**

Speaker: Anton Leykin

"Local cohomology"

Scribe notes by Jeremy Martin:
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**12 December**

Speaker: Anton Leykin

"Local cohomology, II"

See previous talk for scribe notes

Related material which may be of interest:
"Shellable complexes are Cohen-Macaulay" (notes by Jeremy Martin):
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*Last updated 12/12/02, 2:15 PM*