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Advances in Algebra and Geometry |
| April 28, 2007 to May 04, 2007 |
| Organized By: David Ellwood, Joe Harris, Craig Huneke, Hugo Rossi, Frank-Olaf Schreyer, Bernd Sturmfels, Julius Zelmanowitz |
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| Return to Workshop Description |
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Stanley decompositions
Tuesday May 1, 2007
11:00AM - 12:00PM
Speakers:
Juergen Herzog
Abstract:
We discuss the widely open conjecture of Stanley concerning the socalled Stanley decompositions of Zn-graded modules. This conjecture predicts a combinatorial description of the depth of such modules. We also discuss its relationship to prime filtrations and show that Stanley’sc onjecture implies a another conjecture of Stanley on partitionable simplicial complexes. Finally I report on recent work of my student Soleyman Jahan who showed, using Alexander duality, that for squarefree monomial ideals Stanley’s conjecture can be reinterpreted to give a conjecture relating the regularity of such ideals to data of its Stanley decomposition. This leads to a new conjecture predicting a combinatorial description of regularity of general Zn-graded modules.
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