Commutative Algebra and Noncommutative Algebraic Geometry -

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Résumé :
In the 2012-13 academic year, the Mathematical Sciences Research Institute, Berkeley, hosted programs in Commutative Algebra (Fall 2012 and Spring 2013) and Noncommutative Algebraic Geometry and Representation Theory (Spring 2013). There have been many significant developments in these fields in recent years; what is more, the boundary between them has become increasingly blurred. This was apparent during the MSRI program, where there were a number of joint seminars on subjects of common interest: birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, and tilting theory, to name a few. These volumes reflect the lively interaction between the subjects witnessed at MSRI. The Introductory Workshops and Connections for Women Workshops for the two programs included lecture series by experts in the field. The volumes include a number of survey articles based on these lectures, along with expository articles and research papers by participants of the programs.

Sommaire:
Preface David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford and Michel Van den Bergh; 1. When is a squarefree monomial ideal of linear type? Ali Alilooee and Sara Faridi; 2. Modules for elementary abelian groups and hypersurface singularities David J. Benson; 3. Ideals generated by superstandard tableaux Andrew Berget, Winfried Bruns and Aldo Conca; 4. Zariski topologies on stratified spectra of quantum algebras Kenneth A. Brown and Kenneth R. Goodearl; 5. The derived category of a graded Gorenstein ring Jesse Burke and Greg Stevenson; 6. Singularities with respect to Mather?Jacobian discrepancies Lawrence Ein and Shihoko Ishii; 7. Reduction numbers and balanced ideals Louiza Fouli; 8. Unipotent and Nakayama automorphisms of quantum nilpotent algebras Kenneth R. Goodearl and Milen T. Yakilmov; 9. Formal fibers of prime ideals in polynomial rings William Heinzer, Christel Rotthaus and Sylvia Wiegand; 10. Bounding the socles of powers of squarefree monomial ideals J?rgen Herzog and Takayuki Hibi; 11. An intriguing ring structure on the set of d-forms J?rgen Herzog, Leila Sharifan and Matteo Varbaro; 12. On the subadditivity problem for maximal shifts in free resolutions J?rgen Herzog and Hema Srinivasan; 13. The cone of Betti tables over a rational normal curve Manoj Kummini and Steven V. Sam; 14. Adjoint associativity - an invitation to algebra in ?-categories Joseph Lipman.