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Commutative Algebra and Noncommutative Algebraic Geometry

Volume 2. Research Articles

Part of Mathematical Sciences Research Institute Publications

Editors:
David Eisenbud, University of California, Berkeley
Srikanth B. Iyengar, University of Utah
Anurag K. Singh, University of Utah
J. Toby Stafford, University of Manchester
Michel Van den Bergh, Fonds Wetenschappelijk Onderzoek (FWO), Belgium

David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford, Michel Van den Bergh, Ali Alilooee, Sara Faridi, David J. Benson, Andrew Berget, Winfried Bruns, Aldo Conca, Kenneth A. Brown, Kenneth R. Goodearl, Jesse Burke, Greg Stevenson, Lawrence Ein, Shihoko Ishii, Louiza Fouli, Milen T. Yakilmov, William Heinzer, Christel Rotthaus, Sylvia Wiegand, Jürgen Herzog, Takayuki Hibi, Leila Sharifan, Matteo Varbaro, Hema Srinivasan, Manoj Kummini, Steven V. Sam, Joseph Lipman

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Date Published: November 2015
availability: Available
format: Hardback
isbn: 9781107149724

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Description

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. Volume 2 focuses on the most recent research.
- High-quality articles survey the current state of knowledge in this extremely active field
- Focuses on areas of common interest which emphasise the lively interaction between commutative algebra and noncommutative algebraic geometry
- Valuable to researchers and graduate students studying algebra and algebraic geometry
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Product details
- Date Published: November 2015
- format: Hardback
- isbn: 9781107149724
- length: 302 pages
- dimensions: 234 x 156 x 18 mm
- weight: 0.6kg
- contains: 10 b/w illus.
- availability: Available
Table of Contents
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 Jürgen Herzog and Takayuki Hibi
11. An intriguing ring structure on the set of d-forms Jürgen Herzog, Leila Sharifan and Matteo Varbaro
12. On the subadditivity problem for maximal shifts in free resolutions Jürgen 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.
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Editors
David Eisenbud, University of California, Berkeley
David Eisenbud is a Professor in the Department of Mathematics at the University of California, Berkeley.
Srikanth B. Iyengar, University of Utah
Srikanth B. Iyengar is a Professor in the Department of Mathematics at the University of Utah.
Anurag K. Singh, University of Utah
Anurag K. Singh is a Professor in the Department of Mathematics at the University of Utah.
J. Toby Stafford, University of Manchester
J. Toby Stafford is a Professor in the Department of Mathematics at the University of Manchester.
Michel Van den Bergh, Fonds Wetenschappelijk Onderzoek (FWO), Belgium
Michel Van den Bergh is Director of Research at the Research Foundation - Flanders (FWO) in Belgium.
Series editor Cam Learning use ONLY
Mathematical Sciences Research Institute
Contributors
David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford, Michel Van den Bergh, Ali Alilooee, Sara Faridi, David J. Benson, Andrew Berget, Winfried Bruns, Aldo Conca, Kenneth A. Brown, Kenneth R. Goodearl, Jesse Burke, Greg Stevenson, Lawrence Ein, Shihoko Ishii, Louiza Fouli, Milen T. Yakilmov, William Heinzer, Christel Rotthaus, Sylvia Wiegand, Jürgen Herzog, Takayuki Hibi, Leila Sharifan, Matteo Varbaro, Hema Srinivasan, Manoj Kummini, Steven V. Sam, Joseph Lipman