This contributed volume is a follow-up to the 2013 volume of the same title, published in honor of noted Algebraist David Eisenbud’s 65th birthday. It brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Category Theory, Combinatorics, Computational Algebra, Homological Algebra, Hyperplane Arrangements, and Non-commutative Algebra.
The book aims to showcase the area and aid junior mathematicians and researchers who are new to the field in broadening their background and gaining a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.
Table of Content
1. Berstein-Sato Polynomials in Commutative Algebra (J. Alvarez Montaner, J. Jeffries, L. Nunez-Betancourt).- 2. Lower Bounds on Betti Numbers (A. Boocher, E. Grifo).- 3. The Simplest Minimal Free Resolutions in P1 x P1 (N. Botbol, A. Dickenstein, H. Schenck).- 4. The Simplest Minimal Free Resolutions in P1 x P1 (W. Bruns, A. Conca, M. Varbaro).- 5.The Eisenbud-Green-Harris Conjecture (G. Caviglia, A. De Stefani, E. Sbarra).- 6. Fibers of Rational Maps and Elimination Matrices (M. Chardin, L. Buse).- 7. Three Takes on Almost Complete Intersection Ideals of Grade 3 (L.W. Christensen, O. Veliche, J. Weyman).- 8. Stickelberger and the Eigenvalue Theorem (D.A. Cox).- 9. Multiplicities and Mixed Multiplicities of Filtrations (S.D. Cutkosky, H. Srinivasan).- 10. Stanley-Reisner Rings (R. Froberg).- 11. Symbolic Rees Algebras (E. Grifo, A. Seceleanu).- 12. The Alexander-Hirschowitz Theorem and Related Problems (H. Tai Ha, P. Mantero).- 13. Depth Functions and Symbolic Depth Functions of Homogeneous Ideals (H. Tai Ha, N.V. Trung).- 14. Algebraic Geometry, Commutative Algebra, and Combinatorics (B. Harbourne).- 15. Maximal Cohen-Macaulay Complexes and Their Uses (S.B. Iyengar, L. Ma, K. Schwede, M.E. Walker).- 16. Subadditivity of Syzygies of Ideals and Related Problems (J. Mc Cullough).- 17. Applications of Liaison (J. Migliore, U. Nagel).- 18. Survey on Regularity of Symbolic Powers of an Edge Ideal (N.C. Minh, T. Vu).- 19. Applications of Differential Graded Algebra Techniques in Commutative Algebra (S. Nasseh, S.K. Sather-Wagstaff).- 20. Regularity Bounds by Projection (W. Niu).- 21. The Zariski-Riemann Space of Valuation Rings (B. Olberding).- 22. Rational Points and Trace Forms on a Finite Algebra Over a Real Closed Field (D.P. Patil, J.K. Verma).- 23. Diagrams in Commutative Algebra (I. Peeva).- 24. Hermite Reciprocity and Schwartzenberger Bundles (C. Raicu, S.V. Sam).- 25. Generation in Module Categories and Derived Categories of Commutative Rings (R. Takahashi).- 26.Existence and Constructions of Totally Reflexive Modules (A. Vraciu).- 27. Local Cohomology – An Invitation (U. Walther, W. Zhang).- 28. Which Properties of Stanley-Reisner Rings and Simplicial Complexes are Topological? (V. Welker).
About the author
Irena Peeva is a Professor of Mathematics at Cornell University. Her primary work is in Commutative Algebra, and her primary research is focused on Free Resolutions and Hilbert Functions. She is the author of Graded Syzygies (Springer, 2011), coauthor of Minimal Free Resolutions Over Complete Intersections (Springer, 2016), and the editor of Commutative Algebra (Springer, 2013).
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