Preface 1 Polyhedral Geometry and Linear Optimization 2 Commutative Algebra 3 Affine and Graded Algebras 4 Rees Algebras and Normality 5 Hilbert Series and Gorenstein Rings 6 Stanley–Reisner Rings and Edge Ideals 7 Edge Ideals of Graphs 8 Toric Ideals and Affine Varieties 9 Linear and Reed–Muller Type Codes 10 Monomial Subrings 11 Monomial Subrings of Graphs 12 Edge Subrings and Combinatorial Optimization 13 Normality of Rees Algebras of Monomial Ideals 14 Combinatorics of Symbolic Rees Algebras of Edge Ideals of Clutters 15 Combinatorial Optimization and Blowup Algebras 16 The Containment Problem and the Resurgence of Ideals A Procedures for Macaulay2 and Normaliz B Graph Diagrams Bibliography Notation Index Index
Biography
Rafael H. Villarreal is a Professor at Centro de Investigaci´on y de Estudios Avanzados del Instituto Polit´ecnico Nacional (Cinvestav), earned a Ph.D. degree from Rutgers University(1986). He has published 102 research papers in collaboration with 60 co-authors from various countries, has supervised 11 doctoral dissertations, and has systematically employed combinatorial and computational methods in commutative algebra, and its relation to toric ideals, polyhedral geometry, evaluation codes, combinatorial optimization, algebraic graph theory, graphs and clutters, and topics on monomial Cremona transformations.
