CONNECTIONS BETWEEN ALGEBRA, COMBINATORICS, AND GEOMETRY

- Provides a snapshot of research in the intersections among algebra, combinatorics, and geometry, three areas of mathematics with a rich history of interaction.
- Includes exercises and solutions that will be useful for coursework and self-study.
- Each chapter is authored by top researchers in their field.
Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

Table of contents (9 chapters)
1.A Somewhat Gentle Introduction to Differential Graded Commutative Algebra
2.Four Lectures on Secant Varieties
3.Regina Lectures on Fat Points
4.A Good Leaf Order on Simplicial Trees
5.A Survey of Stanley–Reisner Theory
6.Numerical Computation of the Hilbert Function and Regularity of a Zero Dimensional Scheme
7.Regularity of Squarefree Monomial Ideals
8.Planar Graphs and the Koszul Algebra Structure for Trivariate Monomial Ideals
9.Non-Gorenstein Isolated Singularities of Graded Countable Cohen–Macaulay Type