Viviana Ene & Ezra Miller 
Multigraded Algebra and Applications [PDF ebook] 
NSA 24, Moieciu de Sus, Romania, Аugust 2016

This volume contains research papers and surveys reflecting the topics discussed at the EMS Summer School on Multigraded Algebra and Applications held in Romania in August 2016. The school, which served as the 24th National School on Algebra, presented the main research directions of combinatorial commutative algebra with a strong focus on its applications in combinatorics, statistics, and biology. Recent progress in the field has led to new insights and suggested algebraic techniques for solving real-world data analysis problems. The summer school and resulting proceedings volume have raised numerous novel questions and encouraged a more interdisciplinary approach for young researchers when considering problems in pure and applied mathematical research.






Featured topics in this volume include toric rings, binomial edge ideals, Betti numbers for numerical semigroup rings, and Waldschmidt constants. Researchers and graduate students interested in the developments of the field will find this book useful for their studies.  

Table of Content

Ambro, F: On Toric Face Rings II.- Bigdeli, M., Herzog, J. and Lu, D: Toric Rings, Inseparability and Rigidity.- Seyed Fakhari, S. A: On the Stanley Depth and the Schmitt–Vogel Number of Squarefree Monomial Ideals.- Saeedi Madani, S: Binomial Edge Ideals: A Survey.- Malara, G. and Szpond, J: On Codimension Two Flats in Fermat-type Arrangements.- Olteanu, O: The Monomial Ideal of Independent Sets Associated to a Graph.- Rychlewicz, K: A Bound on Degrees of Primitive Elements of Toric Ideals of Graphs.- Stamate, D. I: Betti Numbers for Numerical Semigroup Rings.- Szemberg, T. and Szpond, J: Waldschmidt Constants for Stanley-Reisner Ideals of a Class of Graphs.

About the author

Viviana Ene is a professor in the Faculty of Mathematics and Computer Science at Ovidius Universit in Constanta, Romania.




Ezra Miller is a professor in the Mathematics Department at Duke University.