Combinatorial Structures In Algebra And Geometry: Nsa 26, Constanța, Romania, August 26–september 1, 2018 (springer Proceedings In Mathematics & Statistics (331))

"This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past - for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic properties of line bundles in geometry and multiplier ideals in algebra. This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-319-90493-1). ." -- Prové de l'editor Front Matter ....Pages i-viii Nearly Normally Torsionfree Ideals (Claudia Andrei-Ciobanu)....Pages 1-13 Gröbner–Nice Pairs of Ideals (Mircea Cimpoeaş, Dumitru I. Stamate)....Pages 15-29 Veneroni Maps (Marcin Dumnicki, Łucja Farnik, Brian Harbourne, Tomasz Szemberg, Halszka Tutaj-Gasińska)....Pages 31-42 On the Symbolic Powers of Binomial Edge Ideals (Viviana Ene, Jürgen Herzog)....Pages 43-50 Multigraded Betti Numbers of Some Path Ideals (Nursel Erey)....Pages 51-65 Depth of an Initial Ideal (Takayuki Hibi, Akiyoshi Tsuchiya)....Pages 67-71 Asymptotic Behavior of Symmetric Ideals: A Brief Survey (Martina Juhnke-Kubitzke, Dinh Van Le, Tim Römer)....Pages 73-94 On Piecewise-Linear Homeomorphisms Between Distributive and Anti-blocking Polyhedra (Christoph Pegel, Raman Sanyal)....Pages 95-114 The Bass-Quillen Conjecture and Swan’s Question (Dorin Popescu)....Pages 115-121 Licci Level Stanley-Reisner Ideals with Height Three and with Type Two (Giancarlo Rinaldo, Naoki Terai, Ken-Ichi Yoshida)....Pages 123-142 Homological and Combinatorial Properties of Powers of Cover Ideals of Graphs (S. A. Seyed Fakhari)....Pages 143-159 Fermat-Type Arrangements (Justyna Szpond)....Pages 161-182 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.-- Provided by publisher