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Combinatorial Structures in Algebra and Geometry

NSA 26, Constanța, Romania, August 26–September 1, 2018

  • Conference proceedings
  • © 2020

Overview

Editors:
  1. Dumitru I. Stamate

    1. Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania

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  2. Tomasz Szemberg

    1. Department of Mathematics, Pedagogical University of Cracow, Kraków, Poland

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    You can also search for this editor in PubMed   Google Scholar

  • Presents selected works from algebra, geometry and discrete mathematics, exploring the interaction among these fields
  • Focuses on combinatorial aspects of commutative algebra and algebraic geometry, based on the transdisciplinary approach of the conference
  • Showcases papers from some of the most prominent figures in the field

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 331)

Included in the following conference series:

Conference proceedings info: NSA 2018.

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Table of contents (12 papers)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Nearly Normally Torsionfree Ideals

    • Claudia Andrei-Ciobanu
    Pages 1-13

  3. Gröbner–Nice Pairs of Ideals

    • Mircea Cimpoeaş, Dumitru I. Stamate
    Pages 15-29

  4. Veneroni Maps

    • Marcin Dumnicki, Łucja Farnik, Brian Harbourne, Tomasz Szemberg, Halszka Tutaj-Gasińska
    Pages 31-42

  5. On the Symbolic Powers of Binomial Edge Ideals

    • Viviana Ene, Jürgen Herzog
    Pages 43-50

  6. Multigraded Betti Numbers of Some Path Ideals

    • Nursel Erey
    Pages 51-65

  7. Depth of an Initial Ideal

    • Takayuki Hibi, Akiyoshi Tsuchiya
    Pages 67-71

  8. Asymptotic Behavior of Symmetric Ideals: A Brief Survey

    • Martina Juhnke-Kubitzke, Dinh Van Le, Tim Römer
    Pages 73-94

  9. On Piecewise-Linear Homeomorphisms Between Distributive and Anti-blocking Polyhedra

    • Christoph Pegel, Raman Sanyal
    Pages 95-114

  10. The Bass-Quillen Conjecture and Swan’s Question

    • Dorin Popescu
    Pages 115-121

  11. Licci Level Stanley-Reisner Ideals with Height Three and with Type Two

    • Giancarlo Rinaldo, Naoki Terai, Ken-Ichi Yoshida
    Pages 123-142

  12. Homological and Combinatorial Properties of Powers of Cover Ideals of Graphs

    • S. A. Seyed Fakhari
    Pages 143-159

  13. Fermat-Type Arrangements

    • Justyna Szpond
    Pages 161-182
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  1. Combinatorial Structures in Algebra and Geometry

Keywords

About this book

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 propertiesof 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). 





Editors and Affiliations

  • Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania

    Dumitru I. Stamate

  • Department of Mathematics, Pedagogical University of Cracow, Kraków, Poland

    Tomasz Szemberg

About the editors

Dumitru I. Stamate holds a PhD in Mathematics (2009) from the University of Bucharest, Romania and two MSc degrees in Mathematics (2004), one from the Şcoala Normală Superioară Bucureşti, Romania, and the other from the University of Iași. He is currently an Assistant Professor at the University of Bucharest, Romania. His research focuses on commutative algebra, particularly problems related to free resolutions, computational algebra and combinatorics.


Tomasz Szemberg is a Professor at the Pedagogical University National Education Committee in Krakow, Poland. He completed his PhD in Mathematics (1994) at the Friedrich-Alexander-Universität, Erlangen-Nürnberg, Germany, and his MSc (1990) at the Jagiellonian University, Poland. In 2002, he received his postdoctoral qualification in Mathematical Sciences and in 2014, the academic title of Professor of Mathematical Sciences. His research interests encompass the fields of commutative algebra, algebraic geometry and discrete mathematics.


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