Algebraic and Geometric Methods in Discrete Mathematics
About this Title
Heather A. Harrington, University of Oxford, Oxford, United Kingdom, Mohamed Omar, Harvey Mudd College, Claremont, CA and Matthew Wright, St. Olaf College, Northfield, MN, Editors
Publication: Contemporary Mathematics
Publication Year: 2017; Volume 685
ISBNs: 978-1-4704-2321-6 (print); 978-1-4704-3743-5 (online)
This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas.
The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics.
Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks.
This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.
Graduate students and research mathematicians interested in applications of algebra and geometry.
Table of Contents
- Hirotachi Abo, Anna Seigal and Bernd Sturmfels – Eigenconfigurations of tensors
- Amir Ali Ahmadi and Georgina Hall – Sum of squares basis pursuit with linear and second order cone programming
- Nina Amenta, Jesús A. De Loera and Pablo Soberón – Helly’s theorem: New variations and applications
- Karl-Dieter Crisman and Michael E. Orrison – Representation theory of the symmetric group in voting theory and game theory
- Ruth Davidson, Joseph Rusinko, Zoe Vernon and Jing Xi – Modeling the distribution of distance data in Euclidean space
- Elizabeth Drellich, Andrew Gainer-Dewar, Heather A. Harrington, Qijun He, Christine Heitsch and Svetlana Poznanović – Geometric combinatorics and computational molecular biology: Branching polytopes for RNA sequences
- David Haws, James Cussens and Milan Studený – Polyhedral approaches to learning Bayesian networks
- Christopher J. Hillar and Sarah E. Marzen – Neural network coding of natural images with applications to pure mathematics
- Beauttie Kuture, Oscar Leong, Christopher Loa, Mutiara Sondjaja and Francis Edward Su – Proving Tucker’s Lemma with a volume argument
- Christopher O’Neill and Roberto Pelayo – Factorization invariants in numerical monoids
- Sonja Petrović – A survey of discrete methods in (algebraic) statistics for networks