ALGEBRAIC AND GEOMETRIC METHODS IN DISCRETE MATHEMATICS

• Eigenconfigurations of tensors 10
• Sum of squares basis pursuit with linear and second order cone programming 36
• Helly’s theorem: New variations and applications 64
• Representation theory of the symmetric group in voting theory and game theory 106
• Modeling the distribution of distance data in Euclidean space 126
• Geometric combinatorics and computational molecular biology: Branching polytopes for RNA sequences 146
• Polyhedral approaches to learning Bayesian networks 164
• Neural network coding of natural images with applications to pure mathematics 198
• Proving Tucker’s Lemma with a volume argument 232
• Factorization invariants in numerical monoids 240
• A survey of discrete methods in (algebraic) statistics for networks 260

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.

Authors
• Heather A. Harrington: University of Oxford, Oxford, United Kingdom,
• Mohamed Omar: Harvey Mudd College, Claremont, CA,
• Matthew Wright: St. Olaf College, Northfield, MN