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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.
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