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Exponential sums, hypergeometric sheaves, and monodromy groups
An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fieldsExponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a century to Kloosterman. Grothendieck’s creation o...
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Group theory in a nutshell for physicists
A concise, modern textbook on group theory written especially for physicistsAlthough group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is es...
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Office hours with a geometric group theorist
Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instru...
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Social and economic networks
Networks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy, and how they vote. The many aspects of our lives that are governed by social networks make it critical to understand how they impact behavior, which network structures are likely ...
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The structure of groups with a quasiconvex hierarchy
This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory that generalizes ideas...
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