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AMS Notices: August 2017
Feature Column: Untangling Your Square Dance by David Austin
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Now available for pre-order!

Geometric Group TheoryGeometric Group Theory
Cornelia Druţu
Michael Kapovich
Presenting geometric group theory in a form accessible to advanced graduate students and young research mathematicians, this volume fills a gap in the literature and will be useful to researchers in geometric group theory and its applications.

Advanced Modern Algebra, Third Edition, Volumes 1 and 2Advanced Modern Algebra, Third Edition, Parts 1 and 2
Joseph J. Rotman
The first part of this new edition consists of two courses: Galois theory and Module theory. The second part explores many topics mentioned in the first part in greater depth, including group theory, representation theory, homological algebra, categories, and commutative algebra.

Alice and Bob Meet BanachAlice and Bob Meet Banach
Guillaume Aubrun
Stanisław Szarek
By building a bridge between two distinct but intensively interacting fields, asymptotic geometric analysis and quantum information theory, this book presents deep insights into the behavior of entanglement and related phenomena in a high-dimensional setting.

Bulletin of the AMS

Bulletin of the AMS Hamiltonian and symplectic symmetries: An introduction
( view abstract )
Hamiltonian and symplectic symmetries: An introduction
Classical mechanical systems are modeled by a symplectic manifold $ (M,\omega )$, and their symmetries are encoded in the action of a Lie group $ G$ on $ M$ by diffeomorphisms which preserve $ \omega $. These actions, which are called symplectic, have been studied in the past forty years, following the works of Atiyah, Delzant, Duistermaat, Guillemin, Heckman, Kostant, Souriau, and Sternberg in the 1970s and 1980s on symplectic actions of compact Abelian Lie groups that are, in addition, of Hamiltonian type, i.e., they also satisfy Hamilton's equations. Since then a number of connections with combinatorics, finite-dimensional integrable Hamiltonian systems, more general symplectic actions, and topology have flourished. In this paper we review classical and recent results on Hamiltonian and non-Hamiltonian symplectic group actions roughly starting from the results of these authors. This paper also serves as a quick introduction to the basics of symplectic geometry.


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Research Journals Spotlight
 
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TRAN
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ERT
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