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AMS Notices: August 2017
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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 Laplacian growth, sandpiles, and scaling limits
( view abstract )
Laplacian growth, sandpiles, and scaling limits
Laplacian growth is the study of interfaces that move in proportion to harmonic measure. Physically, it arises in fluid flow and electrical problems involving a moving boundary. We survey progress over the last decade on discrete models of (internal) Laplacian growth, including the abelian sandpile, internal DLA, rotor aggregation, and the scaling limits of these models on the lattice $ \epsilon {\mathbb{Z}}^d$ as the mesh size $ \epsilon $ goes to zero. These models provide a window into the tools of discrete potential theory, including harmonic functions, martingales, obstacle problems, quadrature domains, Green functions, smoothing. We also present one new result: rotor aggregation in $ {\mathbb{Z}}^d$ has $ O(\log r)$ fluctuations around a Euclidean ball, improving a previous power-law bound. We highlight several open questions, including whether these fluctuations are $ O(1)$.

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