Journal cover: Notices of the American Mathematical Society

Notices of the American Mathematical Society

For issues spanning 1954 to 2015, the complete Tables of Contents (TOCs) are fully accessible only by downloading the entire issue in PDF format. From 2016 onwards, the availability and detail of TOCs have significantly improved.

Table of Contents

Featured Articles and Invitations from the AMS

Graph Rules for Recurrent Neural Network Dynamics

Carina Curto and Katherine Morrison

We describe a class of inhibition-dominated neural networks corresponding to directed graphs, and introduce some of the theory that has been developed to study them. The heart of the theory is a set of parameter-independent graph rules that enables us to directly predict features of the dynamics from combinatorial properties of the graph.

Symmetries of Spaces with Lower Curvature Bounds

Catherine Searle

Global Riemannian geometry generalizes the classical Euclidean, spherical, and hyperbolic geometries. One of the major challenges in this area is to understand how local invariants relate to global topological invariants. In this article our main focus is on closed Riemannian manifolds with sectional curvature bounded from below.

The Mathematics of Stable Black Holes

Elena Giorgi

Mathematics is used to represent black holes through a family of mathematical solutions, called the Kerr solution, parametrized by their mass and angular momentum, whose stability is one of the most important open problems in the field of mathematical general relativity. Establishing such a result is fundamental to confirm the relevance of the Kerr black hole as a realistic physical object.

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