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

A Hypermatrix Analog of the General Linear Group

Edinah K. Gnang

Hypermatrices (higher-dimensional matrices) are important because they broaden the scope of matrix concepts such as spectra and group actions. Hypermatrix algebras also illuminate subtle aspects of matrix algebra. In this article we describe an instance where the transition from matrices to hypermatrices shines a light on subtle details of invariant theory and leads to new insights.

Moduli Spaces of Curves: Classical and Tropical

Melody Chan

First, we give an informal and elementary introduction to the idea of a moduli space, and then to moduli spaces of Riemann surfaces and their Deligne-Mumford-Knudsen compactifications. Second, we discuss some tropical geometry, assuming no prior knowledge of the subject, and build up to some recent results on moduli spaces that were obtained using tropical techniques.

Ruminations on Cosmology and Time

David Mumford

“I have been riveted for decades by the breathless bulletins from cosmologists describing the latest twist to their model of space and time at the largest possible scale. This article is partly to share the beauty of this theory with my colleagues but also to express how thoroughly relativity shakes up our deep psychological conviction of the reality of an external physical time.”

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