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

Partial Differential Equations of Mixed Type—Analysis and Applications

Gui-Qiang G. Chen

The aim of this expository paper is to show—through several longstanding fundamental problems in fluid mechanics, differential geometry, and other areas—that many nonlinear PDEs arising in these areas are no longer of standard types, but lie at the boundaries of the classification of PDEs or, indeed, go beyond the classification and are of mixed type.

Stochastic Separation Theorems: How Geometry May Help to Correct AI Errors

Alexander Gorban, Bogdan Grechuk and Ivan Tyukin

AI instabilities and adversarial examples—errors due to minor changes in data or structure—have recently been found in many advanced data-driven AI models. Mounting evidence suggests that these errors are in fact expected in such systems and may not always be cured by larger volumes of data or better training algorithms as long as the AI architecture remains fixed. If errors are inevitable in data-driven AI, then how do we deal with them once they occur?

Tropical Combinatorics

Felipe Rincón, Ngoc Mai Tran and Josephine Yu

In this article we introduce some of the basic constructions in tropical geometry, focusing on linear spaces and Grassmannians for their combinatorial significance. We give pointers to some recent research frontiers and discuss applications in matroid theory, phylogenetic trees, and auction theory.

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