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

An Invitation to Stochastic Mathematical Biology

George Constable, Yvonne Krumbeck and Tim Rogers

Mathematical biologists are increasingly required to confront the essential randomness and uncertainty of the natural world, a challenge that brings with it the opportunities to ask and answer new questions. In this article we survey the growing field of stochastic mathematical biology, revealing the surprising explanatory power of randomness in biology, and highlighting developments and challenges across a spectrum of mathematical areas.

Counting Geodesics, Teichmüller Space, and Random Hyperbolic Surfaces

Scott A. Wolpert

The study of geodesics provides a theme for understanding hyperbolic metrics on finite-area surfaces, as well as the geometry of the moduli space of Riemann surfaces. We begin with the fundamentals of the Teichmüller theory of hyperbolic surfaces. Then we describe how Thurston’s random geodesic metric generalizes to the pressure metric in higher Teichmüller theory and how Mirzakhani’s recursive integration scheme is a tool for understanding random finite-area hyperbolic surfaces.

Graph Pebbling: A Blend of Graph Theory, Number Theory, and Optimization

Glenn Hurlbert and Franklin Kenter

There are many graph-theoretic subjects that could go under the umbrella of “Moving Things Around on Graphs.” While some of these topics model real-world problems, others model pure mathematical problems. The graph pebbling model we discuss here is used to translate a number-theoretic problem into graph theory. We present a range of paradigms within this field and, for each one, share some of the major results, conjectures, and open problems.

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