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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.
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.
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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AMS President Jill Pipher to Congress: "No Longer Secure: Cryptography in the Quantum Era"
Mathematics in the Theory and Practice of Auctions
“How would you, like, start on the concept of algebra?”
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