Generalizations of Fourier analysis, and how to apply them
This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied but needs to be generalized first. Sometimes very satisfactory generalizations exist, while sometimes we have to make do with theories that have some of the desirable properties of Fourier analysis but not all of them. In the latter case, there are intriguing hints that there may be more satisfactory theories yet to be discovered. This article grew out of the Colloquium Lectures at the Joint Meeting of the AMS and the MAA, given in Seattle in January 2016.
Game Theory, Alive Anna Karlin Yuval Peres
By focusing on theoretical highlights and presenting exciting connections between game theory and other fields, this broad overview emphasizes game theory's real-world applications and mathematical foundations.