We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large complicated structures can be treated as approximations of infinite measurable and topological objects. In the limit interesting algebraic structures and new concepts arise which are hard to capture in the finite language but they govern the behavior of the finite objects. A prominent example is the inverse theorem for the Gowers norms on arbitrary abelian groups.
What is the relationship between the idiom of the observer (historian, anthropologist) and the idiom of the actors, dead or alive? This question, which has been addressed from widely different (and usually unrelated) points of view, provides an oblique approach to the cognitive, moral, and political implications of the historian’s craft today.
In settings of incomplete information, we put forward (1) a very conservative ---indeed, purely set-theoretic--- model of the beliefs (including totally wrong ones) that each player may have about the payoff types of his opponents, and (2) a new and robust solution concept, based on mutual belief of rationality, capable of leveraging such conservative beliefs.