This course surveys a number of economic topics of current research interest in which mathematical developments have (and are expected to continue to) contribute crucial advances. These include the theory of matching and pricing, problems of asymmetric information, the principalagent framework, auction theory, mechanism (and information) design, portfolio optimization, and hedging. These topics are partly unified through mathematical techniques such as linear programming (optimal transport and its emerging relevance figure prominently — think of trying to pair N workers with N firms so as to maximize the total surplus), nonsmooth analysis, the calculus of variations, and differential equations. We may also consider topics such as matching with unobservable heterogeneity and/or imperfectly transferable utility, and equilibria involving agents who respond nonlinearly to prices, which go beyond the variational framework.

The necessary mathematics (beyond measure theory and integration) will be developed in parallel with the applications, as well as any necessary background in economics.