This course will cover various topics in Dynamical Systems; topics will differ from year to year. Consult the departmental website for more information.

This course will cover various topics in Dynamical Systems; topics will differ from year to year. Consult the departmental website for more information.

This course will cover various topics in Holomorphic Systems; topics will differ from year to year. Consult the departmental website for more information.

This course will develop advanced methods in linear algebra and introduce the theory of optimization. On the linear algebra side, we will study important matrix factorizations (e.g., LU, QR, SVD), matrix approximations (both deterministic and randomized), convergence of iterative methods, and spectral theorems. On the optimization side, we will introduce the finite element method, linear programming, gradient methods, and basic convex optimization. The course will be focused on fundamental theory, but appropriate illustrative applications may be chosen by the instructor.

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.

Introduction to the basic mathematical techniques in pricing theory and risk management: Stochastic calculus, single-period finance, financial derivatives (tree-approximation and Black-Scholes model for equity derivatives, American derivatives, numerical methods, lattice models for interest-rate derivatives), value at risk, credit risk, portfolio theory.

This is a self-directed reading course in Pure Mathematics. Consult the department for eligibility and enrolment procedures.

In the last twenty years there is a growing interest in the connection between these two fields analogous to the one found in the 1970s by Furstenberg for the Szemeredi theorem but now with the roles reversed. The course will start with the basic Model theory of Fraisse structures and their limits and then continue with study of Logic actions of these limits. The goal is to reach a level where structural Ramsey theory could be used to study these actions.

This should be accessible to students familiar with basic concepts in mathematics who will surely profit from just being exposed to the constructions of Fraisse limits such as, for example, the Urysohn metric space or the Gurarij Banach space.

This is a self-directed reading course in Pure Mathematics. Consult the department for eligibility and enrolment procedures.

This is a self-directed reading course in Applied Mathematics. Consult the department for eligibility and enrolment procedures.

This course is to allow MAT graduate students to get credit for attending various programs offered at the Fields Institute for Research in Mathematical Sciences.

This course is to allow MAT graduate students to get credit for attending various programs offered at the Fields Institute for Research in Mathematical Sciences.

This course is to allow MAT graduate students to get credit for attending various programs offered at the Fields Institute for Research in Mathematical Sciences.

This course tracks the completion of the Master's Supervised Project. Consult the department for eligibility and enrolment procedures.