Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Various phenomena in physics and biology, such as the formation of crystals and the spread of infections are modeled by stochastic growth models. Many of such growth models are macroscopically described by Hamilton-Jacobi partial differential equations. In these models, a random interface is locally approximated by the graph of a solution to a Hamilton-Jacobi equation. Such a solution gives us a macroscopic description of the interface. Microscopically though, the interface is rough and fluctuates about the macroscopic solution. A central limit theorem would provide us with a better description of the interface. Kardar-Parisi-Zhang (KPZ) Equation is a stochastic partial differential equation that is expected to describe the roughness of the interface and can be used to predict the scaling in central limit theorem. In this class I will discuss some stochastic models for which such a central limit theorem can be rigorously verified. I also discuss the theory of regularitystructure of Martin Hairer and its application to KPZ equation.

Prerequisites : Familiarity with PDE, Brownian motion, and Markov Processes

Grading: There will be regular homework assignments.

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