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Functional analysis

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MATH-485: Introduction to stochastic PDEs

Stochastic PDEs are used to model systems that are spatially extended and include a random component. This course gives an introduction to this topic, including some general measure theory, some Gauss

MATH-303: Measures and integration

This course provides an introduction to the theory of measures and integration on abstract measure spaces.

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COM-500: Statistical signal and data processing through applications

Building up on the basic concepts of sampling, filtering and Fourier transforms, we address stochastic modeling, spectral analysis, estimation and prediction, classification, and adaptive filtering, w

MATH-478: Dispersive PDEs

This course will give an introduction to some aspects of nonlinear dispersive partial differential equations. These are time evolution problems that arise in many contexts in physics, such as quantum

MATH-487: Topics in stochastic analysis

This course offers an introduction to topics in stochastic analysis, oriented about theory of multi-scale stochastic dynamics. We shall learn the fundamental ideas, relevant techniques, and in general

MATH-511: Number theory II.a - Modular forms

In this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization.

MATH-665: Functional Data Analysis

A rigorous introduction to the statistical analysis of random functions and associated random operators. Viewing random functions either as random Hilbert vectors or as stochastic processes, we will s

MATH-659: Topics in dispersive PDE

This course assumes familiarity with beginning graduate level real analysis, complex analysis and functional analysis, and also basic harmonic analysis, as well as fundamental concepts from differenti

MATH-647: Topics on the Euler and Navier-Stokes equations

This topics course focuses on recent and classical fundamental results on the Euler and Navier-Stokes equations, such as global existence of weak solutions, (non)uniqueness results, blow-ups, partial