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 Gaussian measure theory and some linear semigroup theory. ...
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 mechanics, electrodynamics, fluid motion and relativity. ...
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 see the interplay between nonparametrics and multivariate ...
Lattice models consist of (typically random) objects living on a periodic graph. We will study some models that are mathematically interesting and representative of physical phenomena seen in the real world. ...
The course aims to introduce the basic concepts and results on metric embeddings, or more precisely on approximate embeddings. This area has been under rapid development since the 90's and it has strong impact on algorithms for discrete optimization proble ...