Speaker: Nathan Ross

Affiliation: School of Mathematics and Statistics at the University of Melbourne

Title: Stein's method and applications

Abstract: Stein's method for distributional approximation is a collection of tools that can be used to bound the error in the approximation of a probability distribution of interest, e.g., that of a sum of random variables, by a well-understood target distribution, e.g., a Gaussian. These same tools have been used to develop functional and concentration inequalities, statistical goodness of fit tests and diagnostics for Markov chain convergence. This lecture series will first introduce the basics of the method through Gaussian and Poisson approximation, and then cover a selection of more recent topics. The assumed background is that of a PhD student planning to do research in probability. The lectures are meant to serve as an entry point to Stein's method, with the goal of making research-level monographs and literature accessible.

Speaker: Soumendu Sundar Mukherjee

Affiliation: Statistics and Mathematics Unit (SMU) at Indian Statistical Institute, Kolkata

Title: Random Tensors

Abstract: Random tensors arise naturally when modeling higher-order interactions between random entities. Understanding the spectra of these objects has important implications in Machine Learning, Statistics and Statistical Physics. In this mini-course, we will study the basic theory of random tensors and some of their myriad applications.