Title of the Course: Convex Geometry and probability in high dimensions
Instructor: Dr. Mohan Ravichandran
Institution: Bogazici University
Dates: 31 August – 4 September 2020
Prerequisites: Linear Algebra, Basic Probability
Level: Junior undergraduate, senior undergraduate, graduate
Abstract: This course will an introduction to Convex Geometry/High dimensional linear analysis, which is an area in the intersection of probability and functional analysis and of prime importance in modern topics such as data science, statistical inference and machine learning.
Content of Lectures:
-Geometric Inequalities (Brunn-Minkowski, Prekopa-Lendler, Brascamp-Lieb)
-Isoperimetric Inequalities (Levy, Borell), Localization
-Metric Embeddings (John’s theorem, Dvoretzky’s theorem)
-Volume Ratios, Steiner and Minkowski Symmetrizations, Santalo’s Inequality
– The hyperplane conjecture. Connection to Mixing time of Geometric Random walks.
Language: EN, TR