Title: Tales of random projections: where probability meets geometry
Abstract – In several areas of mathematics, including probability theory, statistics and asymptotic convex geometry, one is interested in high-dimensional objects, such as measures, data or convex bodies. One common theme is to try to understand what lower-dimensional projections can say about the corresponding high-dimensional objects. We show how this line of inquiry leads to geometric generalizations of several classical results in probability, and how tails of projections can provide insight into high-dimensional measures. Time permitting, we will also talk about related results in the non-commutative setting.