H.B. Keller Colloquium
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. I will describe how this line of inquiry leads to geometric generalizations of some classical results in probability. I will also touch upon some related results in the non-commutative setting, and their relation to some long-standing open problems in convex geometry.