Tales of random projections: where probability meets geometry

In several areas of mathematics, including probability theory, asymptotic functional analysis, statistics and data science, 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 several results that address this question, starting with classical results and moving on to more recent breakthroughs, my own research and some open questions. The talk will be self-contained and accessible to undergraduate students.

Website: https://people.math.harvard.edu/~ana/ons/

Website: https://people.math.harvard.edu/~ana/ons/