# Francesco Cellarosi (Queen's University)

Date

Thursday March 28, 20245:30 pm - 6:30 pm

Location

Jeffery Hall, Room 118Event Category

## Math Club

**Thursday, March 28th, 2024**

**Time:** 5:30 p.m. **Place:** Jeffery Hall, Room 118

**Speaker:** Francesco Cellarosi (Queen's University)

**Title:** Concentration of measure on the sphere

**Abstract:** If we pick a point uniformly at random on a unit sphere, what is the probability that we are in close to the equator?

It turns out that for high-dimensional spheres this probability is very close to 1, showing that the "surface area" is concentrated near the equator. This already counterintuitive statement turns paradoxical if we consider the fact that it must be true for every equator…

We will discuss these facts and their connection with the isoperimetric inequality.