Joe Neeman: Gaussian isoperimetry and related topics I

The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequences of Gaussian isoperimetry and connections to other areas. In probability, we will show applications to concentration and Gaussian noise stability. In analysis, we will show that the Gaussian isoperimetric inequality is equivalent to a certain Sobolev-type inequality. Finally, we will prove the Gaussian isoperimetric inequality (and some stronger versions) using methods from geometric measure theory.