Gaussian Isoperimetry and Related Topics III

Explore the powerful Gaussian isoperimetric inequality and its wide-ranging applications in this 49-minute lecture by Joe Neeman at the Hausdorff Center for Mathematics. Delve into the sharp lower bound on Gaussian surface area for any set in terms of its Gaussian measure, and understand its significance in proving concentration inequalities in high dimensions. Discover the consequences of Gaussian isoperimetry across multiple fields, including probability and analysis. Learn how this concept applies to concentration and Gaussian noise stability in probability theory, and examine its equivalence to a specific Sobolev-type inequality in analysis. Finally, gain insights into proving the Gaussian isoperimetric inequality and its stronger versions using geometric measure theory methods.