Gaussian Isoperimetry and Related Topics I

This course aims to explore the Gaussian isoperimetric inequality and its applications in probability and analysis. By the end of the course, students will understand the sharp lower bound on Gaussian surface area, its implications for concentration inequalities, and its equivalence to certain Sobolev-type inequalities. The teaching method involves proving the Gaussian isoperimetric inequality using geometric measure theory. This course is intended for learners interested in advanced topics in mathematics, particularly in probability and analysis.