November 16 & 18
Guest lectures by Alexander Litvak (University of Alberta)

1. Classical Isoperimetric Inequalities on Euclidean, Spherical, and Gauss Spaces (2 weeks)

- definition of perimeter and boundary measure.
- proofs by various methods (symmetrization, combinatorial, PDE, Convexity).
- connection to Brunn-Minkowski inequality.

2. Isoperimetric Inequalities on Riemannian Manifolds (2 weeks)

- refresher on Riemannian Geometry and comparison theorems.
- background on Integral Currents.
- the Levy-Gromov isoperimetric inequality.
- if time - the Bakry-Ledoux isoperimetric inequality.

3. Optimal Transport (2 weeks)

- Background on existence, uniqueness and regularity of optimal-transport map.
- McCann's proof of the Euclidean isoperimetric inequality using optimal-transport.
- 1 week advanced topic TBD.

4. Applications in Asymptotic Geometric Analysis (3 weeks)

- Classical Convex Geometry.
- Dvoretsky's theorem.
- Quotient-of-Subspace Theorem.
- Other applications time permitting.