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  2. Isoperimetric inequalities in high-dimensional convex sets

Isoperimetric inequalities in high-dimensional convex sets

Nachdiplom lectures, ETH Zurich

September-December, 2025

 

  • Lecturer: Boaz Klartag
  • Thursdays, 10:15 - 12:00 at HG G 43
  • First lecture: September 25, 2025

Lecture notes

  • Lecture 1: the cube and the sphere in high dimensions
  • Lecture 2: geometric inequalities and symmetrization processes
  • Lecture 3: the thin shell theorem and the Johnson-Lindenstrauss lemma
  • Lecture 4: Dvoretzky's theorem
  • Lecture 5: duality and the Santalo and Bourgain-Milman inequalities
  • Lecture 6: log-concave probability measures and isotropic constants
  • Lecture 7: the logarithmic Laplace transform and M-ellipsoids
  • Lecture 8: from thin-shell to slicing convex bodies and the Bochner method
  • Lecture 9: coupling exponential tilts of log-concave measures
English