Course outline:
(tentative so far, subject to regular updates, based on four 90-min lectures/week)

See the list of relevant papers whose content will be covered in this course. The lecture notes are distributed through this site or directly here

Week 1:

  1. Introduction to DGFF & its scaling limit     (notes for lecture 1)
  2. First results: Maximum and intermediate values     (notes for lecture 2)
  3. Intermediate level sets: factorization    (notes for lecture 3)
  4. Intermediate level sets: nailing the limit    (notes for lecture 4)

Week 2:

  1. Comparison inequalities for Gaussian processes     (notes for lecture 5)
  2. Concentration for the maximum of Gaussian processes     (notes for lecture 6)
  3. Connection to Branching Random Walk     (notes for lecture 7)
  4. Tightness of the maximum of DGFF     (notes for lecture 8)

Week 3:

  1. Extremal local extrema     (notes for lectures 9-10)
  2. Nailing the intensity measure     (notes for lecture 10)
  3. Local structure of extremal points     (notes for lectures 11-12)
  4. Local structure continued

Week 4:

  1. Random walk in DGFF landscape     (notes for lecture 13)
  2. Effective resistance control
  3. Consequences for random walk driven by DGFF
  4. Conclusion, open problems and conjectures