• Course description 
  
• Part I. Flat world.
   Lecture 1. From billiards to flat surfaces 
   Lecture 2. Magic Wand Theorem 
   Lecture 3. Square-tiled surfaces 
   Lecture 4. Arnold's problem on interval exchange transformations 
    Homework assignment 
   Lecture 5. Solutions to homework assignment 
  
  Part II. Hyperbolic world.
   Lecture 6. Mirzakhani´s count of simple closed geodesics 
   Lecture 7. Train tracks. Integral measured laminations. Proof of Mirzakhani´s count 
    Homework assignment 
   Exercise session on train-tracks and multicurves.
  
  Part III. Bridges between different worlds.
   Lecture 8. Random square-tiled surfaces of large genus and random multicurves on surfaces of large genus 
   Exercise session on Deligne–Mumford compactification and on Witten–Kontsevich correlators
   Lecture 9. Enumeration of meanders and Masur–Veech volumes of moduli spaces of quadratic differentials 
  
• Suggestions for reading before bed