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