•     Panorama of geometry and dynamics in moduli spaces (March-April 2026)  

     Lecture 1. Random hyperbolic surfaces (Riemann surfaces seen without glasses). Translation surfaces. 
     Lecture 2. Translation surfaces and Abelian differentials. Masur-Veech measure. Magic Wand Theorem. Geodesics and horocycles on modular surface 
     Lecture 3. Teichmüller Theorem. Square-tiled surfaces. Count of Masur-Veech volume through separatrix diagrams 
       Homework assignment 1 
     Lecture 4. Count of flat closed geodesics and of saddle connections. Siegel-Veech formula 
     Lecture 5. Solution of the problems from the homework assignment 
     Lecture 6. Mirzakhani's count of simple closed geodesics 
     Lecture 7. Train tracks. Measured laminations. Proof of Mirzakhani's count 
       Homework assignment 2 
     Lecture 8. Count of square-tiled surfaces and of simple closed hyperbolic geodesics (after joint works with V.Delecroix, E.Goujard and P.Zograf) 
     Lecture 9. Idea of renormalization. Windtree model. Lyapunov exponents 
     Lecture 10. Lyapunov exponents of the Teichmüller geodesic flow 
     Lecture 11. Arnold's problem on "interval exchange permutations" 
       The original formulation with comments by V. Arnold. 
       Complement to homework assignment 2 
       Solutions of selected problems from homework assignment 2 
     Lecture 12. Solution of Arnold's problem and large genus asymptotics (after joint works with V.Delecroix, E.Goujard and P.Zograf) 

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