Dynamics, geometry, and the moduli space of Riemann surfaces

Alex Wright (Stanford)

Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.

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On considération u(n)=somme cosbln (n)/n^a est convergente de même somme sinbln(n)/n^a est convergente puisque l angle bln(n) appartiennent [-π, π] et[-π/2, π/2], résumé quelques soit a appartiennent [0, l infini] les deux somme sont convergent de même les produits la seule relations de l amplitude u^2+v^2 c'est F(2a),