turkmath.org

Maryam Mirzakharni reproved Witten's conjecture (Kontsevich's theorem) via her topological recursion by integratiing over her version of Mcshane's identity relevant to Weil-Petersson form on DM moduli space and its compactification. In this talk, I will represent Maryam Mirzakharn's work and also Francois Labourie's work on higher Teichmuller theory, which leads to conjecturally the existance of Higher moduli space, its compactification and higher generalized Witten's conjecture.