This talk is based on a joint work by A.Alekseev,N.Kawazumi,Y.Kuno and F.Naef,and is a sequel to the talk by Nariya Kawazumi.In Part Ⅱ,after a brief review
Quantum Teichmüller theory produces unitary representations in infinite dimensional Hilbert spaces of the mapping class groups of punctured surfaces.A dire
In the eighties,Penner gave an elementary construction of pseudo-Anosov mapping classes.We give an overview on recent results concerning the dilatation(and
In this talk we prove that the quasihyperbolic metric is quasiinvariant under a quasisymmetric mapping in the suitable metric space.Meanwhile,we also show t
In the mapping class group of a closed connected oriented surface of genus 2,we explicitly write the identity as a product of 7 right Dehn twist and show th
The aim of this lecture is to present a new method for counting unrooted,unsensed and circular maps.It is based on the recent results by the author and his
A crystallographic group is an isometry group acting on a Euclidean space En whose translation subgroup forms an n-dimensional lattice.For example,a so-call
As part of his work on geometrization of 3-manifolds,Thurston conjectured that circle packing maps converge to the Riemann mappings for bounded simply conne
Given a reductive representation from surface group into a Lie group G,there exists a equivariant harmonic map from the universal cover of a fixed Riemann s