Ihara initiated to study a certain Galois representation which may be seen as an arithmetic analogue of the Artin representation of a pure braid group.
We are considering Hurwitz spaces stratified by the number of critical values.Belyi pairs constitute the zero-dimensional strata,and it is suggested to stud
I will describe how the enumeration of genus g dessins denfant with n labeled boundary components can be obtained via integration over the moduli space of s
Let G be a direct product of 3 copies of an infinite symmetric group.We show that unitary reprtesentations of G generate constructions in a spirit of topolo
There are several different ways of compactifying Teichmuller spaces.In this talk,I will consider how their differences disappear if we consider the "reduct
I will present a construction of continuous etale homotopy fixed points of smooth varieties over a field under the Galois action.I will then discuss how the
We have recently defined the notion of a Feynman category and in subsequent work shown that morphisms of such a category form a Hopf algebra.A particular ca
A compact Riemann surface is called extremal if it contains an embedded metric disc of the largest possible radius.In this talk we show how extremality can
In view of results of Goldman and Turaev,the free vector space over the free loops on an(connected)oriented surface has a natural Lie bialgebra structure.Th
We explain a method to construct higher category extensions of holonomy representations of homotopy path groupoids my means of Chens formal homology connect