Abstract:
Associated with every surface is a simplicial complex whose vertices are isotopy classes of simple closed curves known as the Curve Complex. Although this complex is an interesting object of study, it has been used to solve many questions related to mapping class groups and Teichmüller theory. In this talk I will introduce and discuss various properties of the Curve Complex, as well as discuss some of its applications. This talk is meant to be accessible to everyone, so no prior knowledge is being assumed.