A Geometric Vision of Relations on the Grothendieck-Teichmuller Group
Sheldon Joyner, Ph.D.
Brandeis University
One approach to the study of the absolute Galois group of the field of rational numbers is to consider its embedding into a group first defined by Drinfel’d known as the Grothendieck-Teichmuller group, GT. Here I will discuss an approach to understand the relations on this group using paths in specific moduli spaces. Simple relations on paths translate into relations on GT, via an action of groups of homotopy classes of paths on sections of certain bundles with connection on the relevant moduli spaces, by means of parallel transport along paths.
Sheldon Joyner is a South African number theorist. After completing his MSc at Stellenbosch University in South Africa, he came to the States in 2000, where he studied first at the University of Arizona and later at Purdue University. He spent three years in a postdoctoral fellowship at the University of Western Ontario, before returning to the States to lecture at Brandeis University.
