A History and Survey of the Subject by Pierre Lochak

Explore the history and survey of Grothendieck-Teichmüller theory in this comprehensive lecture by Pierre Lochak. Delve into the origins of this significant mathematical concept, which emerged from Alexandre Grothendieck's Esquisse d'un Programme and was further developed by mathematicians like Y. Ihara, V. Drinfeld, and P. Deligne. Examine the theory's foundation in the non-abelian nature of the fundamental group in classical algebraic topology. Discover the bifurcation in the theory's development, comparing the original profinite version containing the absolute Galois group Gal(Q) with Deligne's prounipotent approach using rational homotopy theory and mixed Tate motives. Gain insights into both the "linear" and "nonlinear" versions of the theory, their applications, and their connections to other areas of mathematics such as Multiple Zeta Values and deformation theory.