# Development of Galois-Teichmüller Theory and Anabelian Geometry

 October 25 Monday, 17:10--18:00 M. Asada, H. Nakamura, N. Takao, H. Tsunogai; Easy walking in GT theory and anabelian geometry, II In this talk we shall introduce some basic notions to understand pro-l (pro-unipotent) aspects of the title of this conference for a wider public of mathematicians including graduate students. The Galois actions on the pro-l fundamental group of algebraic curves have been an important subject to find arithmetic nature of anabelian curves since Ihara's works on $P^1-\{0,1,\infty\}$ in 1980's. We explain weight filtration, associated Lie algebras and derivation algebras in the case of hyperbolic curves, and generalization to configuration spaces of curves. A fundamental result concerned here is injectivity of a sequence of derivation algebras and its stability, that leads to settlement of Oda's conjecture on the common Galois factor of the universal pro-l monodromy representation. If time allows, we mention relationships of Grothendieck-Teichmüller Lie algebra, Zagier's conjecture on multiple zeta values and Ihara's stable derivation algebra.