John Coates is Sadleirian Professor of Pure Mathematics at the University of Cambridge. Minhyong Kim is Professor of Pure Mathematics in the Department of Mathematics at University College London. Florian Pop is a Professor of Mathematics at the University of Pennsylvania. Mohamed Saidi is an Associate Professor in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter. Peter Schneider is a Professor in the Mathematical Institute at the University of Münster.

• List of contributors; Preface; 1. Lectures on anabelian phenomena in geometry and arithmetic Florian Pop; 2. On Galois rigidity of fundamental groups of algebraic curves Hiroaki Nakamura; 3. Around the Grothendieck anabelian section conjecture Mohamed Saïdi; 4. From the classical to the noncommutative Iwasawa theory (for totally real number fields) Mahesh Kakde; 5. On the ΜH(G)-conjecture J. Coates and R. Sujatha; 6. Galois theory and Diophantine geometry Minhyong Kim; 7. Potential modularity - a survey Kevin Buzzard; 8. Remarks on some locally Qp-analytic representations of GL2(F) in the crystalline case Christophe Breuil; 9. Completed cohomology - a survey Frank Calegari and Matthew Emerton; 10. Tensor and homotopy criteria for functional equations of l-adic and classical iterated integrals Hiroaki Nakamura and Zdzisław Wojtkowiak.

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