David Burns is a Professor in the Department of Mathematics at King's College, London. Kevin Buzzard is Professor of Pure Mathematics at the Imperial College, London. Jan Nekovář is a Professor in the Faculté de Mathématiques at the Université de Paris VI (Pierre et Marie Curie).

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• Preface; List of participants; 1. Stark–Heegner points and special values of L-series Massimo Bertolini, Henri Darmon and Samit Dasgupta; 2. Presentations of universal deformation rings Gebhard Böckle; Eigenvarieties Kevin Buzzard; 3. Nontriviality of Rankin-Selberg L-functions and CM points Christophe Cornut and Vinayak Vatsal; 4. A correspondence between representations of local Galois groups and Lie-type groups Fred Diamond; 5. Non-vanishing modulo p of Hecke L–values and application Haruzo Hida; 6. Serre's modularity conjecture: a survey of the level one case Chandrashekhar Khare; 7. Two p-adic L-functions and rational points on elliptic curves with supersingular reduction Masato Kurihara and Robert Pollack; 8. From the Birch and Swinnerton-Dyer Conjecture to non-commutative Iwasawa theory via the Equivariant Tamagawa Number Conjecture - a survey Otmar Venjakob; 9. The André-Oort conjecture - a survey Andrei Yafaev; 10. Locally analytic representation theory of p-adic reductive groups: a summary of some recent developments Matthew Emerton; 11. Modularity for some geometric Galois representations - with an appendix by Ofer Gabber Mark Kisin; 12. The Euler system method for CM points on Shimura curves Jan Nekovář; 13. Représentations irréductibles de GL(2,F ) modulo p Marie-France Vignéras.