Preface; List of contributors; 1. On the local structure of ordinary Hecke algebras at classical weight one points M. Dimitrov; 2. Vector bundles on curves and p-adic Hodge theory L. Fargues and J.-M. Fontaine; 3. Around associators H. Furusho; 4. The stable Bernstein center and test function for Shimura varieties T. J. Haines; 5. Conditional results on the birational section conjecture over small number fields Y. Hoshi; 6. Blocks for mod p representations of GL2(Qp) V. Paskunas; 7. From étale P+-representations to G-equivariant sheaves on G/P P. Schneider, M.-F. Vigneras and G. Zabradi; 8. Intertwining of ramified and unramified zeros of Iwasawa modules C. Khare and J.-P. Wintenberger.