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The main objective of this conference is to gather together young researchers interested in special values of L-functions and periods.

These objects are at the crossroads of many recent important developments in arithmetic geometry, such as Euler systems or the theory of motives. The different talks will portray the variety of viewpoints with which L-functions and periods are studied at present.

In particular, L-functions of motivic or automorphic origin, both in characteristic zero and in positive characteristic, are linked to periods of very different nature, such as Mahler measures or Feynman integrals. These L-functions are the subject of very deep conjectures (such as the ones put forward by Beilinson and by Bloch and Kato), and their relations with periods are also studied in an experimental fashion (for example in the work of Boyd or Broadhurst).

A particular and very explicit case of the conjectures of Bloch and Kato is given by the celebrated conjecture of Birch and Swinnerton-Dyer (BSD), which will be a central theme of the conference, with a particular focus on the p-adic methods (such as Iwasawa theory, or Euler systems) which have been used to solve the BSD conjecture in some particular cases.