The purpose of this instructional workshop is to provide a gentle introduction into the fascinating area of period maps. The first part will be devoted to the classical theory of periods over the complex numbers. Some of the topics we wish to discuss would be Hodge structures and their variations, Griffiths' transversality, key examples and mixed Hodge modules.

In the p-adic setting our main goal is to understand the construction and properties of Scholze's period map. After some background lectures on p-divisible groups, adic spaces and perfectoid spaces, we will discuss the Gross-Hopkins period map and the Lubin and Drinfeld towers, Shimura varieties at infinite level and the Hodge-Tate period map. The workshop will conclude with a series of 3 lectures on the paper of Scholze and Weinstein.

Registration is free but mandatory.