The purpose of the workshop is to provide a gentle introduction into this fascinating area of mathematics. We envision it divided into two parts. 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, Torelli’s theorem, K3 surfaces, Mumford-Tate groups.

In the $p$-adic setting our main goal is to understand the construction and properties of Scholze’s period map. This requires the introduction of many new ideas and constructions that are still foreign to many number theorists, in particular to our trainees. We will have to provide background lectures on $p$-divisible groups, adic spaces, Shimura varieties, Grothendieck-Messing theory and more. After that, a good starting point, which is in retrospect a special case, is the Gross-Hopkins period map. The highlight of this part of the workshop would then be the discussion, and presently known properties, of Scholze’s (or the Hodge-Tate) period map.

FULL EVENT INFORMATION AND SCHEDULE - Montreal-Toronto Workshop in Number Theory: Period Maps