In the special year, we are going to have various activities on topics on modern number theory, especially those related to Birch and Swinnerton-Dyer conjecture. The BSD conjecture is one of the Millennium Prize Problems set by CMI, and is one of the most important problems in number theory. The Study of it involves many subjects:

1) Automorphic forms and Langlands corrrespondence.  Many arithmetic problems can be translated ones in terms of automorphic forms, making the problems more concrete and accessible. There are plentiful of tools to study automorphic forms -- analytic, geometric, topological....These methods are useful in proving the lower bound for the arithmetic objects in BSD conjecture. Experts on this topic we are inviting include Christopher Skinner and Eric Urban.

2) Special cycles and Euler systems: these are important tools to prove upper bound for Selmer groups.   We are inviting John Coates, Henri Darmon, David Loeffler and Sarah Zerbes to visit.

3) Geometry of Shimura varieties, and new results coming from the revolutional discovery of perfectoid spaces by Scholze and his colleagues. Shen Xu in our department is an expert of these area, and we are inviting Shimura variety experts Wei Zhang, Shouwu Zhang, Kai-Wen Lan, Laurent Fargues, etc to visit and give seminar talks and mini-courses.

4) Representations theory:  the p-adic representation theory, p-adic Langlands correspondence and Archimedean representation theory. We are going to invite Benjamin Schraen, Vytautas Paskunas and Dihua Jiang etc to visit and give talks and courses.

One example of problems that we plan to work out through communication and collaboration during the special year is full BSD formula for all elliptic curves over rationals of analytic rank 0 and 1.