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Program Description
This is a gentle introduction to recent progress in number theory around Shimura varieties and Rapoport-Zink spaces. The two arithmetric-geometric objects have been essential in the development of the Langlands program. To explain the idea some local-global analogy would be helpful. Shimura varieties are defined over number fields and often parametrizing abelian varieties with extra structure. Their local analogues are Rapoport-Zink spaces, defined over non-archimedean local fields and parametrizing p-divisible groups with extra structure. (Note that p-divisible groups themselves may be thought of as the local analogues of abelian varieties in a similar sense.) Shimura varieties and Rapoport-Zink spaces have been crucial geometric inputs in establishing global and local Langlands correspondences especially, and their interplay has been of central interest. An instance of the interplay is a p-adic uniformization of (suitable subvarieties of) Shimura varieties by Rapoport-Zink spaces.
  Until recently most applications have been limited to the classical Langlands correspondence and derived from the study of the so-called PEL-type case of the above geometric objects. Moreover our knowledge of Rapoport-Zink spaces had not extended much beyond some simple cases such as Lubin-Tate spaces and Drinfeld spaces (even in those cases our understanding is incomplete). However recent advances are breaking the boundaries: for instances we are going beyond the PEL case and beginning to understand the p-adic extension of the classical Langlands program. This intensive lectures series provides an opportunity to catch up with the current developments through 3 lectures on each of the four specialized topics by prominent young mathematicians in the field. 
  The program will start off on Monday with survey lectures aimed at non-specialists, thereby building some background materials and ushering the audience into the program. The main lectures are given from Tuesday through Thursday.

Invited Speakers
  Przemyslaw Chojecki (Jussieu)
  Wansu Kim (Cambridge)
  Keerthi Madapusi Pera (Harvard)
  Yoichi Mieda (Kyoto)
  Dong Uk Lee (IBS)
  Sug Woo Shin (MIT/KIAS)

 Youn-Seo Choi (KIAS)
 Sug Woo Shin (MIT/KIAS)


 Kangwon Lee (kwlee@kias.re.kr)