It is hard to give a precise answer. Beyond class field theory (in its cohomological/idelic form) and classical modular forms and modular curves, familiarity with Galois cohomology (such as Tate local/global duality -- see chapter II of Serre's book) and basic Galois deformation theory (as in the article of Mazur) will be assumed for the course of Kisin/Tiloouine, as will some basic Iwasawa theory (such as the elementary nonsense with Lambda-modules, etc., as in the book of Washington or perhaps the survey article by Greenberg) in the course of Skinner/Bellaiche, and for my course with Brinon on p-adic Hodge theory some preparatory notes will be posted by early March and it will be assumed that everyone has learned the basic concepts developed there. Oh, and the adelic viewpoint on automorphic forms is sure to come up, and schemes and their cohomology will come up in an essential way is pretty much every course and 4th-week minicourse. But it's likely that many participants will have strong background for some courses and weaker background for others. In any event, the application process will probably be quite stiff, as I am expecting that the combination of the topics and the location will lead to a flood of applications. One good thing is that the main courses (and hopefully the mini-courses) will have written-up lecture notes, so people who are not able to attend should find those to be useful once they are completed (probably within a year after the summer school ends, but hopefully earlier).
Note there is also a Park City program this summer on the arithmetic of L-functions, and that will have fewer prerequisites (in case the above seems like too much to you). Regards, Brian
----感謝孫大帥，讓我知道自已的愚蠢