There has been exciting progress recently on two (three ?) connected topics: the extension of the Taylor-Wiles method to situations where the standard (im)parity condition fails, and the relation of deformation theory (starting with Hida's idea) with the Leopoldt conjecture. The salient points (not all of this is quite recent) are the paper(s) of Calegari and Geraghty, Calegari's paper on stable (completed) homology for congruence groups, and the Khare-Thorne paper on Leopoldt; the construction of new Galois representations by Harris-Lan-Thorne-Taylor and Scholze, in particular for torsion classes, is also a crucial advance. Finally,
Calegari's paper reveals new relations with problems in K-theory on which our kowledge does not seem to have improved much since the Batelle meetings.
The small meeting (workshop) will be limited to the researchers involved in this developments. The aim is to obtain an up-to date integrated picture of these developments as well as their interrelations.
Connected theories such as completed cohomology should be reviewed, as well as some complements in K-theory. A number of younger mathematicians, mostly at the post-doc level, will be invited.
There is a limited amount of money for financing TRAVEL for the junior participants. The persons who could not pay for this on their research funds should write to
stating the estimated amount. (Local expenses, housing and food, will not be reimbursed.)
Laurent Clozel (Université Paris-Sud)
Francesco Calegari (University of Chicago)
Hida’s conjecture and the Leopoldt conjecture
Simplicial deformation rings