Title: Towards Chabauty-Kim loci for the polylogarithmic quotient over an arbitrary number field
Abstract: Let K be a number field and let S be an open
subscheme of Spec O_K.
Minhyong Kim has developed a method for
bounding the set of S-valued points on a
hyperbolic curve X over S; his method opens
a new avenue in the quest for an "effective
Mordell conjecture".
But although Kim's approach has lead to the
construction of explicit bounds in special
cases, the problem of realizing the potential
effectivity of his methods remains a difficult
and beautiful open problem.
In the case of the thrice punctured line, this
problem may be approached via the methods of
mixed Tate motives. Using these methods we
are able to describe an algorithm; its output upon
halting is provably the set of integral points, while
its halting depends on conjectures.

## Date:

Mon, 09/11/2015 - 16:00 to 17:45

## Location:

Ross Building, room 70, Jerusalem, Israel