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.

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