Jay Swar

On Rational Points of Varieties and Symplectic Geometry

Selmer spaces, generalizing Selmer groups, connect the study of rational points of varieties to that of moduli spaces of local Galois representations. In particular, the Chabauty-Kim method allows one to obtain effective algorithms for computing the rational points of curves if one can explicitly write non-zero functions on certain Selmer spaces with a prescribed vanishing locus. In this talk, I'll give a general construction for candidates of such functions coming from structures on moduli spaces of Galois representations which were suggested by the arithmetic topology analogy. This is joint work with Minhyong Kim.