**Title**: *Beyond Abel and Jacobi
*

**Abstract**: The classical theorem of Abel and Jacobi characterises the zeroes and
poles of a meromorphic function on a compact Riemann surface (or
smooth projective variety) using a map which is nowadays called the
Abel-Jacobi homomorphism.
Following the work of many algebraic geometers over the past 150
years, this result has been successively refined and studied for
higher-dimensional varieties. The most sophisticated version of this
refinement is via the theory of "motives" as first proposed by
Grothendieck. The most elaborate conjectural refinements of the
Abel-Jacobi theorem are those of Bloch and Beilinson.
As with most conjectures, there have been many attempts to construct
counter-examples. One method is to construct "minimal" instances of
these conjectures for "well-understood" varieties where the
conjectures do not (as yet) follow from known results. Such examples
were constructed by Griffiths, Mumford-Roitman and many others which
led to the more precise formulations of the conjectures that we see
today.
In this talk, the speaker will attempt to explain some ideas and
examples behind this elaborate framework and present his own work in
its context.