Andrea Miller (Harvard)<BR><BR>

"On a Conjecture of Murre for some mixed Shimura varieties"<BR><BR>

<b>Abstract:</b>
In the first part of my talk I will give a short introduction to
Shimura varieties and Chow motives and recall some of
their properties.
I will then state a conjecture of J.Murre concerning a motivic
decomposition of the Chow-motive of a smooth projective
variety. This yields a strengthening  of Grothendieck's conjecture C
for rational equivalence.
In the  last part I will show how to prove this conjecture in the
case of a universal 9-dimensional abelian variety (with additional 
structure)
over a unitary Shimura variety.