Tree-terated integrals and motives related to the fundamental group

by Prof. Spencer Bloch (University of Chicago, USA)

Thursday 19 Jan 2012, 16:00 → 17:00 Asia/Kolkata

AG-69 (Colaba Campus)

I will describe how to associate a motive to a graph labeled by points in an algebraic variety. The periods of this motive will be generalizations of iterated integrals which in simple cases yield a special class of Shintani zeta functions. When the variety is an affine curve, realizations of the motive will have dimension given by the chromatic polynomial of the graph applied to the cohomology of the curve. When the graph is simply a string with n points, one gets the motive of the fundamental group ring modulo the (n+1)st power of the augmentation ideal.