A report on recent results and outstanding problems concerning motives associated to graphs.
(0.1). The purpose of this paper is to construct a spectral sequence from the motivic cohomology of a field F to its algebraic K-theory:
The cosimplicial scheme ∆ • = ∆ was used in  to define higher Chow groups. In this note, we let t tend to 0 and replace ∆ • by a degenerate version Q • = Q to define an additive version of the higher Chow groups. For a field k, we show the Chow group of 0-cycles on Q n in this theory is isomorphic to the absolute (n − 1)-Kähler forms Ω n−1 k. An… (More)
0. Introduction 0.1. Secondary (Chern-Simons) characteristic classes associated to bundles with connection play an important role in differential geometry. We propose to investigate a related construction for algebraic bundles. Non-flat algebraic connections for bundles on complex pro-jective manifolds are virtually non-existent (we know of none), and a… (More)
Prototypical respiratory-facial-postural actions ('emotional effector patterns') related to six basic emotions had been extracted from an ensemble of physiological reactions present in subjects reliving intense emotional situations (Bloch & Santibañez, 1972). Subjects reproducing these actions could evoke the corresponding subjective experience, which… (More)
To Kazuya Kato, with fondness and profound respect, on the occasion of his fiftieth birthday
— We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a… (More)
Local Fourier transforms, analogous to the ℓ-adic local Fourier transforms , are constructed for connections over k((t)). Following a program of Katz , a meromorphic connection on a curve is shown to be rigid, i.e. determined by local data at the singularities, if and only if a certain infinitesimal rigidity condition is satisfied. As in , the… (More)