Motives, Polylogarithms and Hodge Theory, Part I

Description

Motives, Polylogarithms and Hodge Theory is a two-volume collection of works exploring motivic cohomology and motivic homotopy theory, the periods of modular forms, and the variational aspects of Hodge theory.

Topics include: outstanding open questions in the stable homotopy theory of motives (V. Voevodsky); motivic cohomology, Galois cohomology, and algebraic differential characters (A. Beilinson, S. Bloch, F. Bogomolov, H. Esnault, and Y. Tschinkel); traces of the values of modular functions at quadratic irrationalities (D. Zagier); and theory of classical and elliptic polylogarithms (A. Goncharov and A. Levin). Also presented are papers by J. Wildeshaus and by Z. Wojkowiak, describing the recent progress towards a proof of various versions of Zagier’s conjecture; a foundational paper by C. Simpson on geometric n-stacks and their applications to non-abelian Hodge structures; and papers on the geometric applications of non-abelian Hodge theory by D. Arapura, L. Katzarkov, T. Pantev, A. Reznikov, and C. Teleman.

Publications