Fall 2006 seminar on motives with applications in physics

This is the continuation of the Fall 2005 learning seminar on motives and the Spring 2006 Motives-Arithmetic-Physics Seminar.

The preceeding seminars are not prerequisites and everyone is welcome to attend. We meet Fridays 2-4 in MCS 180.

This semester we will be particularly focusing on Mixed Tate motives and the work of Goncharov, but tangents are always appreciated.


Sept 15
David Fried, Deligne-Goncharov (ref. 1), I
Sept 22
Karen Yeats, Hodge realizations. (see refs 7, 8 and chapter 22 of 9)
Sept 29
Karen Acquista, Goncharov's Galois Symmetries ... (ref 2), I
Oct 6
Karen Acquista, Goncharov's Galois Symmetries ... (ref 2), II
Oct 13
Karen Yeats, Bloch-Kriz style mixed tate motives. (ref 5)
Oct 20
Dirk Kreimer, Limiting mixed Hodge Structures and iterated Feynman graphs. (ref 10 and 11)
Oct 27
David Fried, Hyperbolic geometry and motives. (ref 3)
Nov 3
Karen Yeats, Francis Brown's thesis. (ref 6, see also ref 13). We'll end a bit early so that people can leisurely get to Noriko Yui's talk in the Geometry Seminar.
Nov 17
Cancelled on account of Current Developments in Mathematics.
Dec 1
Dec 8
Karen Acquista, motivic complexes. (see refs 13 (motivic complexes), 14, 15 (two papers for the future), and 16 (K-theory))


  1. Pierre Deligne and Alexander B. Goncharov, Groupes fondamentaux motiviques de Tate mixte. Ann. Scient. Éc. Norm. Sup. 38 no 1, (2005) 1-56 (also arXiv:math.NT/0302267).
  2. Goncharov, Galois symmetries of fundamental groupoids and noncommutative geometry
  3. Goncharov, Volumes of hyperbolic manifolds and mixed Tate motives
  4. Goncharov and Manin, Multiple zeta-motives and moduli spaces M0,n
  5. Bloch and Kriz, Mixed Tate motives
  6. Francis Brown's thesis, arXiv:math.AG/0606419
  7. Luca Barbieri-Viale, On the theory of 1-motives, arXiv:math.AG/0502476
  8. Annette Huber, Realization of Voevodsky's motives, J. Alg. Geom. 9 (2000) 755-799, Corregendum, J. Alg. Geom. 13 (2004), 195-207
  9. Yves André, Une introduction aux motifs: motifs purs, motifs mixtes, périodes, Panoramas et Synthèses 17 (2004)
  10. Dirk Kreimer, The residues of quantum field theory - numbers we should know, arXiv:hep-th/0404090, and in "Noncommutative Geometry and Number Theory", C.Consani, M.Marcolli, eds., p187-204
  11. Spencer Bloch, Motives associated to graphs
  12. Marc Levine, Mixed motives and homotopy theory of schemes III: Lecture 3. Mixed Tate Motives Talk at the Asian-French Summer School in Algebraic Geometry and Number Theory, IHÉS, July 17-29, 2006.
  13. Francis Brown, Multiple polylogarithms and periods of moduli spaces M0,n Talk at "Théorie des champs, périodes et polylogarithmes", IHÉS, June 12-16, 2006.
  14. Lichtenbaum, Values of zeta-functions at non-negative integers.
  15. Kapranov, Double affine Hecke algebras and 2-dimensional local fields.
  16. Fesenko, Analysis on arithmetic schemes
  17. Kahn, Algebraic K-theory, algebraic cycles, and arithmetic geometry.