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))
- 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).
- Goncharov, Galois symmetries of fundamental groupoids and
- Goncharov, Volumes of hyperbolic manifolds and mixed Tate motives
- Goncharov and Manin, Multiple zeta-motives and moduli spaces M0,n
- Bloch and Kriz, Mixed Tate motives
- Francis Brown's thesis, arXiv:math.AG/0606419
- Luca Barbieri-Viale, On the theory of 1-motives, arXiv:math.AG/0502476
- Annette Huber, Realization of Voevodsky's motives, J. Alg. Geom. 9 (2000) 755-799, Corregendum, J. Alg. Geom. 13 (2004), 195-207
- Yves André, Une introduction aux motifs: motifs purs, motifs mixtes, périodes, Panoramas et Synthèses 17 (2004)
- 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.,
- Spencer Bloch, Motives associated to graphs
- 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.
- Francis Brown, Multiple polylogarithms and periods of moduli spaces M0,n Talk at "Théorie des champs, périodes et polylogarithmes", IHÉS, June 12-16, 2006.
- Lichtenbaum, Values of zeta-functions at non-negative integers.
- Kapranov, Double affine Hecke algebras and 2-dimensional local fields.
- Fesenko, Analysis on arithmetic schemes
- Kahn, Algebraic K-theory, algebraic cycles, and arithmetic geometry.