ISBN:1-57146-090-X
Year Published: 2002
Page: 414
Binding: Hardcover
Description
The present volume contains papers of the
participants in the
International Press
Conference on Motives, polylogarithms and
non-abelian Hodge
theory
which took place at UC Irvine in June 1998.
The conference
commemorated
the twentieth anniversary of the remarkable
Irvine lectures of
Spencer Bloch on
"Higher regulators, algebraic K-theory
and zeta functions of
elliptic curves". The conference presented
some of the best
recent research in algebraic K-theory, Hodge
theory, motivic
cohomology and polylogarithms. The research
program of the
conference was organized around three main
lecture series:
VladimirVoevodsky taught a minicourse overviewing
the recent
developments in motivic cohomology and motivic
homotopy theory;
Don Zagier lectured on new results describing
the periods of
holomorphic and non-holomorphic modular forms;
and Carlos Simpson
lectured on the theory of geometric n-stacks
and its applications
to the variational aspects of non-abelian
Hodge theory.
Table of Contents
I. MOTIIVES
Open Problems in the Motivic Stable Homotopy
Theory, I,By
Vladimir Voevodsky
1 Introduction
2 Slice filtration
3 Main conjectures
4 Slice-wise cellular spectra
5 Reformulations in terms of rigid homotopy
groups
6 Rigid homology and rigid Adams spectral
sequence
7 Slice spectral sequence and convergence
problems
8 Possible strategies of the proof
Remarks on n-motives and correspondences
at the generic point, By
AIexander Beilinson
1 Introduction
2 The setting
3 Some natural injective n-motives
4 Some applications
Relative algebraic differential characters,
By Spencer Bloch and
Helene Esnault
1 Introduction
2 Relative Cohomology
3 Splitting Principle
4 Universal construction via the Weil algebra
5 The image of C2 in a family of curves
Commuting elements in Galois groups of function
fields, By Fedor
Bogomolov and Yuri Tschinkel
2 Classes of functions
3 Reductions
4 AF-functions and geometry
5 Galois theory
6 Valuations
Mixed Hodge Structures and Iterated Integrals,
I, by Zdzislaw
Wojtkowiak
0 Introduction
1 Monodromy of iterated integrals
2 Mixed Hodge structures
3 Cosimplicial objects and mixed motives
4 Coefficients
5 The conjecture (real form)
6 Proof of the conjecture
7 The conjecture (complex form)
8 Functional equations on P1(C) \ {O,1,oo}
9 Coefficients on P1Q\ {O,1,oo}
10 Examples
11 Iterated extensions
12 Exotic zeta functions
13 Problems
Appendix A. Tangential base points and monodromy
of iterated
integrals
Appendix B. Group Zariski closure
II POLYLOGARITHMS AND SPECIAL FUNCTIONS
Traces of singular moduli, by Don Zagier
Introduction
1 The trace of j(α)
2 A recursion for the numbers t(d)
3 Proof of the first recursion for t(d)
4 Proof of the second recursion for t(d)
5 Relation to Borcherds's theorem
6 Hecke operators
7 First generalization: other discriminants
8 Second generalization: other groups
9 Third generalization: other weights
Explicit Regulator maps on polylogarithmic
motivic complexes, By
A. B. Goncharov
1 Introduction
2 The main result
3 Arakelov motivic complexes: examples
4 Proofs
An explicit formula for the motivic elliptic
polylogarithm, By
Andrey Levin
1 Introduction
2 The basic functions and symbols
3 Explicit expressions for functions Ф for
an elliptic curve
over a field
On the Eisenstein symbol, By Jorg Wildeshaus
0 Introduction
1 The elliptic motivic polylogarithm
2 The formalism of elliptic Bloch groups
3 The proofs
ISBN:1-57146-091-8
Year Published: 2002
Page: 334
Binding: Hardcover
Description
The present volume contains papers of the
participants in the
International Press
Conference on Motives, polylogarithms and
non-abelian Hodge
theory
which took place at UC Irvine in June 1998.
The conference
commemorated
the twentieth anniversary of the remarkable
Irvine lectures of
Spencer Bloch on
"Higher regulators, algebraic K-theory
and zeta functions of
elliptic curves". The conference presented
some of the best
recent research in algebraic K-theory, Hodge
theory, motivic
cohomology and polylogarithms. The research
program of the
conference was organized around three main
lecture series:
VladimirVoevodsky taught a minicourse overviewing
the recent
developments in motivic cohomology and motivic
homotopy theory;
Don Zagier lectured on new results describing
the periods of
holomorphic and non-holomorphic modular forms;
and Carlos Simpson
lectured on the theory of geometric n-stacks
and its applications
to the variational aspects of non-abelian
Hodge theory.
Table of Contents
III HODGE THEORY
Algebraic aspects of higher nonabelian Hodge
theory, By Carlos
Simpson
1 Introduction
2 Varieties with abelian fundamental group
3 Nonabelian cohomology
4 Zoology
5 Cartesian families and base change
6 Very presentable n-stacks
7 Geometric n-stacks
8 Formal groupoids of smooth type
9 Formal categories related to Hodge theory
10 Presentability and geometricity results
Higgs bundles, integrability, and holomorphic
forms By Donu
Arapura
1 Consequences of the abelian theory
2 Higgs bundles and all that
3 A Nonabelian Analogue of b1 = 2q
4 Quaternionic geometry and Lagrangian maps
5 Integrability of Hitchin'smap
6 Cohomology support loci
7 Characteristic Cones and Products of Higgs
Bundles
8 Shafarevich Maps
9 Powers of the canonical bundle
Nonabelian (p, p) classes, by Ludmil Katzarkov
and Tony Pantev
1 Introduction
2 Preliminaries on D-varieties
3 Nonabelian Hodge structures
4 The Gauss-Manin connection
5 The main theorem
Appendix A. Tangent stacks
The structure of Kahler groups, I: second
cohomology, by
Alexander Reznikov
0 Introduction
1 A geometric picture for rigid representations
2 Proof of the Superrigidity Lemma
3 Variation of Hodge structure, corresponding
to rigid
representations to SO(2, n)
4 Variations of Hodge structure, corresponding
to a rigid
representationo Sp(4)
5 Variations of Hodge structure, corresponding
to a rigid
representation
to Sp(2n), and proof of the Superrigidity
Lemma (3)
6 Regulators, I: proof of the Main Theorem
7 Regulators, II: proof of Theorems 0.1,
0.2
8 Nonrigid representations
9 Three-manifolds groups are not Kahler
10 Central extensions of lattices in PSU(2,
1)
11 Smooth hypersurfaces in ball quotients
which are not K (π,1)
Some Hodge theory from Lie algebras, by Constantin
Teleman
Introduction
1 Refresher on cyclic homology
2 Homology of gl(A)
3 Conjectures and some results for g(A)
4 Loop groups
5 Hodge-to de Rham spectral sequence for
X
ISBN #: 1-57146-112-4
Year of Publication: 2003
Page: 80
Binding: Softcover
Description
This volume contains most of the series of
lectures presented
during the half-year program of Low-Dimensional
Topology, held at
The Morningside Center of Mathematics, of
the Chinese Academy of
Sciences, Beijing. The order of contents
is based on the
chronological order in which the lectures
were presented.
This book is the third volume of the series
in New Studies in
Advanced Mathematics. The other two volumes
are: Morse Theory,
Minimax Theory, and their Applications to
Nonlinear Differential
Equations, and Lectures on Partial Differential
Equations:
Proceedings in Honor of Louis Nirenberg's
75th Birthday.
Table of Contents
Definition of the Seiberg- Witten (SW) invariants
of 4-manifolds
- John W. Morgan
Computation of SW invariants for certain
4-manifolds - John W.
Morgan
Heegaard splittings of 3-manifolds - Martin
Scharlemann
Dehn filling - C. McA. Gordon
Dehn's Lemma and the Loop Theorem - Hyam
Rubinstein Polyhedral
Geometry - Hyam Rubinstein
Triangulations of 3-manifolds - Hyam Rubinstein
Description
Index Theory is one of the most exciting
discoveries of 20th
century mathematics. The story
of the four great mathematicians who uncovered
index theory is
told in this book. Their
own essays of historical importance, articles
written by
Donaldson, Witten, Yau and others...
and a large photo section make this title
a valuable document for
everyone having an
interest to understand mathematics and mathematicians.
1. A Personal History ・M. Atiyah
2. Sir Michael Atiyah: a brief biography
・Nigel
Hitchin
3. A Letter from Raoul Bott ・R. Bott
4. Geometry in Oxford c. 1980-85 ・Simon
Donaldson
5. Recollections about my teacher, Michael
Atiyah ・
G. Lusztig
6. Memories of Sir Michael Atiyah ・Louis
Nirenberg
7. Being a graduate student of Michael Atiyah
・G. B.
Segal
8. Michael Atiyah and the Physics/ Geometry
Interface
・E. Witten
9. Mathematics: Queen and Servant of the
Sciences ・
M. Atiyah
10. The Conscience of Science ・M. Atiyah
11. Interview with Raoul Bott
12. The Life and Works of Raoul Bott ・Loring
W. Tu
13. Lessons from Graduate School ・Robin
Forman
14. The Beautiful Vision of Raoul Bott ・Nancy
Hingston
15. Some Reminiscences about Raoul Bott ・Peter
Landweber
16. Reminiscences of Working with Raoul Bott
・Loring
W. Tu
17. Lessons from Raoul Bott ・E. Witten
18. Correspondence with Prof. Todd ・J.A.
Todd & F.
Hirzebruch
19. Kunihiko Kodaira: Mathematician, Friend
and
Teacher ・F. Hirzebruch
20. Bonn's Max Planck Institute: A New Building
and a
New Era ・Allyn Jackson
21. Singularities in the Work of Frederich
Hirzebruch
・Egbert Brierskorn
22. Frederich Hirzebruch and Mathematics
in Post-war
Germany ・Klaus Hulek
23. In Honor of the 50th Anniversary of Hirzebruch's
Doctorate ・Matthias Kreck
24. A Tribute to Warren Ambrose - Is Singer
25. Singer痴 Berkeley Seminar ・D. Freed
& J. Lott
26. Which Singer is That? ・Richard V. Kadison
27. Reminiscenes of a Mathematics Student,
40 years
ago ・Hugo Ross
28. Is Singer ・Dan Stroock
29. I. M. Singer ・Frank Warner
30. Is Singer's Contributions to Geometry
and Physics ・
E. Witten
31. My Friendship with Singer ・S. T. Yau
32. Letter to Raoul, Fritz, and Is ・M. Atiyah
33. Letter to Fritz, Is and Michael ・R.
Bott
34. Letter to Michael, Raoul and Iz ・F Hirzebruch
35. Letters to Michael, Raoul and Fritz・I.M.
Singer
36. The Evolution of Modern Analysis ・R.
G. Douglas
37. A Happy Collaboration ・Lars Garding
38. Memories of the Gang of Four - Albert
Weinstein