Fields Institute Communications, Volume: 56
2009; 336 pp; hardcover
ISBN-13: 978-0-8218-4494-6
Expected publication date is September 30, 2009.
Spencer J. Bloch has, and continues to have, a profound influence on the
subject of Algebraic K-Theory, Cycles and Motives. This book, which is
comprised of a number of independent research articles written by leading
experts in the field, is dedicated in his honour, and gives a snapshot
of the current and evolving nature of the subject. Some of the articles
are written in an expository style, providing a perspective on the current
state of the subject to those wishing to learn more about it. Others are
more technical, representing new developments and making them especially
interesting to researchers for keeping abreast of recent progress.
Graduate students and research mathematicians interested in algebraic geometry, Hodge theory, K-theory, Motives, and algebraic cycles.
- D. Arapura -- Varieties with very little transcendental cohomology
- A. Beilinson -- mathcal{E}-factors for the period determinants of curves
- H. Esnault and A. Ogus -- Hodge cohomology of invertible sheaves
- H. Gillet -- Arithmetic intersection theory on Deligne-Mumford stacks
- S. Gorchinskiy -- Notes on the biextension of Chow groups
- B. Kahn -- Demonstration geometrique du theoreme de Lang-Neron et formules de Shioda-Tate
- S.-i. Kimura -- Surjectivity of the cycle map for Chow motives
- N. M. Kumar, A. P. Rao, and G. V. Ravindra -- On codimension two subvarieties in hypersurfaces
- M. Levine -- Smooth motives
- J. D. Lewis -- Cycles on varieties over subfields of mathbb{C} and cubic equivalence
- S. Lichtenbaum -- Euler characteristics and special values of zeta-functions
- J. Murre and D. Ramakrishnan -- Local Galois symbols on Etimes E
- V. K. Murty -- Semiregularity and Abelian varieties
- N. Naumann, M. Spitzweck, and P. A. Ostvar -- Chern classes, K-theory and Landweber exactness
- over nonregular base schemes
- V. Snaith -- Adams operations and motivic reduced powers
- J. Stienstra -- Chow forms, Chow quotients and quivers with superpotential
AMS/IP Studies in Advanced Mathematics, Volume: 46
2009; 396 pp; hardcover
ISBN-13: 978-0-8218-4836-4
Expected publication date is October 18, 2009.
This is a two-volume series research monograph on the general Lagrangian
Floer theory and on the accompanying homological algebra of filtered A_infty-algebras.
This book provides the most important step towards a rigorous foundation
of the Fukaya category in general context. In Volume I, general deformation
theory of the Floer cohomology is developed in both algebraic and geometric
contexts. An essentially self-contained homotopy theory of filtered A_infty
algebras and A_infty bimodules and applications of their obstruction-deformation
theory to the Lagrangian Floer theory are presented. Volume II contains
detailed studies of two of the main points of the foundation of the theory:
transversality and orientation. The study of transversality is based on
the virtual fundamental chain techniques (the theory of Kuranishi structures
and their multisections) and chain level intersection theories. A detailed
analysis comparing the orientations of the moduli spaces and their fiber
products is carried out. A self-contained account of the general theory
of Kuranishi structures is also included in the appendix of this volume.
Graduate students and research mathematicians interested in symplectic geometry, low-dimensional topology, mirror symmetry, and sting theory.
- Introduction
- Review: Floer cohomology
- The A_infty algebra associated to a Lagrangian submanifold
- Homotopy equivalence of A_infty algebras
- Homotopy equivalence of A_infty bimodules
- Spectral sequences
AMS/IP Studies in Advanced Mathematics, Volume: 46
2009; 805 pp; hardcover
ISBN-13: 978-0-8218-4837-1
Expected publication date is October 18, 2009.
This is a two-volume series research monograph on the general Lagrangian
Floer theory and on the accompanying homological algebra of filtered A_infty-algebras.
This book provides the most important step towards a rigorous foundation
of the Fukaya category in general context. In Volume I, general deformation
theory of the Floer cohomology is developed in both algebraic and geometric
contexts. An essentially self-contained homotopy theory of filtered A_infty
algebras and A_infty bimodules and applications of their obstruction-deformation
theory to the Lagrangian Floer theory are presented. Volume II contains
detailed studies of two of the main points of the foundation of the theory:
transversality and orientation. The study of transversality is based on
the virtual fundamental chain techniques (the theory of Kuranishi structures
and their multisections) and chain level intersection theories. A detailed
analysis comparing the orientations of the moduli spaces and their fiber
products is carried out. A self-contained account of the general theory
of Kuranishi structures is also included in the appendix of this volume.
Graduate students and research mathematicians interested in symplectic geometry, low-dimensional topology, mirror symmetry, and sting theory.
Courant Lecture Notes, Volume: 19
2009; 201 pp; softcover
ISBN-13: 978-0-8218-4888-3
Expected publication date is October 4, 2009.
This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.
Graduate students and research mathematicians interested in fluid mechanics.