Ebook: Geometries in Interaction: GAFA special issue in honor of Mikhail Gromov

Reprint from GAFA, Vol. 5 (1995), No. 2. Enlarged by a short biography of Mikhail Gromov and a list of publications. In the last decades of the XX century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. CONTRIBUTORS: J. Bourgain, J. Cheeger, J. Cogdell, A. Connes, Y. Eliashberg, H. Hofer, F. Lalonde, W. Luo, G. Margulis, D. McDuff, H. Moscovici, G. Mostow, S. Novikov, G. Perelman, I. Piatetski-Shapiro, G. Pisier, X. Rong, Z. Rudnick, D. Salamon, P. Sarnak, R. Schoen, M. Shubin, K. Wysocki, and E. Zehnder. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of Geometry and its applications to Functional Analysis, PDE, Analytic Number Theory and Physics.

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Reprint from GAFA, Vol. 5 (1995), No. 2. Enlarged by a short biography of Mikhail Gromov and a list of publications. In the last decades of the XX century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. CONTRIBUTORS: J. Bourgain, J. Cheeger, J. Cogdell, A. Connes, Y. Eliashberg, H. Hofer, F. Lalonde, W. Luo, G. Margulis, D. McDuff, H. Moscovici, G. Mostow, S. Novikov, G. Perelman, I. Piatetski-Shapiro, G. Pisier, X. Rong, Z. Rudnick, D. Salamon, P. Sarnak, R. Schoen, M. Shubin, K. Wysocki, and E. Zehnder. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of Geometry and its applications to Functional Analysis, PDE, Analytic Number Theory and Physics.
Content:
Front Matter....Pages i-xvi
Aspects of Long Time Behaviour of Solutions of Nonlinear Hamiltonian Evolution Equations....Pages 105-140
Collapsed Riemannian Manifolds with Bounded Diameter and Bounded Covering Geometry....Pages 141-163
Unitarity and Functoriality....Pages 164-173
The Local Index Formula in Noncommutative Geometry....Pages 174-243
Lagrangian Intersections in Contact Geometry....Pages 244-269
Properties of Pseudo-Holomorphic Curves in Symplectisations II: Embedding Controls and Algebraic Invariants....Pages 270-328
Bilinear Forms on Exact Operator Spaces and B(H) ? B(H)....Pages 329-363
Local Non-Squeezing Theorems and Stability....Pages 364-386
On Selberg’s Eigenvalue Conjecture....Pages 387-401
The Differential of a Quasi-Conformal Mapping of a Carnot-Caratheodory Space....Pages 402-433
The Semiclassical Electron in a Magnetic Field and Lattice Some Problems of Low Dimensional “Periodic” Topology....Pages 434-444
Widths of Nonnegatively Curved Spaces....Pages 445-463
On the Conformal and CR Automorphism Groups....Pages 464-481
L 2 Riemann-Roch Theorem for Elliptic Operators....Pages 482-527

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Reprint from GAFA, Vol. 5 (1995), No. 2. Enlarged by a short biography of Mikhail Gromov and a list of publications. In the last decades of the XX century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. CONTRIBUTORS: J. Bourgain, J. Cheeger, J. Cogdell, A. Connes, Y. Eliashberg, H. Hofer, F. Lalonde, W. Luo, G. Margulis, D. McDuff, H. Moscovici, G. Mostow, S. Novikov, G. Perelman, I. Piatetski-Shapiro, G. Pisier, X. Rong, Z. Rudnick, D. Salamon, P. Sarnak, R. Schoen, M. Shubin, K. Wysocki, and E. Zehnder. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of Geometry and its applications to Functional Analysis, PDE, Analytic Number Theory and Physics.
Content:
Front Matter....Pages i-xvi
Aspects of Long Time Behaviour of Solutions of Nonlinear Hamiltonian Evolution Equations....Pages 105-140
Collapsed Riemannian Manifolds with Bounded Diameter and Bounded Covering Geometry....Pages 141-163
Unitarity and Functoriality....Pages 164-173
The Local Index Formula in Noncommutative Geometry....Pages 174-243
Lagrangian Intersections in Contact Geometry....Pages 244-269
Properties of Pseudo-Holomorphic Curves in Symplectisations II: Embedding Controls and Algebraic Invariants....Pages 270-328
Bilinear Forms on Exact Operator Spaces and B(H) ? B(H)....Pages 329-363
Local Non-Squeezing Theorems and Stability....Pages 364-386
On Selberg’s Eigenvalue Conjecture....Pages 387-401
The Differential of a Quasi-Conformal Mapping of a Carnot-Caratheodory Space....Pages 402-433
The Semiclassical Electron in a Magnetic Field and Lattice Some Problems of Low Dimensional “Periodic” Topology....Pages 434-444
Widths of Nonnegatively Curved Spaces....Pages 445-463
On the Conformal and CR Automorphism Groups....Pages 464-481
L 2 Riemann-Roch Theorem for Elliptic Operators....Pages 482-527
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