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The hypoelliptic Laplacian and Ray-Singer metrics [[electronic resource] /] / Jean-Michel Bismut, Gilles Lebeau
| The hypoelliptic Laplacian and Ray-Singer metrics [[electronic resource] /] / Jean-Michel Bismut, Gilles Lebeau |
| Autore | Bismut Jean-Michel |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, : Princeton University Press, 2008 |
| Descrizione fisica | 1 online resource (378 p.) |
| Disciplina | 515/.7242 |
| Altri autori (Persone) | LebeauGilles |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Differential equations, Hypoelliptic
Laplacian operator Metric spaces |
| Soggetto non controllato |
Alexander Grothendieck
Analytic function Asymptote Asymptotic expansion Berezin integral Bijection Brownian dynamics Brownian motion Chaos theory Chern class Classical Wiener space Clifford algebra Cohomology Combination Commutator Computation Connection form Coordinate system Cotangent bundle Covariance matrix Curvature tensor Curvature De Rham cohomology Derivative Determinant Differentiable manifold Differential operator Dirac operator Direct proof Eigenform Eigenvalues and eigenvectors Ellipse Embedding Equation Estimation Euclidean space Explicit formula Explicit formulae (L-function) Feynman–Kac formula Fiber bundle Fokker–Planck equation Formal power series Fourier series Fourier transform Fredholm determinant Function space Girsanov theorem Ground state Heat kernel Hilbert space Hodge theory Holomorphic function Holomorphic vector bundle Hypoelliptic operator Integration by parts Invertible matrix Logarithm Malliavin calculus Martingale (probability theory) Matrix calculus Mellin transform Morse theory Notation Parameter Parametrix Parity (mathematics) Polynomial Principal bundle Probabilistic method Projection (linear algebra) Rectangle Resolvent set Ricci curvature Riemann–Roch theorem Scientific notation Self-adjoint operator Self-adjoint Sign convention Smoothness Sobolev space Spectral theory Square root Stochastic calculus Stochastic process Summation Supertrace Symmetric space Tangent space Taylor series Theorem Theory Torus Trace class Translational symmetry Transversality (mathematics) Uniform convergence Variable (mathematics) Vector bundle Vector space Wave equation |
| ISBN |
1-282-45837-X
9786612458378 1-4008-2906-2 |
| Classificazione | SK 620 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Introduction -- Chapter 1. Elliptic Riemann-Roch-Grothendieck and flat vector bundles -- Chapter 2. The hypoelliptic Laplacian on the cotangent bundle -- Chapter 3. Hodge theory, the hypoelliptic Laplacian and its heat kernel -- Chapter 4. Hypoelliptic Laplacians and odd Chern forms -- Chapter 5. The limit as t → +∞ and b → 0 of the superconnection forms -- Chapter 6. Hypoelliptic torsion and the hypoelliptic Ray-Singer metrics -- Chapter 7. The hypoelliptic torsion forms of a vector bundle -- Chapter 8. Hypoelliptic and elliptic torsions: a comparison formula -- Chapter 9. A comparison formula for the Ray-Singer metrics -- Chapter 10. The harmonic forms for b → 0 and the formal Hodge theorem -- Chapter 11. A proof of equation (8.4.6) -- Chapter 12. A proof of equation (8.4.8) -- Chapter 13. A proof of equation (8.4.7) -- Chapter 14. The integration by parts formula -- Chapter 15. The hypoelliptic estimates -- Chapter 16. Harmonic oscillator and the J0 function -- Chapter 17. The limit of A'2φb,±H as b → 0 -- Bibliography -- Subject Index -- Index of Notation |
| Record Nr. | UNINA-9910781084803321 |
Bismut Jean-Michel
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| Princeton, : Princeton University Press, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 / / Gerd Faltings
| Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 / / Gerd Faltings |
| Autore | Faltings Gerd |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (113 pages) |
| Disciplina | 516.3/5 |
| Altri autori (Persone) | ZhangShouwu |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Geometry, Algebraic
Riemann-Roch theorems |
| Soggetto non controllato |
Addition
Adjoint Alexander Grothendieck Algebraic geometry Analytic torsion Arakelov theory Asymptote Asymptotic expansion Asymptotic formula Big O notation Cartesian coordinate system Characteristic class Chern class Chow group Closed immersion Codimension Coherent sheaf Cohomology Combination Commutator Computation Covariant derivative Curvature Derivative Determinant Diagonal Differentiable manifold Differential form Dimension (vector space) Divisor Domain of a function Dual basis E6 (mathematics) Eigenvalues and eigenvectors Embedding Endomorphism Exact sequence Exponential function Generic point Heat kernel Injective function Intersection theory K-group Levi-Civita connection Line bundle Linear algebra Local coordinates Mathematical induction Morphism Natural number Neighbourhood (mathematics) Parameter Projective space Pullback (category theory) Pullback (differential geometry) Pullback Riemannian manifold Riemann–Roch theorem Self-adjoint operator Smoothness Sobolev space Stochastic calculus Summation Supertrace Theorem Transition function Upper half-plane Vector bundle Volume form |
| ISBN | 1-4008-8247-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- LIST OF SYMBOLS -- LECTURE 1. CLASSICAL RIEMANN-ROCH THEOREM -- LECTURE 2. CHERN CLASSES OF ARITHMETIC VECTOR BUNDLES -- LECTURE 3. LAPLACIANS AND HEAT KERNELS -- LECTURE 4. THE LOCAL INDEX THEOREM FOR DIRAC OPERATORS -- LECTURE 5. NUMBER OPERATORS AND DIRECT IMAGES -- LECTURE 6. ARITHMETIC RIEMANN-ROCH THEOREM -- LECTURE 7. THE THEOREM OF BISMUT-VASSEROT -- REFERENCES |
| Record Nr. | UNINA-9910154744103321 |
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Faltings Gerd
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| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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