close
1.

電子ブック
ＥＢ
1. Enumerative Invariants in Algebraic Geometry and String Theory
Dan Abramovich, Kai Behrend, Marco Manetti, Marcos Mariño, F. Takens, Michael Thaddeus, Ravi Vakil, Centro internazionale matematico estivo.
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2008
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Preface
Lectures on Gromov-Witten Invariants of Orbifolds / D. Abramovich
Introduction / 1：
What This Is / 1.1：
Introspection / 1.2：
Where Does All This Come From? / 1.3：
Acknowledgements / 1.4：
Gromov-Witten Theory / 2：
Kontsevich's Formula / 2.1：
Set-Up for a Streamlined Proof / 2.2：
The Space of Stable Maps / 2.3：
Natural Maps / 2.4：
Boundary of Moduli / 2.5：
Gromov-Witten Classes / 2.6：
The WDVV Equations / 2.7：
Proof of WDVV / 2.8：
About the General Case / 2.9：
Orbifolds/Stacks / 3：
Geometric Orbifolds / 3.1：
Moduli Stacks / 3.2：
Where Do Stacks Come Up? / 3.3：
Attributes of Orbifolds / 3.4：
Etale Gerbes / 3.5：
Twisted Stable Maps / 4：
Stable Maps to a Stack / 4.1：
Twisted Curves / 4.2：
Transparency 25: The Stack of Twisted Stable Maps / 4.3：
Twisted Curves and Roots / 4.5：
Valuative Criterion for Properness / 4.6：
Contractions / 5：
Gluing and Rigidified Inertia / 5.2：
Evaluation Maps / 5.3：
The Boundary of Moduli / 5.4：
Orbifold Gromov-Witten Classes / 5.5：
Fundamental Classes / 5.6：
WDVV, Grading and Computations / 6：
The Formula / 6.1：
Quantum Cohomology and Its Grading / 6.2：
Grading the Rings / 6.3：
Examples / 6.4：
Other Work / 6.5：
Mirror Symmetry and the Crepant Resolution Conjecture / 6.6：
The Legend of String Cohomology: Two Letters of Maxim Kontsevich to Lev Borisov / A：
The Legend of String Cohomology / A.1：
The Archaeological Letters / A.2：
References
Lectures on the Topological Vertex / M. Marino
Introduction and Overview
Chern-Simons Theory
Basic Ingredients
Perturbative Approach
Non-Perturbative Solution
Framing Dependence
The 1/N Expansion in Chern-Simons Theory
Topological Strings
Topological Strings and Gromov-Witten Invariants
Integrality Properties and Gopakumar-Vafa Invariants
Open Topological Strings
Toric Geometry and Calabi-Yau Threefolds
Non-Compact Calabi-Yau Geometries: An Introduction
Constructing Toric Calabi-Yau Manifolds
Examples of Closed String Amplitudes
The Topological Vertex
The Gopakumar-Vafa Duality
Framing of Topological Open String Amplitudes
Definition of the Topological Vertex
Gluing Rules
Explicit Expression for the Topological Vertex
Applications
Symmetric Polynomials
Floer Cohomology with Gerbes / M. Thaddeus
Floer Cohomology
Newton's Second Law
The Hamiltonian Formalism
The Arnold Conjecture
Floer's Proof
Morse Theory / 1.5：
Bott-Morse Theory / 1.6：
Morse Theory on the Loop Space / 1.7：
Re-Interpretation #1: Sections of the Symplectic Mapping Torus / 1.8：
Re-Interpretation #2: Two Lagrangian Submanifolds / 1.9：
Product Structures / 1.10：
The Finite-Order Case / 1.11：
Givental's Philosophy / 1.12：
Gerbes
Definition of Stacks
Examples of Stacks
Morphisms and 2-Morphisms
Definition of Gerbes
The Gerbe of Liftings
The Lien of a Gerbe
Classification of Gerbes
Allowing the Base Space to Be a Stack
Definition of Orbifolds
Twisted Vector Bundles / 2.10：
Strominger-Yau-Zaslow / 2.11：
Orbifold Cohomology and Its Relatives
Cohomology of Sheaves on Stacks
The Inertia Stack
Orbifold Cohomology
Twisted Orbifold Cohomology
The Case of Discrete Torsion
The Fantechi-Gottsche Ring / 3.6：
Twisting the Fantechi-Gottsche Ring with Discrete Torsion / 3.7：
Twisting It with an Arbitrary Flat Unitary Gerbe / 3.8：
The Loop Space of an Orbifold / 3.9：
Addition of the Gerbe / 3.10：
The Non-Orbifold Case / 3.11：
The Equivariant Case / 3.12：
A Concluding Puzzle / 3.13：
Notes on the Literature
Notes to Lecture 1
Notes to Lecture 2
Notes to Lecture 3
The Moduli Space of Curves and Gromov-Witten Theory / R. Vakil
The Moduli Space of Curves
Tautological Cohomology Classes on Moduli Spaces of Curves, and Their Structure
A Blunt Tool: Theorem * and Consequences
Stable Relative Maps to P[superscript 1] and Relative Virtual Localization
Applications of Relative Virtual Localization
Towards Faber's Intersection Number Conjecture 3.23 via Relative Virtual Localization / 7：
Conclusion / 8：
List of Participants
Preface
Lectures on Gromov-Witten Invariants of Orbifolds / D. Abramovich
Introduction / 1：
2.

電子ブック
ＥＢ
2. Calculus of Variations and Nonlinear Partial Differential Equations
Luigi Ambrosio, Luis Caffarelli, Michael G. Crandall, Bernard Dacorogna, Lawrence C. Evans, Nicola Fusco, Paolo Marcellini, Elvira Mascolo, F. Takens, Centro internazionale matematico estivo., Luis A. Caffarelli, E. Mascolo
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2008
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Transport Equation and Cauchy Problem for Non-Smooth Vector Fields / Luigi Ambrosio
Introduction / 1：
Transport Equation and Continuity Equation within the Cauchy-Lipschitz Framework / 2：
ODE Uniqueness versus PDE Uniqueness / 3：
Vector Fields with a Sobolev Spatial Regularity / 4：
Vector Fields with a BV Spatial Regularity / 5：
Applications / 6：
Open Problems, Bibliographical Notes, and References / 7：
References
Issues in Homogenization for Problems with Non Divergence Structure / Luis Caffarelli ; Luis Silvestre
Homogenization of a Free Boundary Problem: Capillary Drops
Existence of a Minimizer / 2.1：
Positive Density Lemmas / 2.2：
Measure of the Free Boundary / 2.3：
Limit as ε → 0 / 2.4：
Hysteresis / 2.5：
The Construction of Plane Like Solutions to Periodic Minimal Surface Equations / 2.6：
Existence of Homogenization Limits for Fully Nonlinear Equations / 3.1：
Main Ideas of the Proof / 4.1：
A Visit with the ∞-Laplace Equation / Michael G. Crandall4.2：
Notation
The Lipschitz Extension/Variational Problem
Absolutely Minimizing Lipschitz iff Comparison With Cones
Comparison With Cones Implies ∞-Harmonic
∞-Harmonic Implies Comparison with Cones
Exercises and Examples
From ∞-Subharmonic to ∞-Superharmonic
More Calculus of ∞-Subharmonic Functions
Existence and Uniqueness
The Gradient Flow and the Variational Problem for <$>\parallel|Du|\parallel_{L^\infty}<$>
Linear on All Scales
Blow Ups and Blow Downs are Tight on a Line / 7.1：
Implications of Tight on a Line Segment / 7.2：
An Impressionistic History Lesson / 8：
The Beginning and Gunnar Aronosson / 8.1：
Enter Viscosity Solutions and R. Jensen / 8.2：
Regularity / 8.3：
Modulus of Continuity
Harnack and Liouville
Comparison with Cones, Full Born
Blowups are Linear
Savin's Theorem
Generalizations, Variations, Recent Developments and Games / 9：
What is Δ∞ for H(x, u, Du)? / 9.1：
Generalizing Comparison with Cones / 9.2：
The Metric Case / 9.3：
Playing Games / 9.4：
Miscellany / 9.5：
Weak KAM Theory and Partial Differential Equations / Lawrence C. Evans
Overview, KAM theory
Classical Theory / 1.1：
The Lagrangian Viewpoint
The Hamiltonian Viewpoint
Canonical Changes of Variables, Generating Functions
Hamilton-Jacobi PDE
KAM Theory / 1.2：
Generating Functions, Linearization
Fourier series
Small divisors
Statement of KAM Theorem
Weak KAM Theory: Lagrangian Methods
Minimizing Trajectories
Lax-Oleinik Semigroup
The Weak KAM Theorem
Domination
Flow invariance, characterization of the constant c
Time-reversal, Mather set
Weak KAM Theory: Hamiltonian and PDE Methods
Adding P Dependence / 3.2：
Lions-Papanicolaou-Varadhan Theory / 3.3：
A PDE construction of <$>\bar {H}<$>
Effective Lagrangian
Application: Homogenization of Nonlinear PDE
More PDE Methods / 3.4：
Estimates / 3.5：
An Alternative Variational/PDE Construction
A new Variational Formulation
A Minimax Formula
A New Variational Setting
Passing to Limits
Application: Nonresonance and Averaging
Derivatives of <$>{\overline {\bf H}}^k<$>
Nonresonance
Some Other Viewpoints and Open Questions
Geometrical Aspects of Symmetrization / Nicola Fusco
Sets of finite perimeter
Steiner Symmetrization of Sets of Finite Perimeter
The Pòlya-Szegö Inequality
CIME Courses on Partial Differential Equations and Calculus of Variations / Elvira Mascolo
Transport Equation and Cauchy Problem for Non-Smooth Vector Fields / Luigi Ambrosio
Introduction / 1：
Transport Equation and Continuity Equation within the Cauchy-Lipschitz Framework / 2：
3.

電子ブック
ＥＢ
3. Symplectic 4-Manifolds and Algebraic Surfaces
Denis Auroux, Fabrizio Catanese, Marco Manetti, Paul Seidel, Bernd Siebert, Ivan Smith, F. Takens, G. Tian, Gang Tian, Centro internazionale matematico estivo.
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Lefschetz Pencils, Branched Covers and Symplectic Invariants / Denis Auroux ; Ivan Smith
Introduction and Background / 1：
Symplectic Manifolds / 1.1：
Almost-Complex Structures / 1.2：
Pseudo-Holomorphic Curves and Gromov-Witten Invariants / 1.3：
Lagrangian Floer Homology / 1.4：
The Topology of Symplectic Four-Manifolds / 1.5：
Symplectic Lefschetz Fibrations / 2：
Fibrations and Monodromy / 2.1：
Approximately Holomorphic Geometry / 2.2：
Symplectic Branched Covers of <$>{\op CP}^2<$> / 3：
Symplectic Branched Covers / 3.1：
Monodromy Invariants for Branched Covers of <$>{\op CP}^2<$> / 3.2：
Fundamental Groups of Branch Curve Complements / 3.3：
Symplectic Isotopy and Non-Isotopy / 3.4：
Symplectic Surfaces from Symmetric Products / 4：
Symmetric Products / 4.1：
Taubes' Theorem / 4.2：
Fukaya Categories and Lefschetz Fibrations / 5：
Matching Paths and Lagrangian Spheres / 5.1：
Fukaya Categories of Vanishing Cycles / 5.2：
Applications to Mirror Symmetry / 5.3：
References
Differentiable and Deformation Type of Algebraic Surfaces, Real and Symplectic Structures / Fabrizio Catanese
Introduction
Lecture 1: Projective and Kähler Manifolds, the Enriques Classification, Construction Techniques
Projective Manifolds, Kähler and Symplectic Structures
The Birational Equivalence of Algebraic Varieties
The Enriques Classification: An Outline / 2.3：
Some Constructions of Projective Varieties / 2.4：
Lecture 2: Surfaces of General Type and Their Canonical Models: Deformation Equivalence and Singularities
Rational Double Points
Canonical Models of Surfaces of General Type
Deformation Equivalence of Surfaces
Isolated Singularities, Simultaneous Resolution
Lecture 3: Deformation and Diffeomorphism, Canonical Symplectic Structure for Surfaces of General Type
Deformation Implies Diffeomorphism
Symplectic Approximations of Projective Varieties with Isolated Singularities
Canonical Symplectic Structure for Varieties with Ample Canonical Class and Canonical Symplectic Structure for Surfaces of General Type / 4.3：
Degenerations Preserving the Canonical Symplectic Structure / 4.4：
Lecture 4: Irrational Pencils, Orbifold Fundamental Groups, and Surfaces Isogenous to a Product
Theorem of Castelnuovo-De Franchis, Irrational Pencils and the Orbifold Fundamental Group
Varieties Isogenous to a Product
Complex Conjugation and Real Structures
Beauville Surfaces / 5.4：
Lecture 5: Lefschetz Pencils, Braid and Mapping Class Groups, and Diffeomorphism of ABC-Surfaces / 6：
Surgeries / 6.1：
Braid and Mapping Class Groups / 6.2：
Lefschetz Pencils and Lefschetz Fibrations / 6.3：
Simply Connected Algebraic Surfaces: Topology Versus Differential Topology / 6.4：
ABC Surfaces / 6.5：
Epilogue: Deformation, Diffeomorphism and Symplectomorphism Type of Surfaces of General Type / 7：
Deformations in the Large of ABC Surfaces / 7.1：
Manetti Surfaces / 7.2：
Deformation and Canonical Symplectomorphism / 7.3：
Braid Monodromy and Chisini' Problem / 7.4：
Smoothings of Singularities and Deformation Types of Surfaces / Marco Manetti
Quotient Singularities
RDP-Deformation Equivalence
Relative Canonical Model
Automorphisms of Canonical Models / 2.5：
The Kodaira Spencer Map / 2.6：
Moduli Space for Canonical Surfaces
Gieseker's Theorem
Constructing Connected Components: Some Strategies
Outline of Proof of Gieseker Theorem
Smoothings of Normal Surface Singularities
The Link of an Isolated Singularity
The Milnor Fibre
<$>{\op Q}<$>-Gorenstein Singularities and Smoothings
T-Deformation Equivalence of Surfaces
A Non Trivial Example of T-Deformation Equivalence / 4.5：
Double and Multidouble Covers of Normal Surfaces
Flat Abelian Covers
Flat Double Covers
Automorphisms of Generic Flat Double Covers
Example: Automorphisms of Simple Iterated Double Covers
Flat Multidouble Covers / 5.5：
Stability Criteria for Flat Double Covers
Restricted Natural Deformations of Double Covers
Openess of N (a, b,c)
RDP-Degenerations of Double Covers
RDP-Degenerations of <$>{\op P}^1 \times {\op P}^1<$>
Proof of Theorem 6.1
Moduli of Simple Iterated Double Covers / 6.6：
Lectures on Four-Dimensional Dehn Twists / Paul Seidel
Definition and First Properties
Floer and Quantum Homology
Pseudo-Holomorphic Sections and Curvature
Lectures on Pseudo-Holomorphic Curves and the Symplectic Isotopy Problem / Bernd Siebert ; Gang Tian
Pseudo-Holomorphic Curves
Almost Complex and Symplectic Geometry
Basic Properties of Pseudo-Holomorphic Curves
Moduli Spaces
Applications
Pseudo-Analytic Inequalities
Unobstructedness I: Smooth and Nodal Curves
Preliminaries on the <$>\overline {\partial}<$>-Equation
The Normal <$>\overline {\partial}<$>-Operator
Immersed Curves
Smoothings of Nodal Curves
The Theorem of Micallef and White
Statement of Theorem
The Case of Tacnodes
The General Case
Unobstructedness II: The Integrable Case
Motivation
Special Covers
Description of the Deformation Space
The Holomorphic Normal Sheaf
Computation of the Linearization
A Vanishing Theorem / 5.6：
The Unobstructedness Theorem / 5.7：
Application to Symplectic Topology in Dimension Four
Monodromy Representations - Hurwitz Equivalence
Hyperelliptic Lefschetz Fibrations
Braid Monodromy and the Structure of Hyperelliptic Lefschetz Fibrations
Symplectic Noether-Horikawa Surfaces
The <$>{\scr C}^0<$>-Compactness Theorem for Pseudo-Holomorphic Curves
Statement of Theorem and Conventions
The Monotonicity Formula for Pseudo-Holomorphic Maps
A Removable Singularities Theorem
Proof of the Theorem
Second Variation of the <$>\overline {\partial}_J<$>-Equation and Applications / 8：
Comparisons of First and Second Variations / 8.1：
Moduli Spaces of Pseudo-Holomorphic Curves with Prescribed Singularities / 8.2：
The Locus of Constant Deficiency / 8.3：
Second Variation at Ordinary Cusps / 8.4：
The Isotopy Theorem / 9：
Statement of Theorem and Discussion / 9.1：
Pseudo-Holomorphic Techniques for the Isotopy Problem / 9.2：
The Isotopy Lemma / 9.3：
Sketch of Proof / 9.4：
List of Participants
Lefschetz Pencils, Branched Covers and Symplectic Invariants / Denis Auroux ; Ivan Smith
Introduction and Background / 1：
Symplectic Manifolds / 1.1：
4.

電子ブック
ＥＢ
4. Nonlinear and Optimal Control Theory
Andrei A. Agrachev, A. Stephen Morse, Paolo Nistri, Eduardo D. Sontag, Gianna Stefani, Héctor J. Sussmann, F. Takens, Vadim I. Utkin, Centro internazionale matematico estivo.
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2008
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Geometry of Optimal Control Problems and Hamiltonian Systems / A.A. Agrachev
Lagrange Multipliers' Geometry / 1：
Smooth Optimal Control Problems / 1.1：
Lagrange Multipliers / 1.2：
Extremals / 1.3：
Hamiltonian System / 1.4：
Second Order Information / 1.5：
Maslov Index / 1.6：
Regular Extremals / 1.7：
Geometry of Jacobi Curves / 2：
Jacobi Curves / 2.1：
The Cross-Ratio / 2.2：
Coordinate Setting / 2.3：
Curves in the Grassmannian / 2.4：
The Curvature / 2.5：
Structural Equations / 2.6：
Canonical Connection / 2.7：
Coordinate Presentation / 2.8：
Affine Foliations / 2.9：
Symplectic Setting / 2.10：
Monotonicity / 2.11：
Comparison Theorem / 2.12：
Reduction / 2.13：
Hyperbolicity / 2.14：
References
Lecture Notes on Logically Switched Dynamical Systems / A.S. Morse
The Quintessential Switched Dynamical System Problem
Dwell-Time Switching
Switching Between Stabilizing Controllers
Switching Between Graphs
Switching Controls with Memoryless Logics
Introduction
The Problem
The Solution
Analysis
Collaborations / 3：
The Curse of the Continuum / 4：
Process Model Class / 4.1：
Controller Covering Problem / 4.2：
A Natural Approach / 4.3：
A Different Approach / 4.4：
Which Metric? / 4.5：
Construction of a Control Cover / 4.6：
Supervisory Control / 5：
The System / 5.1：
Slow Switching / 5.2：
Analysis of the Dwell Time Switching Logic / 5.3：
Flocking / 6：
Leaderless Coordination / 6.1：
Symmetric Neighbor Relations / 6.2：
Measurement Delays / 6.3：
Asynchronous Flocking / 6.4：
Leader Following / 6.5：
Input to State Stability: Basic Concepts and Results / E.D. Sontag
ISS as a Notion of Stability of Nonlinear I/O Systems
Desirable Properties
Merging Two Different Views of Stability
Technical Assumptions
Comparison Function Formalism
Global Asymptotic Stability
0-GAS Does Not Guarantee Good Behavior with Respect to Inputs
Gains for Linear Systems
Nonlinear Coordinate Changes
Input-to-State Stability
Linear Case, for Comparison
Feedback Redesign
A Feedback Redesign Theorem for Actuator Disturbances
Equivalences for ISS
Nonlinear Superposition Principle / 3.1：
Robust Stability / 3.2：
Dissipation / 3.3：
Using "Energy" Estimates Instead of Amplitudes / 3.4：
Cascade Interconnections
An Example of Stabilization Using the ISS Cascade Approach
Integral Input-to-State Stability
Other Mixed Notions
Dissipation Characterization of iISS
Superposition Principles for iISS
Cascades Involving iISS Systems
An iISS Example / 5.5：
Input to State Stability with Respect to Input Derivatives
Cascades Involving the D[superscript k]ISS Property
Dissipation Characterization of D[superscript k]ISS
Superposition Principle for D[superscript k]ISS
A Counter-Example Showing that D[superscript 1]ISS [not equal] ISS
Input-to-Output Stability / 7：
Detectability and Observability Notions / 8：
Detectability / 8.1：
Dualizing ISS to OSS and IOSS / 8.2：
Lyapunov-Like Characterization of IOSS / 8.3：
Superposition Principles for IOSS / 8.4：
Norm-Estimators / 8.5：
A Remark on Observers and Incremental IOSS / 8.6：
Variations of IOSS / 8.7：
Norm-Observability / 8.8：
The Fundamental Relationship Among ISS, IOS, and IOSS / 9：
Systems with Separate Error and Measurement Outputs / 10：
Input-Measurement-to-Error Stability / 10.1：
Review: Viscosity Subdifferentials / 10.2：
RES-Lyapunov Functions / 10.3：
Output to Input Stability and Minimum-Phase / 11：
Response to Constant and Periodic Inputs / 12：
A Remark Concerning ISS and H[subscript infinity] Gains / 13：
Two Sample Applications / 14：
Additional Discussion and References / 15：
Generalized Differentials, Variational Generators, and the Maximum Principle with State Constraints / H.J. Sussmann
Preliminaries and Background
Review of Some Notational Conventions and Definitions
Generalized Jacobians, Derivate Containers, and Michel-Penot Subdifferentials
Finitely Additive Measures
Cellina Continuously Approximable Maps
Definition and Elementary Properties
Fixed Point Theorems for CCA Maps
GDQs and AGDQs
The Basic Definitions
Properties of GDQs and AGDQs
The Directional Open Mapping and Transversality Properties
Variational Generators
Linearization Error and Weak GDQs
GDQ Variational Generators
Examples of Variational Generators
Discontinuous Vector Fields
Co-Integrably Bounded Integrally Continuous Maps
Points of Approximate Continuity
The Maximum Principle
Sliding Mode Control: Mathematical Tools, Design and Applications / V.I. Utkin
Examples of Dynamic Systems with Sliding Modes
VSS in Canonical Space
Control of Free Motion
Disturbance Rejection
Comments for VSS in Canonical Space
Preliminary Mathematical Remark
Sliding Modes in Arbitrary State Spaces: Problem Statements
Sliding Mode Equations: Equivalent Control Method
Problem Statement
Regularization
Boundary Layer Regularization
Sliding Mode Existence Conditions
Design Principles
Decoupling and Invariance / 7.1：
Regular Form / 7.2：
Block Control Principle / 7.3：
Enforcing Sliding Modes / 7.4：
Unit Control / 7.5：
The Chattering Problem
Discrete-Time Systems
Discrete-Time Sliding Mode Concept / 9.1：
Linear Discrete-Time Systems with Known Parameters / 9.2：
Linear Discrete-Time Systems with Unknown Parameters / 9.3：
Infinite-Dimensional Systems
Distributed Control of Heat Process
Flexible Mechanical System
Control of Induction Motor
List of Participants
Geometry of Optimal Control Problems and Hamiltonian Systems / A.A. Agrachev
Lagrange Multipliers' Geometry / 1：
Smooth Optimal Control Problems / 1.1：
5.

電子ブック
ＥＢ
5. Hyperbolic Systems of Balance Laws
Alberto Bressan, P. A. Marcati, Pierangelo Marcati, J.-M Morel, Denis Serre, F. Takens, Mark Williams, Kevin Zumbrun, Centro internazionale matematico estivo.
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2007
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6.

電子ブック
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6. Inverse Problems and Imaging
Ana Carpio, Luis L. Bonilla, Luis López Bonilla, Oliver Dorn, Miguel Moscoso, Frank Natterer, George C. Papanicolaou, Maria Luisa Rapún, F. Takens, Alessandro Teta, Centro internazionale matematico estivo., George Papanicolaou
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2008
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7.

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7. Representation Theory and Complex Analysis
J.M Morel, Andrea D'Agnolo, Edward Frenkel, Masaki Kashiwara, Massimo Picardello, Massimo A. Picardello, F. Takens, Enrico Casadio Tarabusi, Alain Valette, David A. Vogan, Nolan R. Wallach, Centro internazionale matematico estivo., Michael Cowling
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Applications of Representation Theory to Harmonic Analysis of Lie Groups (and Vice Versa) / Michael Cowling
Basic Facts of Harmonic Analysis on Semisimple Groups and Symmetric Spaces / 1：
Structure of Semisimple Lie Algebras / 1.1：
Decompositions of Semisimple Lie Groups / 1.2：
Parabolic Subgroups / 1.3：
Spaces of Homogeneous Functions on G / 1.4：
The Plancherel Formula / 1.5：
The Equations of Mathematical Physics on Symmetric Spaces / 2：
Spherical Analysis on Symmetric Spaces / 2.1：
Harmonic Analysis on Semisimple Groups and Symmetric Spaces / 2.2：
Regularity of the Laplace-Beltrami Operator / 2.3：
Approaches to the Heat Equation / 2.4：
Estimates for the Heat and Laplace Equations / 2.5：
Approaches to the Wave and Schrodinger Equations / 2.6：
Further Results / 2.7：
The Vanishing of Matrix Coefficients / 3：
Some Examples in Representation Theory / 3.1：
Matrix Coefficients of Representations of Semisimple Groups / 3.2：
The Kunze-Stein Phenomenon / 3.3：
Property T / 3.4：
The Generalised Ramanujan-Selberg Property / 3.5：
More General Semisimple Groups / 4：
Graph Theory and its Riemannian Connection / 4.1：
Cayley Graphs / 4.2：
An Example Involving Cayley Graphs / 4.3：
The Field of p-adic Numbers / 4.4：
Lattices in Vector Spaces over Local Fields / 4.5：
Adeles / 4.6：
Carnot-Caratheodory Geometry and Group Representations / 4.7：
A Decomposition for Real Rank One Groups / 5.1：
The Conformal Group of the Sphere in R[superscript n] / 5.2：
The Groups SU(1, n + 1) and Sp(1, n + 1) / 5.3：
References
Ramifications of the Geometric Langlands Program / Edward Frenkel
Introduction
The Unramified Global Langlands Correspondence
Classical Local Langlands Correspondence
Langlands Parameters
The Local Langlands Correspondence for GL[subscript n]
Generalization to Other Reductive Groups
Geometric Local Langlands Correspondence over C
Geometric Langlands Parameters
Representations of the Loop Group
From Functions to Sheaves
A Toy Model
Back to Loop Groups
Center and Opers
Center of an Abelian Category
Opers
Canonical Representatives
Description of the Center
Opers vs. Local Systems
Harish-Chandra Categories / 6：
Spaces of K-Invariant Vectors / 6.1：
Equivariant Modules / 6.2：
Categorical Hecke Algebras / 6.3：
Local Langlands Correspondence: Unramified Case / 7：
Unramified Representations of G(F) / 7.1：
Unramified Categories [characters not reproducible]-Modules / 7.2：
Categories of G[[t]]-Equivariant Modules / 7.3：
The Action of the Spherical Hecke Algebra / 7.4：
Categories of Representations and D-Modules / 7.5：
Equivalences Between Categories of Modules / 7.6：
Generalization to other Dominant Integral Weights / 7.7：
Local Langlands Correspondence: Tamely Ramified Case / 8：
Tamely Ramified Representations / 8.1：
Categories Admitting ([characters not reproducible], I) Harish-Chandra Modules / 8.2：
Conjectural Description of the Categories of ([characters not reproducible], I) Harish-Chandra Modules / 8.3：
Connection between the Classical and the Geometric Settings / 8.4：
Evidence for the Conjecture / 8.5：
Ramified Global Langlands Correspondence / 9：
The Classical Setting / 9.1：
The Unramified Case, Revisited / 9.2：
Classical Langlands Correspondence with Ramification / 9.3：
Geometric Langlands Correspondence in the Tamely Ramified Case / 9.4：
Connections with Regular Singularities / 9.5：
Irregular Connections / 9.6：
Equivariant Derived Category and Representation of Real Semisimple Lie Groups / Masaki Kashiwara
Harish-Chandra Correspondence
Beilinson-Bernstein Correspondence
Riemann-Hilbert Correspondence
Matsuki Correspondence
Construction of Representations of G[subscript R]
Integral Transforms / 1.6：
Commutativity of Fig. 1 / 1.7：
Example / 1.8：
Organization of the Note / 1.9：
Derived Categories of Quasi-abelian Categories
Quasi-abelian Categories
Derived Categories
t-Structure
Quasi-equivariant D-Modules
Definition
Sumihiro's Result
Pull-back Functors
Push-forward Functors
External and Internal Tensor Products / 3.6：
Semi-outer Hom / 3.7：
Relations of Push-forward and Pull-back Functors / 3.8：
Flag Manifold Case / 3.9：
Equivariant Derived Category
Sheaf Case
Induction Functor
Constructible Sheaves
D-module Case
Equivariant Riemann-Hilbert Correspondence
Holomorphic Solution Spaces
Countable Sheaves
C[superscript infinity]-Solutions
Definition of RHom[superscript top] / 5.4：
DFN Version / 5.5：
Functorial Properties of RHom[superscript top] / 5.6：
Relation with the de Rham Functor / 5.7：
Whitney Functor
The Functor RHom[characters not reproducible]
Elliptic Case
Twisted Sheaves
Twisting Data
Twisted Sheaf
Morphism of Twisting Data
Tensor Product
Inverse and Direct Images
Twisted Modules
Equivariant Twisting Data
Character Local System / 7.8：
Twisted Equivariance / 7.9：
Twisting Data Associated with Principal Bundles / 7.10：
Twisting (D-module Case) / 7.11：
Ring of Twisted Differential Operators / 7.12：
Equivariance of Twisted Sheaves and Twisted D-modules / 7.13：
Convolutions / 7.14：
Integral Transform Formula
Application to the Representation Theory
Notations
Quasi-equivariant D-modules on the Symmetric Space
Construction of Representations
Integral Transformation Formula
Vanishing Theorems / 10：
Preliminary / 10.1：
Calculation (I) / 10.2：
Calculation (II) / 10.3：
Vanishing Theorem / 10.4：
List of Notations
Index
Amenability and Margulis Super-Rigidity / Alain Valette
Amenability for Locally Compact Groups
Definition, Examples, and First Characterizations
Stability Properties
Lattices in Locally Compact Groups
Reiter's Property (P[subscript 1])
Reiter's Property (P[subscript 2])
Amenability in Riemannian Geometry
Measurable Ergodic Theory
Definitions and Examples
Moore's Ergodicity Theorem
The Howe-Moore Vanishing Theorem
Margulis' Super-rigidity Theorem
Statement
Mostow Rigidity
Ideas to Prove Super-rigidity, k = R
Proof of Furstenberg's Proposition 4.1 - Use of Amenability
Margulis' Arithmeticity Theorem
Unitary Representations and Complex Analysis / David A. Vogan, Jr
Compact Groups and the Borel-Weil Theorem
Examples for SL(2, R)
Harish-Chandra Modules and Globalization
Real Parabolic Induction and the Globalization Functors
Examples of Complex Homogeneous Spaces
Dolbeault Cohomology and Maximal Globalizations
Compact Supports and Minimal Globalizations
Invariant Bilinear Forms and Maps between Representations
Open Questions
Quantum Computing and Entanglement for Mathematicians / Nolan R. Wallach
The Basics
Basic Quantum Mechanics
Bits
Qubits
Quantum Algorithms
Quantum Parallelism
The Tensor Product Structure of n-qubit Space
Grover's Algorithm
The Quantum Fourier Transform
Factorization and Error Correction
The Complexity of the Quantum Fourier Transform
Reduction of Factorization to Period Search
Error Correction
Entanglement
Measures of Entanglement
Three Qubits
Measures of Entanglement for Two and Three Qubits
Four and More Qubits
Four Qubits
Some Hilbert Series of Measures of Entanglement
A Measure of Entanglement for n Qubits
Applications of Representation Theory to Harmonic Analysis of Lie Groups (and Vice Versa) / Michael Cowling
Basic Facts of Harmonic Analysis on Semisimple Groups and Symmetric Spaces / 1：
Structure of Semisimple Lie Algebras / 1.1：
8.

電子ブック
ＥＢ
8. SPDE in Hydrodynamic: Recent Progress and Prospects
Sergio Albeverio, Giuseppe Da Prato, Franco Flandoli, Giuseppe Prato, Michael Röckner, Michael Rückner, Yakov G. Sinai, IÍ¡Akov GrigorÊ〓evich SinaÄ­, F. Takens, Centro internazionale matematico estivo.
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2008
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9.

電子ブック
ＥＢ
9. Mixed Finite Elements, Compatibility Conditions, and Applications
Daniele Boffi, Franco Brezzi, Leszek F. Demkowicz, Ricardo G. Durán, Richard S. Falk, Michel Fortin, Lucia Gastaldi, F. Takens, Centro internazionale matematico estivo.
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2008
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目次情報: 続きを見る
Preface
Mixed Finite Element Methods / Ricardo G. Durán
Introduction / 1：
Preliminary Results / 2：
Mixed Approximation of Second Order Elliptic Problems / 3：
A Posteriori Error Estimates / 4：
The General Abstract Setting / 5：
References
Finite Elements for the Stokes Problem / Daniele Boffi ; Franco Brezzi ; Michel Fortin
The Stokes Problem as a Mixed Problem
Mixed Formulation / 2.1：
Some Basic Examples
Standard Techniques for Checking the Inf-Sup Condition
Fortin's Trick / 4.1：
Projection onto Constants / 4.2：
Verfürth's Trick / 4.3：
Space and Domain Decomposition Techniques / 4.4：
Macroelement Technique / 4.5：
Making Use of the Internal Degrees of Freedom / 4.6：
Spurious Pressure Modes
Two-Dimensional Stable Elements / 6：
The MINI Element / 6.1：
The Crouzeix-Raviart Element / 6.2：
<$>P_1^{NC} - P_0<$> Approximation / 6.3：
Qk − Pk−1 Elements / 6.4：
Three-Dirnensional Elements / 7：
The Crouseix-Raviart Element / 7.1：
Qk − Pk − 1 Elements / 7.3：
Pk − Pk − 1 Schemes and Generalized Hood-Taylor Elements / 8：
Pk − Pk − 1 Elements / 8.1：
Generalized Hood-Taylor Elements / 8.2：
Nearly Incompressible Elasticity, Reduced Integration Methods and Relation with Penalty Methods / 9：
Variational Formulations and Admissible Discretizations / 9.1：
Reduced Integration Methods / 9.2：
Effects of Inexact Integration / 9.3：
Divergence-Free Basis, Discrete Stream Functions / 10：
Other Mixed and Hybrid Methods for Incompressible Flows / 11：
Polynomial Exact Sequences and Projection-Based Interpolation with Application to Maxwell Equations / Leszek Demkowicz
Exact Polynomial Sequences
One-Dimensional Sequences
Two-Dimensional Sequences / 2.2：
Commuting Projections and Projection-Based Interpolation Operators in One Space Dimension
Commuting Projections: Projection Error Estimates / 3.1：
Commuting Interpolation Operators: Interpolation Error Estimates / 3.2：
Localization Argument / 3.3：
Commuting Projections and Projection-Based Interpolation Operators in Two Space Dimensions
Definitions and Commutativity
Polynomial Preserving Extension Operators
Right-Inverse ofthe Curl Operator: Discrete Friedrichs Inequality
Projection Error Estimates
Interpolation Error Estimates
Commuting Projections and Projection-Based Interpolation Operators in Three Space Dimensions
Polynomial Preserving, Right-Inverses of Grad, Curl, and Div Operators: Discrete Friedrichs Inequalities / 5.1：
Projection and Interpolation Error Estimates / 5.4：
Application to Maxwell Equations: Open Problems
Time-Harmonic Maxwell Equations
So Why Does the Projection-Based Interpolation Matter?
Open Problems
Finite Element Methods for Linear Elasticity / Richard S. Falk
Finite Element Methods with Strong Symmetry
CompositeElements
Noncomposite Elements of Arnold and Winther
Exterior Calculus on <$>{\op R}^n<$>
Differentia Forms
Basic Finite Element Spaces and their Properties
Differential Forms with Values in a Vector Space
Mixed Formulation of the Equations of Elasticity with Weak Symmetry
From the de Rham Complex to an Elasticity Complex with Weak Symmetry
Well-Posedness of the Weak Symmetry Formulation of Elasticity
Conditions for Stable Approximation Schemes
Stability of Finite Element Approximation Schemes
Refined Error Estimates
Examples of Stable Finite Element Methods for the Weak Symmetry FormulationofElasticity
Arnold, Falk, Winther Families / 11.1：
Arnold, Falk, Winther Reduced Elements / 11.2：
PEERS / 11.3：
A PEERS-Like Method with Improved Stress Approximation / 11.4：
Methods of Stenberg / 11.5：
Finite Elements for the Reissner-Mindlin Plate
A Variational Approach to Dimensional Reduction
The First Variational Approach
An Alternative Variational Approach
The Reissner-Mindlin Model
Properties of the Solution
Regularity Results
Finite Element Discretizations
Abstract Error Analysis
Applications of the Abstract Error Estimates
The Durán-Liberman Element [33]
The MITC Triangular Families
The Falk-Tu Elements With Discontinuous Shear Stresses [35] / 8.3：
Linked Interpolation Methods / 8.4：
The Nonconforming Element of Arnold and Falk [11] / 8.5：
Some Rectangular Reissner-Mindlin Elements
Rectangular MITC Elements and Generalizations [20, 17, 23, 48]
DL4 Method [31]
Ye's Method
Extension to Quadrilaterals
Other Approaches
Expanded Mixed Formulations
SimpleModificationoftheReissner-MindlinEnergy
Least-Squares Stabilization Schemes
Discontinuous Galerkin Methods [9], [8]
Methods Using Nonconforming Finite Elements
A Negative-Norm Least Squares Method / 11.6：
Summary / 12：
List of Participants
Preface
Mixed Finite Element Methods / Ricardo G. Durán
Introduction / 1：
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