Introduction -- Four Hamiltonian Systems -- Small Vibrations of Tetrahedral Molecules -- The Hydrogen Atom in Crossed Fields -- Quadratic Spherical Pendula -- Fractional Monodromy in the 1: - 2 Resonance System -- The Tetrahedral Group -- Local Properties of Equilibria -- References -- Index.Modern notions and important tools of classical mechanics are used in the study of concrete examples tha…
Siegel Domains -- Homogeneous Siegel Domains -- Normal Siegel Domains -- Other Realizations -- Automorphism Group -- Classification of Square Domains -- Symmetric Bounded Domains -- Szegö Kernel and Poisson Kernel -- Homogeneous Bounded Domains.
On Existence of Solutions of Semilinear Impulsive Functional Differential Equations with Nonlocal Conditions -- On Banach-Lie Algebras, Spectral Decompositions and Complex Polarizations -- Commuting Triples of Subnormal Operators and Related Moment Problems -- The Equality of the Reduced and the Full C*-Algebras and the Amenability of a Topological Groupoid -- ?-Numerical Radius in Banach Space…
to Projective Duality -- Actions with Finitely Many Orbits -- Local Calculations -- Projective Constructions -- Vector Bundles Methods -- Degree of the Dual Variety -- Varieties with Positive Defect -- Dual Varieties of Homogeneous Spaces -- Self-dual Varieties -- Singularities of Dual Varieties.Projective duality is a very classical notion naturally arising in various areas of mathematics, suc…
Generalities on Poisson Structures -- Poisson Cohomology -- Levi Decomposition -- Linearization of Poisson Structures -- Multiplicative and Quadratic Poisson Structures -- Nambu Structures and Singular Foliations -- Lie Groupoids -- Lie Algebroids.Poisson manifolds play a fundamental role in Hamiltonian dynamics, where they serve as phase spaces. They also arise naturally in other mathematical …
to Symmetric Spaces and Their Compactifications -- Compactifications of Symmetric and Locally Symmetric Spaces -- Restrictions of Unitary Representations of Real Reductive Groups.Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the…
The Plancherel Theorem for a Reductive Symmetric Space -- The Paley—Wiener Theorem for a Reductive Symmetric Space -- The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space.Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three indepen…
Results on topological spaces -- Rings and modules -- Integral extensions -- Factorial rings -- Field extensions -- Finitely generated algebras -- Gradings and filtrations -- Inductive limits -- Sheaves of functions -- Jordan decomposition and some basic results on groups -- Algebraic sets -- Prevarieties and varieties -- Projective varieties -- Dimension -- Morphisms and dimension -- Tangent s…
Parafree Groups -- The Finitary Andrews-Curtis Conjecture -- Cuts in Kähler Groups -- Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries -- Solved and Unsolved Problems Around One Group -- Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators -- Survey on Classifying Spaces for Families of Subgroups -- Are Unitarizable Groups Amenable? -- Probabil…
Gaudin Model and Opers -- Integrable Models with Unstable Particles -- Quantum Reduction in the Twisted Case -- Representation Theory and Quantum Integrability -- Connecting Lattice and Relativistic Models via Conformal Field Theory -- Elliptic Spectral Parameter and Infinite-Dimensional Grassmann Variety -- Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. II -- Weil-Petersson …