GLn (R) actions on Posn(R) -- Measures, Integration, and Quadratic Model -- Special Functions on Posn(R) -- Invariant Differential Operators on Posn(R) -- Poisson duality and zeta functions -- Eisenstein Series: First Part -- Geometric and Analytic Estimates -- Eisenstein Series: Second Part.Posn(R) and Eisenstein Series provides an introduction, requiring minimal prerequisites, to the analysis…
Introduction, Exemples -- Topologies sur les domaines de ?N -- Continuité par rapport au domaine -- Existence de formes optimales -- Dérivation par rapport au domaine -- Propriétés géométriques de l’optimum -- Relaxation, homogénéisation.Ce livre est une initiation aux approches modernes de l’optimisation mathématique de formes. Il s’appuie sur les seules connaissances de premiè…
Absolute Values -- Valuations -- Extension of Valuations -- Henselian Fields -- Structure Theory -- Applications of Valuation Theory.Absolute values and their completions -like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valu…
Solving Polynomial Equations -- Resultants -- Computation in Local Rings -- Modules -- Free Resolutions -- Polytopes, Resultants, and Equations -- Polyhedral Regions and Polynomials -- Algebraic Coding Theory -- The Berlekamp-Massey-Sakata Decoding Algorithm.In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpens…
Trigonometric Fundamentals -- Introductory Problems -- Advanced Problems -- Solutions to Introductory Problems -- Solutions to Advanced Problems.103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solv…
Characteristic Classes of Singular Varieties -- Lectures on the Geometry of Flag Varieties -- Combinatorial K-theory -- Morse Functions and Cohomology of Homogeneous Spaces -- Integrable Systems and Gromov-Witten Theory -- Multiplying Schubert Classes -- Lectures on Characteristic Classes of Constructible Functions -- Algebraic K-theory of Schemes -- Gromov-Witten Invariants and Quantum Cohomol…
Shilov Boundary for Normed Algebras -- BMO-Mappings in the Plane -- Harmonic Forms on Non-Orientable Surfaces -- Periodic Fatou Components and Singularities of the Inverse Function -- On the Normality of Topological Target Manifolds for Riemann-Hilbert Problems -- Geometric Aspects of Generalized Analytic Functions -- The Riemann-Hilbert Boundary Value Problem on a Cut Plane -- On the Logarithm…
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.
Basic Facts -- Closed Subsets -- Generating Subsets -- Quotient Schemes -- Morphisms -- Faithful Maps -- Products -- From Thin Schemes to Modules -- Scheme Rings -- Dihedral Closed Subsets -- Coxeter Sets -- Spherical Coxeter Sets.The present text is an introduction to the theory of association schemes. We start with the de?nition of an association scheme (or a scheme as we shall say brie?y), a…
Foundational Material -- De Rham Cohomology and Harmonic Differential Forms -- Parallel Transport, Connections, and Covariant Derivatives -- Geodesics and Jacobi Fields -- Symmetric Spaces and Kähler Manifolds -- Morse Theory and Floer Homology -- Variational Problems from Quantum Field Theory -- Harmonic Maps.