Topological Aspects of Four-Manifolds -- The Theory of Donaldson Invariants -- The Theory of Seiberg-Witten Invariants -- Supersymmetry in Four Dimensions -- Topological Quantum Field Theories in Four Dimensions -- The Mathai-Quillen Formalism -- The Seiberg-Witten Solution of N = 2 SUSY Yang-Mills Theory -- The u-plane Integral -- Some Applications of the u-plane Integral -- Further Developmen…
Noncommutative Geometry -- Poisson Geometry and Deformation Quantization -- Applications in Physics -- Topological Quantum Field Theory.This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challeng…
Knot Invariants and Configuration Space Integrals (Christine Lescop) -- Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces (Raimar Wulkenhaar) -- Introduction to String Compactification (Anamaria Font, Stefan Theisen) -- Index Theorems and Noncommutative Topology (Thierry Fack).This volume offers an introduction, in the form of four extensive lectures, to some recent develo…
Introduction -- The Ernst Equation -- Riemann-Hilbert Problem and Fay's Identity -- Analyticity Properties and Limiting Cases -- Boundary Value Problems and Solutions -- Hyperelliptic Theta Functions and Spectral Methods -- Physical Properties -- Open Problems -- Riemann Surfaces and Theta Functions -- Ernst Equation and Twister Theory -- Index.Exact solutions to Einstein`s equations have been …
Lie Groups -- Subgroups -- Lie Algebra -- A Little Kinematics -- Line Geometry -- Representation Theory -- Screw Systems -- Clifford Algebra -- A Little More Kinematics -- The Study Quadric -- Statics -- Dynamics -- Constrained Dynamics -- Differential Geometry.Geometric Fundamentals of Robotics provides an elegant introduction to the geometric concepts that are important to applications in rob…
1 Relativity based on symmetry -- 1.1 Space-time transformation based on relativity -- 1.2 Step 6 - Identification of invariants -- 1.3 Relativistic velocity addition -- 1.4 Step 7 - The velocity ball as a bounded symmetric domain -- 1.5 Step 8 - Relativistic dynamics -- 1.6 Notes -- 2 The real spin domain -- 2.1 Symmetric velocity addition -- 2.2 Projective and conformal commutativity and asso…
From the contents: Part I Control Applications of Polynomial Positivity Control Applications of Sum of Squares Programming; Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition; A Sum-of-Squares Approach to Fixed-Order H8-Synthesis; LMI Optimization for Fixed-Order H8 Controller Design; An LMI-based Technique for Robust Stability Analysis of Linear Systems with Polynomial P…
Holomorphic Functions -- Complex Manifolds -- Differential Forms, Vector Bundles, Sheaves -- Infinitesimal Deformation -- Theorem of Existence -- Theorem of Completeness -- Theorem of Stability.From the reviews: "The author, who with Spencer created the theory of deformations of a complex manifold, has written a book which will be of service to all who are interested in this by now vast subject…
Neuroscience -- Spatiotemporal Dynamics of Visual Perception Across Neural Maps and Pathways -- Symmetry, Features, and Information -- Neural Networks -- Geometric Approach to Multilayer Perceptrons -- A Lattice Algebraic Approach to Neural Computation -- Eigenproblems in Pattern Recognition -- Image Processing -- Geometric Framework for Image Processing -- Geometric Filters, Diffusion Flows, a…
Linear Algebra Topics -- Affine Geometry -- Projective Geometry -- Advanced Calculus Topics -- Point Set Topology -- Combinatorial Topology -- Algebraic Topology -- Differential Topology -- Differential Geometry -- Algebraic Geometry.Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory …