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Poincaré disk model
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Circle Orthogonal & Poincaré Disk
Covers circle orthogonal and Poincaré disk concepts in geometry.
Conformal Maps and Hyperbolic Geometry
Explores conformal maps, hyperbolic geometry, and isometric properties of disks.
Lie Algebra: Casimirs and Poincaré
Explores Lie algebra, Casimirs, and Poincaré in SO(3) transformations.
Untitled
Non-Euclidean Geometries
Explores non-Euclidean geometries, including hyperbolic geometry and the tractricoid model, challenging Euclidean principles and introducing projective geometry.
Symmetries and Groups in Quantum Mechanics
Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.
Lie Theorems and Group Algebra
Covers Lie theorems, group algebra, Ado's theorem, and spacetime symmetries.
Poincaré Group and Lorentz Subgroup
Explores the Poincaré group and Lorentz subgroup in theoretical physics.
Conformal Symmetries in Euclidean and AdS Spaces
Explores conformal symmetries in Euclidean and AdS spaces, isometries, induced metric, Poincaré coordinates, and boundary structure.
Lie Algebra Representation
Delves into Lie algebra representation and Lorentz subgroup concepts.
Untitled
Mixing Time Changes of Nilflows
Delves into mixing time changes in nilflows, emphasizing the delicate nature of mixing and its dependence on singularities.
Quantum Field Theory: Lorentz and Poincaré Groups Representations
Explores Lorentz and Poincaré groups representations, Poincaré algebra, and Lagrangians in Quantum Field Theory.
Dynamics of Singular Riemann Surface Foliations
Explores the dynamics of singular Riemann surface foliations, focusing on vector fields, linear parts, and coordinate changes.
Renormalization Group in Field Theory
Explores the Renormalization Group in field theory, discussing scaling functions, critical exponents, and Gaussian fixed points.
Euclidean Geometry: Operations and Constructions
Covers the fundamental operations and constructions in Euclidean geometry, focusing on algebraic interpretations and ruler-and-compass constructions.
Markov Chains and Applications
Explores Markov chains, their properties, and algorithmic applications, emphasizing information quantification and state monotonicity.
Lie Groups: Representations and Transformations
Explores Lie groups, scalar fields, and vector spaces transformations.
Quantum Field Theory: Poincaré Group
Explores Einsteinian relativity, the Lorentz group, and Poincaré transformations, emphasizing proper and non-orthochronous components.
Surface of Revolution
Explains the parametric equations of surfaces of revolution generated by curves in space.
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