Abstract Variational Problems

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Related lectures (33)

Bilinear Forms: Theory and Applications

Covers the theory and applications of bilinear forms in various mathematical contexts.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Conformity and Compliancy in Geometry

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Quadratic Forms and Symmetric Bilinear Forms

Explores quadratic forms, symmetric bilinear forms, and their properties.

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Weingarten Application of Regular Surfaces

Covers the application of the Weingarten map on regular surfaces and the shape operator.

Quantization: Topological Operators

Covers the quantization of topological operators and Ising models on square lattices.

Interpolation of Lagrange: Dualité and Coupling

Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.

Signal Representations

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Pseudo-Euclidean Spaces: Isometries and Bases

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Hilbert Space: State, Evolution, Measurement

Introduces Hilbert space as a big place where quantum systems evolve with unitaries.

Scalar Product: Algebraic Properties

Explores the algebraic properties of the scalar product and their geometric implications.

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, focusing on states, time evolution, and measurement.

Hilbert Spaces: Definition and Properties

Covers the definition and properties of Hilbert spaces, including the Cauchy-Schwarz inequality and norm definition.

Crash Course on Quantum Mechanics

Covers fundamental concepts in quantum mechanics, including vector spaces, superposition, observables, and inner product.

Function Spaces and Hilbert Spaces

Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.

Polarisation Qubit: Thought Experiments

Explores thought experiments with polarisation qubits of photons and the concept of superposition in Hilbert space.

Segal CFT: Hilbert Space Applications

Covers the applications of Segal's Conformal Field Theory in Hilbert spaces.

Lax-Milgram: Variational Problems and Riesz's Theorem Log in to Mediaspace to watch this video

Explores the Lax-Milgram theorem, variational problems, and Riesz's representation theorem in linear elliptic problems.

Weak Formulation of Elliptic PDEs Log in to Mediaspace to watch this video

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

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