Lectures related to Künneth theorem

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Acyclic Models: Cup Product and Cohomology

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

Explains cellular homology and the computation of homology groups using boundary maps.

Shape of Data: Algebraic Topology and Shape Representation

Covers algebraic topology, Betti numbers, and shape representation methods for efficient data shape measurement and analysis.

Quantum Measurement Postulate

Explores the verification of PVM properties and the spectral theorem for unbounded operators in quantum mechanics.

Cellular Homology: Applications

Delves into applying cellular homology to compute homology groups and Euler characteristic, showcasing its practical implications.

Cohomology: Abelian Cochains

Introduces cohomology, focusing on abelian cochains and their correspondence with singular cochains.

Homology: Introduction and Applications

Introduces homology as a tool to distinguish spaces in all dimensions and provides insights into its construction and applications.

Homology and Homotopy

Explores the comparison of long exact sequences for vibrations and the relationship between homotopy and homology groups.

Functional Analysis I

Covers eigenvectors, spectral theorems, and finite sequences in functional analysis.

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

Linear Algebra: Unitary Operators

Delves into unitary operators, self-adjoint properties, and spectral theorems in linear algebra.

Sturm-Liouville Problem: Homogeneous Boundary Conditions Essential Role

Explores the Sturm-Liouville eigenvalue problem, emphasizing the essential role of boundary conditions in ensuring self-adjointness and forming an orthogonal basis.

Spectral Theorem for Operators

Explores the spectral theorem for operators in a Hilbert space.

Coxeter Groups: Spectral Theorem and Sylvester's Criterion

Explores the spectral theorem, Coxeter graphs, eigenvalues, and determinants of positive definite matrices.

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Spectral Theorem: Eigenvalues and Eigenvectors

Covers the spectral theorem, eigenvalues, eigenvectors, and their importance in linear algebra.

Quantum Mechanics: Postulates and Observables

Explains the postulates of quantum mechanics and the representation of observables by operators.

Homotopy Theory in Care Complexes

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

Fractal Uncertainty Principle and Spectral Gaps

Explores the Fractal Uncertainty Principle, transfer operators, spectral properties, and adapted operators.