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Focal subgroup theorem
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Cohomology: Cup Product
Covers the cup product in cohomology, focusing on examples and computations.
Euclidean Isometries: Properties and Applications
Explores the properties and applications of Euclidean isometries in R^2.
Linear Representations: Basics and Examples
Covers linear representations, isomorphism, G modules, and classification of representations of C star and C plus.
Poincaré Irreps 2: Little Group and Induced Representation
Explores Poincaré irreducible representations, Little Group, and induced representation in the context of momentum eigenstates.
Hamiltonian Homeomorphisms on Surfaces
Explores the action of Hamiltonian homeomorphisms on surfaces and discusses related mathematical concepts.
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Bar Construction: Homology Groups and Classifying Space
Covers the bar construction method, homology groups, classifying space, and the Hopf formula.
Geometric McKay correspondence: Du Val singularities and Dynkin diagrams
Explores the derivation of Dynkin diagrams from Du Val singularities.
Fault tolerance: Stabilizer Subgroup
Explores fault tolerance, error propagation, and the Gottesman-Kill Theorem in stabilizer subgroups.
Subgroups and Cosets: Lagrange's Theorem
Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.