Miniaturized Microwave Systems: Topological Wave Control

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Homogeneous Spaces

Explores formogenic spaces, topological groups, quotients, and rotations on the unit sphere.

Quantization: Topological Operators

Covers the quantization process using topological operators and their role in generating symmetries.

Ringed Spaces: Definitions and Properties

Covers the definitions and properties of ringed spaces, including morphisms and examples of locally ringed spaces.

Induced Homomorphisms on Relative Homology Groups

Covers induced homomorphisms on relative homology groups and their properties.

Homotopy: Fundamentals and Examples

Covers the fundamentals of homotopy and its applications in topology.

Topological matter and its exploration

Explores topological matter using quantum gases, covering the SSH and Rice-Mele models, adiabatic pump, and Berry curvature measurement.

CW Complexes

Covers the construction and properties of CW complexes, including weak topology and characteristic maps.

Ward Identities and Symmetries

Delves into Ward identities, symmetries, conserved currents, and conformal symmetry, exploring their implications on correlators and quantum models.

Conformal Field Theory & Operator Product Expansion

Explores Conformal Field Theory and Operator Product Expansion, emphasizing the role of symmetries and the quantization process in CFT.

Anomalous Topological Networks: Theory and Experiment

Explores anomalous robustness in nonreciprocal topological networks, covering topological Floquet states, unitary scattering networks, and practical implementations.