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Explore advanced concepts in photonic engineering through this comprehensive lecture on tailoring resonances and complex energy-momentum dispersion in photonic crystals. Delve into novel approaches for manipulating the real and imaginary parts of photonic resonances at the sub-wavelength scale using periodic arrangements of materials with varying permittivity and geometry. Discover how photonic bands can be transformed from Dirac dispersion to flatband configurations, and examine the unique features of non-Hermitian Hamiltonians in open systems, including exceptional points and bound states in the continuum. Learn about experimental demonstrations across various platforms such as III-V nanophotonics, perovskite metasurfaces, and silicon photonics, featuring different photonic species like dielectric guided resonances, Bloch surface waves, Tamm plasmons, and exciton polaritons.