Veech Groups, Cutting Sequences, and Penetration Spectra - C. Ulcigrai
Explore the mathematical concepts of Veech groups, cutting sequences, and penetration spectra in this comprehensive lecture. Delve into the world of translation surfaces, affine automorphisms, and Veech groups, understanding their definitions and properties. Examine cutting sequences of linear trajectories and their characterizations, including Sturmian sequences and substitutions. Investigate the classical Lagrange spectrum and its generalization to Veech translation surfaces. Learn about affine deformations, Teichmüller curves, and the geometric interpretation of derivation for specific shapes like the octagon. Discover the Bouw-Moeller derivation and its application to renormalization on the Teichmüller disk. Finally, explore Hall Rays in Lagrange Spectra of Veech surfaces and their connection to boundary expansions and saddle connections.