Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits. Geometry is suitable for a semester course in non-Euclidean geometry or as a guide to independent study, with over 200 exercises and several essays on topics including the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.
The focus of this course: - Applications of topology in condensed matter based on bulk-edge correspondence. - Special attention to the most active research topics in topological condensed matter: theory of topological insulators and Majorana fermions, topological classification of “grand ten” symmetry classes, and topological quantum computation - Extensions of topology to further areas of condensed matter, such as photonic and mechanical systems, topological quantum walks, topology in fractionalized systems, driven or dissipative systems.