Explore lattice edge theories for topological phases of matter in this high-energy theory seminar. Delve into the description of edge excitations in (2+1)D topological phases using both continuum field theories and lattice-like edge theories with finite-dimensional Hilbert spaces. Examine several examples of finite-dimensional edge theories, focusing on "ungappable" cases that cannot be gapped by local interactions. Learn about the importance of edge theories, their existence, and the concept of chiral central charge. Distinguish between two types of edges and phases, and understand the strategy behind lattice edge theory. Investigate the addition of scattering terms and gain insights into this complex area of condensed matter physics.