Dive into an advanced lecture on anomalies in condensed matter physics delivered by Max Metlitski from MIT. Explore the general definition of topological phases and invertible phases, illustrated through a 1+1d Majorana chain and its connection to continuum field theory. Examine the concept of bordism invariance and the classification of invertible phases. Investigate invertible phases with Z classification, focusing on Chern Simons response in 2+1d p+ip superconductors. Delve into phases protected by symmetry and their implementation on lattices. Analyze cohomology SPT and Dijkgraaf-Witten theories, with a potential in-depth look at the 2+1D Levin-Gu bosonic Z 2 SPT. Gain valuable insights into cutting-edge research in condensed matter physics through this comprehensive 1 hour and 28 minutes lecture from the Institut des Hautes Etudes Scientifiques (IHES).