Explore symmetries in physics and their quantum modifications in this 55-minute colloquium talk by Jeff Harvey from the University of Chicago. Delve into the concept of "Symmetries, Anomalies and Anomaly Inflow" as Harvey examines how classical symmetries can be altered or eliminated by quantum effects in quantum mechanics and quantum field theory. While focusing on the physics aspects, the talk also connects these concepts to relevant mathematical topics, including topological invariants, characteristic classes, and index theory. Gain insights into the interplay between physics and mathematics in this advanced exploration of quantum phenomena and their impact on symmetries.