Explore a comprehensive lecture on the ramification of supercuspidal parameters delivered by Michael Harris from Columbia University as part of the Theta Series: Representation Theory, Geometry, and Arithmetic conference. Delve into topics such as the local Langlands conjecture, Kaletha's parametrization, the Deligne-Kazhdan correspondence, and V. Lafforgue's global results. Examine concepts like incorrigible representations, globalization, wild ramification, and mixed supercuspidals. Gain insights into the application of purity, Poincaré series, and potential automorphy. This 58-minute talk provides an in-depth exploration of advanced mathematical concepts in representation theory and number theory.