Explore the intricacies of p-adic group representations and their applications in this comprehensive lecture by Jessica Fintzen from the University of Cambridge and Duke University. Delve into the construction of supercuspidal representations, examine epipelagic representations, and analyze concrete examples. Investigate the concept of omni supercuspidal types and their various applications in number theory. Gain insights into congruences of algebraic automorphic forms as the lecture progresses through advanced topics in p-adic mathematics. Enhance your understanding of this complex subject through the expertise of a renowned mathematician in the field.