Why p-adic Numbers Are Better Than Real for Representation Theory

Explore the fascinating world of p-adic numbers and their superiority over real numbers in representation theory in this 58-minute lecture. Delve into the discovery of p-adic numbers over a century ago and their unique ability to unveil aspects of number theory that real numbers cannot. Learn about p-adic fields and their fractal geometry, then witness their application to the complex representation theory of the p-adic group SL(2). Discover the surprising conclusion that close to the identity, all representations are a sum of finitely many simple building blocks arising from nilpotent orbits in the Lie algebra. Gain valuable insights from Monica Nevins in this Colloque des sciences mathématiques du Québec/CSMQ seminar presented by the Centre de recherches mathématiques - CRM.