Monica Nevins (Ottawa): Why p-adic numbers are better than real for representation theory

The p-adic numbers, discovered over a century ago, unveil aspects of number theory that the real numbers alone can’t.  In this talk, we introduce p-adic fields and their fractal geometry, and then apply this to the (complex!) representation theory of the p-adic group SL(2).  We describe a surprising conclusion: that close to the identity, all representations are a sum of finitely many rather simple building blocks arising from nilpotent orbits in the Lie algebra.