The Mathematical Legacy of Hel Braun

Hel Braun (IAS member 1947-1948) was a mathematician who introduced approaches that continue to impact research today.  Braun's research contributions lie in three areas: classical number theory problems about integers, modular and automorphic forms, and Jordan algebras.  I will describe how each of these seemingly distinct topics led Braun naturally to the next, and I will highlight the ongoing impact of some of Braun's work, including in my own research.  Reasons for interest today are largely different from those that motivated Braun and were likely unforeseen at the time.  I will also try to address apparent anomalies, like why you probably are unfamiliar with Braun despite this work's influence.  This colloquium-level talk is intended for a broad mathematical audience.  If your response to the title was "Who's Hel Braun?" this talk is for you.  If you already know who that is but asked "But why Hel Braun?" it is also for you.