Around Beyond Endoscopy

The idea of "Beyond Endoscopy" was first introduced by Langlands in 2001. It proposed an approach to proving Langlands' Functoriality conjectures in general, and in particular outside of the endoscopic cases, which are covered by the stable trace formula. The current landscape of what goes under the banner of "Beyond Endoscopy" two decades later has changed quite a lot, diverging into several different paths, attempting to mix automorphic L-functions and trace formulas in different ways. In this largely expository talk, I will attempt to describe some of these developments and their goals. Time permitting, I will also discuss my own work in one of these directions.