A quick proof of the étale and pro-étale exodromy theorems

Locally constant sheaves are most easily understood as representations of the fundamental group, via the monodromy correspondence. In algebraic geometry, it is often preferable to use the larger class of constructible sheaves, as these are stable under (higher) pushforward. In 2018, Barwick, Glasman, and Haine proved an exodromy correspondence for constructible étale sheaves, using ideas from higher topos theory and profinite stratified homotopy theory. In this talk, I will present a more direct geometric proof of the étale and pro-étale exodromy theorems, based on joint work with Sebastian Wolf.