Recent progress in geometric Langlands

By analogy with Langlands's conjectures in arithmetic, Beilinson and Drinfeld conjectured that D-modules on the space of G-bundles
on an algebraic curve are the same as (certain) coherent sheaves on the space of local systems on the same curve, but for the Langlands
dual group. We will discuss our recent work, joint with Gaitsgory and partially joint with Arinkin, Beraldo, Campbell, Chen, Faergeman,
Lin, and Rozenblyum, verifying this conjecture and some related questions. However, the real focus for the talk will be various starting
points in the theory, with the hope that this helps to give outsiders some feeling for what the subject is about.