Langlands duality for 3-manifolds and Donaldson–Thomas theory

This talk concerns Langlands duality for 3-manifolds using cohomological Donaldson–Thomas theory. I will explain that the structures appearing in 2d geometric Langlands, such as the Eisenstein series functor and the Hecke operators, have 3-dimensional analogues. As a consequence, I will explain some non-trivial computational evidence for the Langlands duality conjecture.