Reconstruction in Algebraic Geometry

A classical theorem of Neukirch and Uchida says that number fields are completely determined by their absolute Galois groups. One might wonder about analogous results for algebraic varieties: in what situations can varieties be “reconstructed” from a group or other algebraic invariant? In this talk, we’ll survey different approaches to this question as well as discuss some recent advances from our joint work with Barwick and Glasman.