Qixiang Wang, speaking at the Institute for Advanced Study workshop on Hodge Theory and O-minimality, argues that certain complex-analytic spaces can be reconstructed purely from an invariant attached to their fundamental group, a phenomenon he compares to Mostow rigidity. He builds on Shinichi Mochizuki's result that hyperbolic curves over p-adic fields are determined by their arithmetic fundamental groups, and introduces a Hodge-theoretic analogue of that group for complex Kahler manifolds. The core result: hyperbolic Riemann surfaces turn out to be uniquely recoverable from this Hodge-theoretic fundamental group, giving a complex-analytic parallel to Mochizuki's arithmetic theorem. Wang sketches the construction from non-abelian Hodge theory, works through the Riemann surface case in detail, and closes with remarks on extending the argument to higher-dimensional varieties if time allows. The talk assumes graduate-level familiarity with Hodge theory and fundamental groups and runs just under an hour, delivered at Simonyi Hall as part of the IAS workshop series.