Speaker: Assaf Hasson Title: On uncountably categorical approximations and Gromov-Hausdorff limits. Abstract: In recent years Zilber and others found intriguing relations between Hrushovski's free amalgamation constructions and conjectures in transcendental number theory (variants on Schanuel's conjecture) and Diophantine geometry (variants on the Conjecture on the Intersection with Tori). However, the other part of the construction, the collapse, though - model theoretically - it can be interpreted as a generalization of the notion of smooth approximation, is still missing an extra-logical interpretation. In the talk I will present recent attempts to introduce a notion of metric approximations of structures, and their connection to both Hrushovski's constructions and to ideas borrowed from mathematical physics. (Joint with Boris Zilber).