Speaker: Yoav Yaffe, McMaster University Title: A "tame" vs. "wild" dividing line in partial-differential fields Abstract: One of the classical "tame" vs. "wild" dividing lines in Model Theory is the existence of a model completion for an elementary class of structures. If such a model completion exists then one gets universal models, e.g. algebraically closed fields of high transcendence degree (over some base field). The classical examples are the class of fields on the "tame" side (since 'algebraically closed fields' is an elementary class); and the class of groups on the "wild" side (since 'existentially closed group', the analog, is a non-elementary class, so e.g. it's not closed under ultra-products). All logical terms will be defined (elementary class, existentially closed, ultra-product, etc.). I'll then describe briefly my work on "non-commutative" partial-differential fields, or Lie differential fields. These are fields with some fixed Lie algebra acting on them as derivations. If the characteristic is 0 and the Lie algebra is finite dimensional then there is a model completion, and one gets "tameness" results for finite systems of (formal) PDEs, e.g. decidability. On the other hand, if the Lie algebra has a finitely generated sub Lie algebra which is not finitely presented, then there is no model completion, hence the corresponding class of Lie differential fields is "wild".