Pillay intends to investigate (1) The spectrum problem for uncountable theories, in particular, for uncountable unidimensional theories, (2) some problems in "applied" stability theory, specifically, Zilber's conjecture for algebraically closed fields, the construction of new strongly minimal groups, and superstable differential fields, (3) groups definable over o-minimal structures. These problems all belong to a branch of the foundation of mathematics known as "model theory", which treats such issues as the consistency of axiom systems (the existence of models) and categoricity (the uniqueness of models).
