Analyticity, algebraicity and definability — on the o-minimal version of Chow’s Theorem

Chow’s theorem says that a compact analytic submanifold of projective space is algebraic. A generalization of this result (proved with Starchenko) says that a complex analytic subvariety of affine space which in addition is definable in some o-minimal structure over the reals is algebraic.

In these 2-3 talks I will speak about the history of this problem, several related and less known results, and the reasons to expect the theorem to be true (not a full proof).

Some minimal background on definability in structures, as well as basics of o-minimality will be assumed.