## Logic Seminar

Zariski-type structures were introduced and studied by Zilber and Hrushovski in their study of strongly minimal sets. A Zariski-type structure is a set $X$ with a collection of compatible Noetherian topologies, one on each $X^n$, and an assignment of dimension to the closed sets, satisfying certain conditions. For example, taking the complex analytic subvarieties of $M^n$, for a compact complex analytic manifold $M$, to be the closed sets and the dimension to be the complex dimension gives a Zariski-type structure. I am showing that a similar statement holds if the manifold is almost complex, i.e., admits an automorphism $J$ of the tangent bundle TM such that $J^2=-Id$, that does not necessarily arise from a holomorphic atlas on the manifold. I will define an almost complex subvariety, and outline the geometric results that are needed to show that the obtained structure is Zariski-type. I will also talk about geometric applications.