Seminar

An almost complex manifold is an even-dimensional real manifold with a complex structure at each tangent space. Unlike the situation for complex manifolds, however, the complex structure might not extend to neighbourhoods around each point.

Model theoretically, one could ask whether there is a theory of almost complex manifolds analogous to the successful model theory of compact complex manifolds. One might also ask about whether, in cases where almost complex manifolds turn out to be honest complex manifolds, this equivalence can be witnessed by a definable map in some ambient model theoretic structure (e.g. an o-minimal expansion of the real field).

In my talk, I will review some basic facts about the model theory of compact complex manifolds, and then formulate some of these questions rigorously.