From Hrushovski counterexamples to Grothendieck period conjecture

In 1988 Hrushovski found counterexamples to the speaker's conjectures that categorical theories are in a certain sense reducible to algebraic geometry.  Actually, the counterexamples are the outcomes of a very special abstract construction which is based on a combinatorial inequality in terms of dimensions of algebraic origin. The counterexamples were originally perceived as unwelcome mathematical pathologies.

We will explain how Hrushovski's construction can be linked to

the theory of classical transcendental functions  and how it leads to certain conjectures  which eventually can be recognised as a form of Grothendieck - Andre period conjecture.