On the simplicity and complexity of analytical functions

A valuation of a simplicity and a complexity of objects of mathematical reality is one of the eternal and everlasting theme. Despite of the great diversity of approaches still there are some common features in different theories of complexity. In the talk I am going to explain my recent results about the valuation of complexity of analytical functions of two variables. In particular, about the unexpected role of elliptic functions in the description of simple (of the complexity one) harmonic functions. Also I will tell about the role of the Weierstrass theorem (the theorem about functions with algebraic theorem of addiction) in the description of simple algebraic functions.
The talk will be held in Russian.