Zipf's Law and Kolmogorov complexity

Zipf's law was discovered as an empirical probability distribution
governing the frequency of usage of words in a language.  Later
it was observed in many other situations. As Terence Tao recently remarked,
it still lacks a convincing and satisfactory mathematical explanation.

In this talk I suggest that at least in certain cases, Zipf's law can be explained as
a special case of   the  a priori distribution introduced and studied by L.~Levin.
The Zipf ranking corresponding to diminishing frequency appears then as the
ordering determined by the growing Kolmogorov complexity.

In my talk, I will explain the basics of theoretical computability theory and
the place of Kolmogorov complexity in it. Extensions of tis construction lead
to interesting new question in the theory of operads.