Szego theorem

Gabor Szego proved the first version of this theorem when he was 20, and he proved it in a stronger version when he was 57. He established asymptotic properties of Toeplitz determinants which nowadays are of crucial importance in many fields.
In fact, Szego theorem can be proved in many ways: via mathematical analysis (Szego, Ibragimov, Widom, Basor-Helton, Deift), with an algebraic approach (Geronimo-Case-Borodin-Okounkov), or else using representation theory arguments (Bump-Diaconis) or statistical mechanics (Johansson).
This talk will try to discuss in an elementary way the various aspects of Szego theorem.