Il teorema di Szego – Alexander Bufetov (CNRS I2M, Marseille and Steklov Mathematical Institute, Moscow )

Venue

Sala Conferenze (Puteano, Centro De Giorgi).

Abstract

#ENG 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. #ITA Gabor Szego dimostro` la prima versione del suo teorema all’eta` di 20 anni, la versione forte a quella di 57. L’asintotica dei determinanti di Toeplitz da lui stabilita risulta oggi fondamentale . Si puo` dimostrare il teorema Szego in modo analitico (Szego stesso, Ibragimov, Widom, Basor-Helton, Deift), algebrico (Geronimo-Case-Borodin-Okounkov), oppure usando argomenti della teoria di rappresentazioni (Bump-Diaconis) o di meccanica statistica(Johansson). Il seminario cerchera` di esporre in modo elementare ed accessibile i varii aspetti del teorema di Szego.

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