scrivo per avvisare che venerdì 19 alle 11, in aula seminari, ci sarà un seminario di Hideki Miyachi (Kanazawa University, Japan), di cui riporto sotto titolo e abstract.

Hideki è ospite del Centro de Giorgi dal 15 al 26 luglio, per un Research in Pairs.

In seguito al seminario, andremo a pranzo con l'ospite (probabilmente al Quore). Vi chiedo di farmi sapere entro mercoledì se pensate di esserci per il pranzo, così da poter prenotare.

Grazie in anticipo, e a presto,

Fabrizio

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Title : Toward Complex Geometry of Teichmueller space
Abstract:
The Teichmueller space of Riemann surfaces of genus g is a deformation space of marked Riemann surfaces of genus g. It is the orbifold universal covering space over Riemann's moduli space of Riemann surfaces, with the Deck transformation group being a quotient group of the mapping class group. TheTeichmueller space has a natural complex structure and is considered the universal space of holomorphic families of Riemann surfaces. It also has a natural Finsler metric on the tangent bundle called the Teichmueller metric, which coincides with the Kobayashi metric. Furthermore, the Teichmueller space of tori is canonically identified with the upper-half space via the generators of lattices, and the Teichmueller metric coincides with the Poincaré metric of curvature -4. In this talk, I will discuss my recent progress on the complex geometry of the Teichmueller space. We will begin with the Teichmueller space of tori to discuss the model case and present results including

    • the characterization of the PluriGreen function and the Poisson integral formula; and
    • the infinitesimal properties of the Teichmueller metric.

If time permits, I would also like to address ongoing problems and conjectures.
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