Weng Lin (Japan, Kyushu, z.z Tübingen und Münster)

Abstract. In this talk, we will study in details the Weil-Petersson geometry (resp. Takhtajan-Zograf geometry) for punctured Riemann surfaces associated to the deformation of complex structures of surfaces (resp. the deformation of punctures). This is an application of our wok on arithmetic Riemann-Roch theorem for a particular class of singular metrics for which the famous Quillen metric formalism on determinants cannot be applied. If time is allowed, we will also talk about our joint work with Zagier (resp. with Wing-Keung To and Kunio Obitsu) on Deligne products for moduli towers (resp. on asymptotic behaviors of TZ metrics).