Arithmetic and Moduli Spaces around Galois-Teichmueller tower

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In this project, researches on anabelian geometry have been developed with rich prospects for number theory and algebraic geometry. In particular, promoted were international interactions of arithmetic researches concerning Galois-Teichmueller tower formed by fundamental groups of algebraic curves and their moduli spaces. In October 2010, we realized the 3rd Seasonal Institute Conference of Mathematical Society of Japan in Kyoto University, and subsequently in October 2012 we published the proceedings volume "Galois-Teichmueller theory and Arithmetic Geometry". Besides, a certain monodromy invariant arising from fundamental groups of once-punctured elliptic curves was studied and research papers on it have been published.