Fundamental groups Geometry and Arithmetic Organizers Yuichiro Hoshi (RIMS), Zhi Hu (USTC), Yu Yang (RIMS) Date August 18, 2019-August 22, 2019 Place USTC, Hefei, Anhui, China Abstracts （PDFファイル） August 18 (Sun) 930 - 1025 Opening 1030 - 1130 Kang Zuo (Mainz University) An algebraic characterization of modular curves 1400 - 1500 Shota Tsujimura (RIMS, Kyoto University) Combinatorial anabelian geometry and resolution of nonsingularities 1530 - 1630 Kazumi Higashiyama (RIMS, Kyoto University) The mono-anabelian geometry of geometrically pro-p arithmetic fundamental groups of second configuration spaces August 19 (Mon) 1030 - 1130 Yuichiro Hoshi (RIMS, Kyoto University) An anabelian open basis for a smooth variety 1400 - 1500 Ippei Nagamachi (The University of Tokyo) On the Hom version of the Grothendieck Conjecture for hyperbolic polycurves of dimension 2 1530 - 1630 Koichiro Sawada (RIMS, Kyoto University) Reconstruction of invariants of configuration spaces of hyperbolic curves from associated Lie algebras August 20 (Tue) 1030 ‐ 1130 Toshiro Hiranouchi (Kyushu Institute of Technology) Fundamental Groups with Restricted Ramification 1400 - 1500 Akira Sarashina (RIMS, Kyoto University) Reconstruction of curves in positive characteristic by their geometric fundamental groups 1530 - 1630 Yu Yang (RIMS, Kyoto University) On the topological and combinatorial structures of pointed stable curves in positive characteristic 1800 ‐ Conference Banquet August 21 (Wed) 1030 - 1130 Naotake Takao (RIMS, Kyoto University) On anabelian geometry of moduli spaces of curves 1400 - 1500 Yu Iijima (Hiroshima University) On the centralizer of the image of the universal outer monodromy representation of the moduli stack of pointed smooth curves 1530 - 1630 Jinbang Yang (Mainz University) Explicit formula of self map on the moduli space of graded Higgs bundles August 22 (Thu) 930 - 1030 Takahiro Murotani (RIMS, Kyoto University) A p-adic analytic approach to the absolute Grothendieck conjecture 1050 - 1150 Ruiran Sun (Mainz University) Ordinary Condition and Lifting of periodic Higgs Bundles 1150 Closing