Research of arithmetic fundamental groups of hyperbolic curves

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By a joint work with Shinichi Mochizuki, we proved the injectivity portion of the combinatorial cuspidalization; moreover, as an arithmetic application of this injectivity, we obtained the faithfulness of the outer Galois representations associated to hyperbolic curves over number or p-adic local fields. Next, I introduced the notion of monodromic fullness for hyperbolic curves and proved an anabelian conjecture-type result for certain monodromically full hyperbolic curves of genus zero. Finally, I proved that in general, the pro-p section conjecture for hyperbolic curves over number fields, as well as p-adic local fields, cannot be resolved in the affirmative.