Research

I work in arithmetic geometry. Recently, my research focuses on curves and their moduli spaces in positive characteristic from the point of view of fundamental groups. I introduced a topological space which I call the moduli space of admissible fundamental groups of curves in positive characteristic, and posed the so-called "Homeomorphism Conjecture". This conjecture says that the moduli spaces of curves in positive characteristic can be reconstructed group-theoretically from the geometric fundamental groups of curves as topological spaces. Moreover, the Homeomorphism Conjecture gives us a new insight into the theory of the anabelian geometry of curves over algebraically closed fields of characteristic p based on the following philosophy: The anabelian properties of pointed stable curves over algebraically closed fields of characteristic p are equivalent to the topological properties of the moduli spaces of admissible fundamental groups.