Shinichi Mochizuki's main research interest is the arithmetic of hyperbolic curves. During the early and mid-1990's, his research centered upon the $p$-adic anabelian geometry and $p$-adic Teichm\"uller theory of hyperbolic curves. Since the late 1990's, however, he has also been concerned with developing a global arithmetic version of Teichm\"uller theory for pairs consisting of a number field equipped with an elliptic curve and understanding the numerous interesting connections between this theory and the absolute and combinatorial anabelian geometry of hyperbolic curves.