Takuro Mochizuki
Mochizuki is probably most famous for proving a conjecture of Kashiwara. People with masochistic tendencies can read on...
Recall that Beilinson, Bernstein, Deligne (and Gabber) proved things like the decomposition theorem and hard Lefschetz for semisimple perverse sheaves of geometric origin. The last assumption is needed since their technique involves reducing to the $\ell$-adic case in positive characteristic.
A while back Kashiwara conjectured that these results should hold more generally for semisimple perverse sheaves (geometric or not) on complex varieties, or more generally for semisimple holonomic (not necessarily regular) $D$-modules. This conjecture is now a theorem due to Mochizuki.
The proof is long and complicated, but here is a quasi-explanation based on my limited understanding.
When $L$ is a semisimple local system on a smooth projective variety $X$, it corresponds, thanks to work of Corlette-Simpson, to a so called harmonic bundle. Suffices it to say that this means that $L$ carries operators similar to $d,\partial, \bar \partial$ on a Kahler manifold, and the usual proof of hard Lefschetz carries over. But this is not enough, since a perverse sheaf is only generically a local system. In other words,
$L$ may only be defined on a Zariski open subset of $X$; constructing the appropriate harmonic object is much more delicate and due, and in this generality, to Mochizuki. I won't attempt to say more other than to mention that
Mochizuki develops the machinery of twistor modules (due to Simpson and Sabbah) to the point where he can show that holomonic semisimple $D$-modules correspond to such things. And this plays a key role in the resolution of the conjecture.