Mitsuhiro Shishikura

• In his Master's thesis, he proved a conjectured of Fatou from 1920 by showing that a rational function of degree has at most nonrepelling periodic cycles.
• He proved that the boundary of the Mandelbrot set has Hausdorff dimension two, confirming a conjecture stated by Mandelbrot and Milnor.

• ' the existence of a transcendental entire function with a doubly connected wandering domain, answering a question of Baker from 1985;
• ' a study of near-parabolic renormalization which is essential in Buff and Chéritat's recent proof of the existence of polynomial Julia sets of positive planar Lebesgue measure.
• A proof of the local connectivity of the Mandelbrot set at some infinitely satellite renormalizable points.
• A proof of the regularity of the boundaries of the high type Siegel disks of quadratic polynomials.