Research Interest:
Dynamical Systems; in particular, the geometry of the Mandelbrot set and other parameter spaces, renormalization theory, post-critically finite maps, self-similar groups.
Publications:
Local connectivity of the Mandelbrot set at some satellite parameters of bounded type.
Joint with Mikhail Lyubich. To appear in GAFA.
Algorithmic aspects of branched coverings III/V. Erasing maps, orbispaces, and the Birman exact sequence.
Joint with Laurent Bartholdi. Groups, Geometry, and Dynamics, 15 (4), 1197-1265, 2021
Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters.
Joint with Mikhail Lyubich and Nikita Selinger. Journal of the AMS, 33 (2020), 653-733
Algorithmic aspects of branched coverings IV/V. Expanding maps.
Joint with Laurent Bartholdi. Transactions of the AMS, 370, 7679--7714, 2018.
Algorithmic aspects of branched coverings II/V. Sphere bisets and their decompositions.
Joint with Laurent Bartholdi. Inventiones Math., 2020.
Algorithmic aspects of branched coverings I. Van Kampen's Theorem for bisets.
Joint with Laurent Bartholdi. Groups, Geometry, and Dynamics, 12 (1), 121--172, 2018.
Algorithmic aspects of branched coverings.
Joint with Laurent Bartholdi. Ann. Fac. Sci. Toulouse, 26 (5), 1219--1296, 2017.
Core entropy of quadratic polymonials.
Joint with Dierk Schleicher. Arnold Mathematical Journal, 25 March 2020.
Homeomorphisms between limbs of the Mandelbrot set.
Joint with Dierk Schleicher. Proceedings of the AMS, electr. published
on Sept. 23, 2011.
The decoration theorem for Mandelbrot and Multibrot sets.
International Mathematics Research Notices, 13, 3985--4028, 2017.
Preprints:
Uniform a priori bounds for neutral renormalization.
Joint with Mikhail Lyubich.
A canonical decomposition of postcritically finite rational maps and their maximal expanding quotients.
Joint with Mikhail Hlushchanka and Dierk Schleicher.