
Research Interests
 Lowdimensional analytic dynamics (rigidity and small divisors)
 Geometric analysis (quasiconformal mappings and elliptic PDEs)
 Renormalization operators (on infinite dimensional spaces)
Research publications and Preprints
 Toplogy of irrationally indifferent attractors,
52 pages, preprint 2017.
 Satellite renormalization of quadratic polynomials, (with M. Shishikura),
71 pages, preprint 2015.
 Statistical properties of quadratic polynomials with a neutral fixed point,
(with A. Avila)
Journal of the European Mathematical Society, Volume 20, Issue 8, 2018, (57 pages), preprint
 Typical orbits of quadratic polynomials with a neutral fixed point: NonBrjuno type
Ann. Sci. 'Ecole Norm. Sup., in Press 2017, (82 pages), preprint
 A proof of the MarmiMoussaYoccoz conjecture for rotation numbers of high type,
(with A. Cheritat)
Invent. Math. 202 (2015), no. 2, 677–742, (66 pages), preprint
 Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type
Commun. Math. Phys. 322 (2013), no. 3, 9991035, (37 pages), preprint
 Combinatorial rigidity for some infinitely renormalizable unicritical polynomials
Conform. Geom. Dyn. 14 (2010), 219255, (37 pages), preprint
Manuscripts in preparation
 Complex Feigenbaum phenomena of high type, (with M. Pedramfar)
 Dimension paradox of irrationall indifferent attractors (with A. De Zotti and F. Yang)
 Topology of isentropes in a two parameter family of unimodal maps, (with S. van Strien)
 Combinatorialanalytic multipliers and the asymptotic geometry of the Mandelbrot set,
 Measurable dynamics of holomorphic maps with a nonlinearizable fixed point,
Other
 Chapter on dynamical systems in the book Mathematics of Planet earth, a primer, World Scientific, 2017.
 One dimensioanl real and complex dynamics, lecture notes of the TCC course, 52 pages, Spring 2014.
 Geometric complex analysis, lecture notes , 98 pages, Autumn 2016.
 Analytic number theory, lecture notes , 66 pages, Winter 2016.
 Dynamics of complex unicritical polynomials, PhD thesis (150 pages), Sept 2009.
 Measurable dynamics of geodesic flow on rank one Riemannian manifolds,
MSc thesis (a survey in Farsi, 109 pages), 2004.
Selected slides of talks
 Satellite renormalization of quadratic polynomials, slides of the
the first two lectures of an eightlecture minicourse at the Simon's semeter at Banach center in Warsaw, September 2015.
 Typical orbits of quadratic polynomials with a neutral fixed point, slides at Seillac, France,
May 2010, and a longer one, slides, at University of Liverpool, Apr 2010.
 Attractors of quadratic polynomials with an irrationally indifferent fixed point, slides at National University of Singapore, 2012.
 Combinatorial rigidity of infinitely renormalizable unicritical polynomials, slides at Roskilde University in Copenhagen, Sept 2010
Gallery of dynamically generated pictures
