【学术报告】The main cubioid and the modulus of renormalization

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Beijing-Saint Petersburg Mathematics Colloquium (online)

 

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Speaker: Vladlen Timorin

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Abstract: The main cubioid (CU) is a central part in the parameter space of cubic polynomials of one complex variable viewed as dynamical systems. It plays a similar role to that of the main cardioid in the (quadratic) Mandelbrot set, hence the title. However, in contrast to the main cardioid, topology and combinatorics of the CU are rather involved. We discuss a dynamical characterization of the CU, a proof of which has been recently completed. The last (most recent) ingredient is an upper bound on the moduli of quadratic-like restrictions. This is a joint project with A. Blokh and L. Oversteegen.

Bio:Vladlen Timorin is a Professor at the Department of Mathematics of the Higher School of Economics, Moscow. His major research interests include Geometry (convex polytopes, toric varieties, projective differential geometry, classical geometric structures), dynamics (rational functions, surgery, invariant laminations), and quadratic forms. Graduated from the Independent Moscow University (NMU) in 1999 and the Faculty of Mechanics and Mathematics of Moscow State University in 2000 Vladlen defended his Ph.D  thesis  at the Steklov Mathematical Institute in 2003 and University of Toronto in 2004. In 2012 he defended his doctoral dissertation "Dynamics and geometry of quadratic rational mappings" at the Institute for Information Transmission Problems. Kharkevich RAS. Vladlen Timorin has experience of working at Stony Brook University, Jacobs University in Bremen and Max Plank Institute. Since 2009 he has been working at the Faculty of Mathematics of the National Research University Higher School of Economics. In particular, Prof. Timorin has been Dean of the Department of Mathematics of HSE for several years. He is member of the Editorial Board of Journal of Dynamical and Control Systems; Managing Editor of Arnold Mathematical Journal; member of the Moscow Mathematical Society; permanent professor and board member of the Independent Moscow University.