Description
Organizers: Balázs Bárány, Károly Simon, István Kolossváry
Talks:
10:00-10:45 Francois Ledrappier
Title: TBA
Abstract: TBA
11:00-11:45 Sascha Troscheit
Title: Continuum trees of real functions and their graphs
Abstract: The Brownian continuum tree (CRT) is an important random metric space that was extensively investigated in the 1990s. It can be constructed by a change of metric from a Brownian excursion function on [0,1]. This change of metric can be applied to all continuous circle mappings to give a continuum tree associated with the function.
In 2008, Picard proved that analytic properties of the function are connected to the dimension theory of its tree: the upper box dimension of the continuum tree coincides with the variation index of the contour function. We will provide a short and direct proof of Picard's theorem through the study of packings. The methods used will inspire different notions of variations and variation indices, and we will link the dimension theory of the tree with the dimension theory of the graph of its contour function.
(Joint with Maik Gröger)
12:15-13:00 Michal Rams
Title: Lyapunov spectrum of matrix cocycles
Abstract: I will give an introduction into calculating of the Lyapunov spectrum of $SL(2,R)$ matrix cocycles, presenting results we got with Lorenzo Diaz and Katrin Gelfert.
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Zoom link: https://us02web.zoom.us/j/83990284896?pwd=TTIzZXlNeFhKTEkrSUptMUJ0ZjBBUT09