Probability and Analysis Symposium

The Probability and Analysis Symposium is part of the 2014 Special year on Stochastics and Statistics

Preliminary programme

9:30am - Professor Thierry Coulhon 

11am - Professor Uta Frieberg 

1:30pm - Professor Michael Barnsley 

Title and abstracts

Professor Michael Barnsley 
Australian National University

Title: New insights concerning probability and analysis on just-touching fractals.
Abstract: I will give an overview of the basic framework, and new results, concerning in particular the explicit construction and properties of families of continuous a.e. transformations and flows on attractors of iterated function systems. Interesting operators, for example Laplacians, and random processes are consequences are consequences of the approach. 

Professor Thierry Coulhon 
Australian National University

Title: Heat kernel estimates, Sobolev type inequalities and Riesz transform on doubling metric measure spaces.
Abstract: Upper and lower Gaussian estimates for the heat kernel are the key to a number of analytic results on doubling metric measure spaces endowed with a Dirichlet form, and they also have a probabilistic interpretation.
We will describe recent  characterisations of the upper estimates in terms of new global Sobolev type inequalities, which simplify and extend known results in this direction.
We will also present a new approach to the lower estimates, which opens the way to a better understanding of Lp boundedness of the Riesz transform on Riemannian manifolds and more general spaces.
This relies on joint works with Frédéric Bernicot, Dorothée Frey, and Adam Sikora.

Professor Uta Freiberg
Universität Stuttgart

Title: Differential operators and generalized trigonometric functions on fractal subsets of the real line

Abstract: Spectral asymptotics of second order differential operators of the form d/dm d/dx on the real line are well known if m is a self similar measure with compact support. We extend the results to some more general cases such as random fractal measures and self conformal measures. Moreover, we give a representation of the eigenfunctions as generalized trigonometric functions. The results were obtained in collaboration with Sabrina Kombrink and Peter Arzt.


Date & time

12 September 2014


Manning Clark Theatre 4


Thierry Coulhon (ANU)
Uta Freiberg (Friedrich-Schiller University)
Michael Barnsley (ANU)


 Brittany Shoard
 +61 2 6125 2897

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