Extra Form
Lecturer Giulio Tiozzo
Dept. Yale Univ.
date Mar 17, 2016
Given a group of isometries of a metric space, one can draw a random sequence of group elements, and look at its action on the space. 
What are the asymptotic properties of such a random walk? 

The answer depends on the geometry of the space. 
Starting from Furstenberg, people considered random walks of this type, and in particular they focused on the case of spaces of negative curvature. 

On the other hand, several groups of interest in geometry and topology act on spaces which are not quite negatively curved (e.g., Teichmuller space) or on spaces which are hyperbolic, but not proper (such as the complex of curves).
We shall explore some results on the geometric properties of such random walks. 
For instance, we shall see a multiplicative ergodic theorem for mapping classes (which proves a conjecture of Kaimanovich), as well as convergence and positive drift for random walks on general Gromov hyperbolic spaces. This also yields the identification of the measure-theoretic  boundary with the topological boundary. 

Attachment '1'
List of Articles
Category Subject Dept. Lecturer
Math Colloquia Topological aspects in the theory of aperiodic solids and tiling spaces file Georgia Institute of Technology, School of Mathematics and School of Physics Jean V. Bellissard
Math Colloquia The significance of dimensions in mathematics file Kyoto Univ./서울대학교 Heisuke Hironaka
Special Colloquia Persistent Homology file Stanford University Gunnar E. Carlsson
Special Colloquia Structures on Persistence Barcodes and Generalized Persistence file Stanford University Gunnar E. Carlsson
Special Colloquia Topological Mapping of Point Cloud Data file Stanford University Gunnar E. Carlsson
Math Colloquia The Shape of Data file Stanford University Gunnar E. Carlsson
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Math Colloquia Random walks in spaces of negative curvature file Yale Univ. Giulio Tiozzo
Math Colloquia Quantum Dynamics in the Mean-Field and Semiclassical Regime file Ecole Polytechnique Francoise Golse
Math Colloquia Entropies on covers of compact manifolds file CNRS (France) François Ledrappier
Special Colloquia Queer Lie Superalgebras file Univ. of Texas, Arlington Dimitar Grantcharov
Math Colloquia Sums of squares in quadratic number rings file Univ. of Kentucky David Leep
Math Colloquia Fano manifolds of Calabi-Yau Type file 서울대학교 Atanas Iliev
Special Colloquia Regularity of solutions of Hamilton-Jacobi equation on a domain file ENS-Lyon Albert Fathi
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Math Colloquia <학부생을 위한 ɛ 강연> Secure computation: Promise and challenges file 송용수 <학부생을 위한 ɛ 강연> Secure computation: Promise and challenges
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