\documentclass[oneside,final,12pt]{book}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{xunicode}
\usepackage{hyperref}
\usepackage{xstring}
\def\rooturl{https://www.math.bgu.ac.il/}
\hyperbaseurl{\rooturl}
\let\hhref\href
\providecommand{\extrahref}[2][]{\LTRfootnote{\LR{\IfBeginWith*{#2}{http}{\nolinkurl{#2}}{\nolinkurl{\rooturl#2}}}}}
\renewcommand{\href}[2]{\IfBeginWith*{#1}{http}{\hhref{#1}{#2}}{\hhref{\rooturl#1}{#2}}\extrahref{#1}}
\usepackage{polyglossia}
\usepackage{longtable}
%% even in English, we sometimes have Hebrew (as in course hours), and we
%% can't add it in :preamble, since it comes after hyperref
%%\usepackage{bidi}
\setdefaultlanguage{english}
\setotherlanguage{hebrew}
%%\setmainfont[Ligatures=TeX]{Libertinus Serif}
\setmainfont[Script=Hebrew,Ligatures=TeX]{LibertinusSerif}[
UprightFont = *-Regular,
BoldFont = *-Bold,
ItalicFont = *-Italic,
BoldItalicFont = *-BoldItalic,
Extension = .otf]
\SepMark{.}
\robustify\hebrewnumeral
\robustify\Hebrewnumeral
\robustify\Hebrewnumeralfinal
% vim: ft=eruby.tex:
\begin{document}
\pagestyle{empty}
\pagenumbering{gobble}
\begin{center}
\vspace*{\baselineskip}
{\Large Department of Mathematics, BGU}
\vspace*{\baselineskip}
\rule{\textwidth}{1.6pt}\vspace*{-\baselineskip}\vspace*{2pt}
\rule{\textwidth}{0.4pt}\\[\baselineskip]
{\Huge BGU Probability and Ergodic Theory (PET) seminar}\\[0.2\baselineskip]
\rule{\textwidth}{0.4pt}\vspace*{-\baselineskip}\vspace{3.2pt}
\rule{\textwidth}{1.6pt}\\[\baselineskip]
\textbf{On} \emph{Thursday, March 31, 2022}
\bigskip
\textbf{At} \emph{11:10 -- 12:00}
\bigskip
\textbf{In} \emph{-101}
\vspace*{2\baselineskip}
{\large\scshape Annette Karrer
%
(Technion)
}
\bigskip
will talk about
\bigskip
{\Large\bfseries The rigidity of lattices in products of trees\par}
\bigskip
\end{center}
\vfill
\textsc{Abstract:}
Each complete CAT(0) space has an associated topological space, called visual boundary, that coincides with the Gromov boundary in case that the space is hyperbolic. A CAT(0) group G is called boundary rigid if the visual boundaries of all CAT(0) spaces admitting a geometric action by G are homeomorphic. If G is hyperbolic, G is boundary rigid. If G is not hyperbolic, G is not always boundary rigid. The first such example was found by Croke-Kleiner.
In this talk we will see that every group acting freely and cocompactly on a product of two regular trees of finite valence is boundary rigid. That means that every CAT(0) space that admits a geometric action of any such group has the boundary homeomorphic to a join of two copies of the Cantor set. The proof of this result uses a generalization of classical dynamics on boundaries introduced by Guralnik and Swenson. I will explain the idea of this generalization by explaining a higher-dimensional version of classical North-south-dynamics obtained this way.
This is a joint work with Kasia Jankiewicz, Kim Ruane and Bakul Sathaye.
% vim: ft=eruby.tex:
\end{document}
% vim: ft=eruby.tex: