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{\Large Department of Mathematics, BGU}

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{\Huge Geometry and Group Theory}\\[0.2\baselineskip]

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\textbf{On} \emph{Sunday, January  8, 2017}
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\textbf{At} \emph{14:30 -- 15:30}
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\textbf{In} \emph{-101}

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{\large\scshape Yaar Solomon 
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  (BGU)
}
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will talk about
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{\Large\bfseries Dense Forests\par}
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\textsc{Abstract:}
A discrete set \$Y\$ in \$R\^{}d\$ is called a dense forest if for every positive \$\textbackslash{}epsilon\$,  \$Y\$ is epsilon close to all line segments of length \$V(\textbackslash{}epsilon)\$, for some function \$V(\textbackslash{}epsilon)\$. 
We will discuss the intuition of this definition and the motivation for having such sets. Then I will present three constructions for dense forests by Bishop-Peres, S.-Weiss, and by Alon, that use basic Diophantine approximations, homogeneous dynamics, and the Lovasz local lemma, respectively. The focus will be on our result (jointly with Barak Weiss) for which I hope to give all the details of the construction. All the definitions and the background will be given in the talk.








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