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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Monday, April 30, 2018}
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\textbf{At} \emph{11:00 -- 12:00}
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\textbf{In} \emph{-101}

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{\large\scshape  Sebastián Donoso 
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  (Universidad de O’Higgins)
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will talk about
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{\Large\bfseries Good lower bounds for multiple recurrence\par}
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\textsc{Abstract:}
In 2005, Bergelson, Host and Kra showed that if \$(X,\textbackslash{}mu,T)\$ is an ergodic measure preserving system and \$A\textbackslash{}subset X\$, then for every \$\textbackslash{}epsilon\textgreater{}0\$ there exists a syndetic set of \$n\textbackslash{}in\textbackslash{}mathbb\{N\}\$ such that
\$\textbackslash{}mu(A\textbackslash{}cap T\^{}\{-n\}A\textbackslash{}cap\textbackslash{}dots\textbackslash{}cap T\^{}\{-kn\}A)\textgreater{}\textbackslash{}mu\^{}\{k+1\}(A)-\textbackslash{}epsilon\$ for
\$k\textbackslash{}leq3\$, extending Khintchine's theorem. This phenomenon is called multiple recurrence with good lower bounds.
Good lower bounds for certain polynomial expressions was studied by
Frantzikinakis but several questions remain open.
In this talk I will survey this topic, and present some progress regarding
polynomial expressions, commuting transformations,
and configurations involving the prime numbers.
This is work in progress with Joel Moreira, Ahn Le and Wenbo Sun.





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{\bfseries Please Note the Unusual Day and Place!}
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