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{\Large Department of Mathematics, BGU}

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{\Huge Colloquium}\\[0.2\baselineskip]

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\textbf{On} \emph{Tuesday, January  2, 2018}
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\textbf{At} \emph{13:00 -- 14:00}
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\textbf{In} \emph{Math -101}

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{\large\scshape Benny Sudakov 
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  (ETH)
}
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will talk about
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{\Large\bfseries Equiangular lines and spherical codes in Euclidean spaces\par}
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\textsc{Abstract:}
A family of lines through the origin in Euclidean space is called
equiangular if any pair of lines defines the same angle. The problem
of estimating the maximum cardinality of such a family in \$R\^{}n\$ was
extensively studied for the last 70 years. Answering a question of
Lemmens and Seidel from 1973, in this talk we show that for every
fixed angle\$\textbackslash{}theta\$ and sufficiently large \$n\$ there are at most
\$2n-2\$ lines in\$R\^{}n\$ with common angle \$\textbackslash{}theta\$. Moreover, this is
achievable only when \$\textbackslash{}theta =\textbackslash{}arccos \textbackslash{}frac\{1\}\{3\}\$. Various extensions
of this result to the more general settings of lines with \$k\$ fixed
angles and of spherical codes will be discussed as well. Joint work
with I. Balla, F. Drexler and P. Keevash.





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{\bfseries Please Note the Unusual Time!}
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