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\textsc{Combinatorics}
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\textsc{Colloquium}
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\textit{Turan theorem:  generalizations and applications}
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Benjamin Sudakov\par
UCLA
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\textbf{Abstract:} In typical extremal problem one wants to determine maximum cardinality
of discrete structure with certain prescribed properties. Probably the
earliest such result was obtain 100 years ago by Mantel who computed the
maximum number of edges in a triangle free graph on n vertices. This was
generalized by Turan for all complete graphs and became a starting point
of Extremal Graph Theory. In this talk we survey several classical
problems and results in this area and present some interesting
applications of Extremal Graph Theory to other areas of mathematics. We
also describe a recent surprising generalization of Turan's theorem
which was motivated by question in Computational Complexity.\vspace{\fill}
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Wednesday, February 25, 2009, 3:00 pm\par
Mathematics and Science Center: W303
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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