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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, December 20, 2016}
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\textbf{At} \emph{14:30 -- 15:30}
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\textbf{In} \emph{Math -101}

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{\large\scshape Adam Sheffer 
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  (California Institute of Technology (Caltech))
}
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will talk about
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{\Large\bfseries Geometric Incidences and the Polynomial Method\par}
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\textsc{Abstract:}
While the topic of geometric incidences has existed for
several decades, in recent years it has been experiencing a
renaissance due to the introduction of new polynomial methods. This
progress involves a variety of new results and techniques, and also
interactions with fields such as algebraic geometry and harmonic
analysis.

A simple example of an incidences problem: Given a set of n points and
set of n lines, both in R\^{}2, what is the maximum number of point-line
pairs such that the point is on the line. Studying incidence problems
often involves the uncovering of hidden structure and symmetries.

In this talk we introduce and survey the topic of geometric
incidences, focusing on the recent polynomial techniques and results
(some by the speaker). We will see how various algebraic and analysis
tools can be used to solve such combinatorial problems.








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