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\begin{document}
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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2019--20--A term}\\[0.2\baselineskip]

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\begin{description}
  \item[Course Name]
    Percolation

  \item[Course Number]
    \LRE{201‭.2‭.0101}

  \item[Course web page]\mbox{}\\
    \url{https://www.math.bgu.ac.il//en/teaching/fall2020/courses/percolation}

  \item[Lecturer]
    Prof. Ariel Yadin,
    \nolinkurl{<yadina@bgu.ac.il>},
    Office 114

\item[Office Hours]
  \url{https://www.math.bgu.ac.il/en/teaching/hours}
\end{description}

\section*{Abstract}




\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}






\section*{Course topics}

This course concerns the physical notion of phase transition, specifically in the model known as ``percolation''.

We will review the main mathematical results regarding percolation and its related counterparts the Ising model, Potts model and Fortuin-Kasteleyn cluster model, starting from works of Ising and Pierles in the beginning of the 20th century and culminating in modern work of Smirnov (for which he was awarded a Fields Medal).

\subparagraph*{The topics in the course are, time permitting:}

\begin{enumerate}
\item{} Percolation on graphs.  Definitions and basic properties.
\item{} Harris' inequality
\item{} van den Berg-Kesten inequality, Reimer's inequality
\item{} Russo's formula
\item{} Burton-Keane Theorem
\item{} Exponential decay of correlations in sub-critical regime
\item{} Planar percolation:  Russo-Seymour-Welsh theory
\item{} Planar percolation: the Harris-Kesten theorem.
\item{} Conformal invariance:  Cardy-Smirnov formula on the triangular lattice
\item{} Percolation on groups
\item{} Critical percolation on non-amenable groups: BLPS
\end{enumerate}

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