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\begin{document}
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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2018--19--A term}\\[0.2\baselineskip]

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\begin{description}
  \item[Course Name]
    Elliptic curves and modular forms

  \item[Course Number]
    \LRE{201‭.2‭.5291}

  \item[Course web page]\mbox{}\\
    \url{https://www.math.bgu.ac.il//en/teaching/fall2019/courses/elliptic-curves-and-modular-forms}

  \item[Lecturer]
    Dr. Daniel Disegni,
    \nolinkurl{<disegni@bgu.ac.il>},
    Office 108

\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}}




    \includepdf[pages=-]{2018-BGU-EllipticMF.pdf}



\section*{Course topics}

\begin{enumerate}
\item{} Lattices.  Doubly periodic functions.
\item{} Riemann surfaces: definition and examples (Riemann sphere, roots, logarithms).
\item{} Riemann surfaces: Euler characteristic, genus, Hurwitz formula.  Riemann--Roch theorem (statement)
\item{} Complex tori and elliptic curves.
\item{} Morphisms between elliptic curves. The group law. Arithmetic of elliptic curves (a glimpse: Mordell's theorem, L-functions, the Birch and Swinnerton-Dyer conjecture).
\item{} The group SL(2,Z). The space of all lattices. The trefoil knot.
\item{} Modular forms for SL(2,Z): finite-dimensionality. Eisenstein series.
\item{} Theta series. Four squares. Even unimodular lattices and sphere packing in dimension 8.
\item{} Hecke operators.  `Reminders' on the Riemann zeta function.  L-functions. Modularity of elliptic curves (statement).
\item{} The Ramanujan conjecture. Expander graphs. The j-invariant. Moonshine.
\item{} Modular curves and their compactification.
\item{} Complex multiplication.
\end{enumerate}

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\end{document}

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