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+		q^k+q^{k-1}-\frac{1}{2}q^{\frac{k}{2}+1} - \frac{3}{2}q^{\frac{k}{2}}-q^{\frac{k}{2}-1} +1& \mbox{si } k \equiv 0 \pmod 2.
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+%\renewcommand{\item}{\item[$\bullet$]}
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+
+
+\title[]{\LARGE{\textsc{Familles denses de courbes modulaires, nombres premiers\\ et \\rang de tenseur symétrique uniforme de la multiplication dans les corps finis}}}
+
+\author[Alexey {\textsc Zykin}]{\textbf{Alexey {\textsc Zykin}$^{\dag}$} \\ (\textbf{1984 - 2017}) \\Laboratoire GAATI \\Université de la Polynésie Française\\
+{\small National Research University Higher School of Economics} \\ Institute for Information Transmission Problems of the Russian Academy of Sciences\\\vspace{1em}\textbf{\textcolor{mycvblue}{en collaboration avec}}\\ \vspace{1em}  \textbf{Stéphane {\textsc Ballet}}\\ Equipe Arithmétique et Théorie de l'Information\\ Institut de Mathématiques de Marseille \\ Aix-Marseille Université}
+
+
+\date[]{\\ \vspace{2em} {\bf Séminaire GAATI}\\  {\bf UPF} \\{\small  Avril  2017}}
+
+\newtheorem{defin}{Définition}
+\newtheorem{theoreme}{Théorème}
+\newtheorem{lemme}{Lemme}
+\newtheorem{corollaire}{Corollaire}
+\newtheorem{proposition}{Proposition}
+\newtheorem{propriete}{Propriété}
+%\newtheorem{exemple}[definition]{Exemple}
+
+\newcommand{\NN}{\ensuremath{\mathbb{N}}}
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+%
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+%\begin{frame}<beamer>
+%\frametitle{Plan}
+%\tableofcontents[currentsection,currentsubsection]
+%\end{frame}
+%}
+%\AtBeginSection[] {
+%\begin{frame}<beamer>
+%\frametitle{Plan}
+%\tableofcontents[currentsection]%,currentsubsection]
+%\end{frame}
+%}
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+\setbeamertemplate{sections/subsections in toc}[sections numbered]
+%\setbeamertemplate{sections in toc}[sections numbered]
+
+\begin{document}
+
+% \begin{frame}[plain]
+%
+%  \begin{center}
+%
+%   {\bf Institut de Mathématiques de Marseille}\\
+%
+%   {\bf Equipe Analyse, Géométrie et Topologie (AGT) }\\
+%
+%   \vspace{2em}
+%
+%   {\bf Séminaire de Géométrie Complexe}\\
+%   Mardi 12 Juin 2018
+%  \end{center}
+%
+%  \begin{center}
+%
+%  \end{center}
+%
+% \end{frame}
+
+\begin{frame}[plain]
+
+ \titlepage
+
+\end{frame}
+
+\begin{frame}[plain]{Plan}
+
+ \tableofcontents
+
+\end{frame}
+
+\section{Introduction}
+
+\subsection{Définitions}
+
+%%%%% SLIDE 1
+\begin{frame}{Définition formelle I}
+
+\end{frame}
+
+%%%%% SLIDE 2
+\begin{frame}{Définition formelle II}
+
+\end{frame}
+
+%%%%% SLIDE 3
+\begin{frame}{Définition formelle III}
+
+\end{frame}
+
+\subsection{Quantités asymptotiques}
+
+%%%%% SLIDE 6
+\begin{frame}
+
+\end{frame}
+
+\section{Algorithme de D.V. et G.V. Chudnovsky (1987)}
+
+\subsection{Avec des places rationnelles}
+
+%%%%% SLIDE 9
+\begin{frame}{Algorithme original de Chudnovsky et Chudnovsky}
+
+\end{frame}
+
+\subsection{Principe}
+
+%%%%% SLIDE 8
+\begin{frame}{Principe pour multiplier avec l'algorithme de Chudnovsky}
+
+\end{frame}
+
+\subsection{Avec des places de degré un et deux}
+
+%%%%% SLIDE 10
+\begin{frame}{Evaluations sur des places de degré 1 et 2}
+
+\end{frame}
+
+\section{Conditions permettant l'utilisation de l'algorithme}
+
+\subsection{Conditions principales}
+
+%%%%% SLIDE 11
+\begin{frame}{Conditions suffisantes pour appliquer l'algorithme}
+
+\end{frame}
+
+\subsection{Applications}
+
+%%%%% SLIDE 11
+\begin{frame}{Le cas des extensions de petits degré}
+
+\end{frame}
+
+\begin{frame}{Algorithme de Chudnovsky sur un corps de fonctions hyperelliptique de genre 2}
+
+\end{frame}
+
+
+\begin{frame}{Exemple pour les \textit{petites} extensions $\F_{16^n}$ de $\F_{16}$}
+
+\end{frame}
+
+\setbeamercovered{transparent}
+
+\begin{frame}
+
+\end{frame}
+
+%%%%%%%%%%%%% T  %%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%% T  %%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%% T  %%%%%%%%%%%%%%%
+
+\section{Nouveau résultats}
+
+\subsection{Bornes uniformes connues}
+
+\begin{frame}
+
+\end{frame}
+
+\subsection{Nouvelles bornes uniformes}
+
+\begin{frame}
+
+\end{frame}
+
+%%%%% SLIDE 14
+\begin{frame}{Corps de fonctions sur $\F_{p^2}$}
+
+\end{frame}
+
+\begin{frame}
+
+\end{frame}
+
+%%%%%%%%%%%%% T  %%%%%%%%%%%%%%%
+
+\begin{frame}
+
+\end{frame}
+
+\begin{frame}
+
+\end{frame}
+
+\section{Conclusions et perspectives}
+
+\subsection{Problèmes et/ou travail en cours}
+
+%%%%% SLIDE 15
+
+\begin{frame}{Conclusion}
+
+\end{frame}
+
+\begin{frame}
+
+\end{frame}
+
+%%%%% SLIDE DE FIN
+
+\begin{frame}[plain]
+ \begin{beamerboxesrounded}%
+  [lower=block title, %
+   upper=block title,%
+   shadow=true]{}
+  \begin{center}
+   {\Large  \textbf{{\color{mycvblue}Thank you for your attention.}}}\\
+   \vspace{3em}
+   {\Large  \textbf{{\color{mycvblue}Questions?}}}\\
+  \end{center}
+ \end{beamerboxesrounded}
+
+\end{frame}
+
+\end{document}