| 1 | \documentclass[9pt,blackandwhite,roman,handout]{beamer} |
| 2 | \usepackage{etex} |
| 3 | |
| 4 | \usefonttheme{professionalfonts} |
| 5 | |
| 6 | |
| 7 | % Setup appearance: |
| 8 | %\usetheme{Warsaw} |
| 9 | \usetheme{Darmstadt} |
| 10 | |
| 11 | %\usecolortheme{seahorse} |
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| 16 | %\setbeamertemplate{navigation symbols}{} |
| 17 | |
| 18 | |
| 19 | |
| 20 | % Standard packages |
| 21 | %\usepackage[frenchb]{babel} |
| 22 | %\usepackage[english]{babel} |
| 23 | \usepackage[utf8]{inputenc} |
| 24 | %\usepackage[T1]{fontenc} |
| 25 | \usepackage{cmbright} |
| 26 | \usepackage[sans]{dsfont} |
| 27 | \usepackage{pifont} |
| 28 | %calscaled=.94, |
| 29 | %frakscaled=.97, |
| 30 | \usepackage[cal=euler,scr=rsfso]{mathalfa}%bb=cm, |
| 31 | %frak=mma, |
| 32 | %scr=esstix |
| 33 | \usepackage{mathrsfs} % pour faire des majuscules calligraphiées \mathcal{blabla} |
| 34 | %\usepackage[french,lined]{algorithm2e} % rajouter linesnumbered dans les arguments pour numéroter les lignes des algos, boxed pour l'encadrement |
| 35 | %\usepackage{extsizes} |
| 36 | %\usepackage{MnSymbol} |
| 37 | \usepackage{graphicx} |
| 38 | \usepackage{mathabx} |
| 39 | \usepackage[all]{xy} |
| 40 | \usepackage{ulem} |
| 41 | |
| 42 | \usepackage{DotArrow} |
| 43 | %\usepackage[varg]{txfonts} |
| 44 | %\usepackage{matptmx} |
| 45 | \usepackage{extpfeil} |
| 46 | %\usepackage{MyMnSymbol} |
| 47 | \usepackage{comment} |
| 48 | %\usepackage{etex} |
| 49 | %usepackage{mathtools} |
| 50 | %\usepackage{fourier} |
| 51 | |
| 52 | \usepackage{ragged2e} |
| 53 | \justifying |
| 54 | |
| 55 | % Setup TikZ |
| 56 | \usepackage{tikz} |
| 57 | \usetikzlibrary{matrix,arrows} |
| 58 | \tikzstyle{block}=[draw opacity=0.7,line width=1.4cm] |
| 59 | |
| 60 | \newcommand{\gk}{$g_k = \left \{ \begin{array}{ll} |
| 61 | q^k+q^{k-1}-q^\frac{k+1}{2} - 2q^\frac{k-1}{2}+1 & \mbox{si } k \equiv 1 \pmod 2,\\ |
| 62 | q^k+q^{k-1}-\frac{1}{2}q^{\frac{k}{2}+1} - \frac{3}{2}q^{\frac{k}{2}}-q^{\frac{k}{2}-1} +1& \mbox{si } k \equiv 0 \pmod 2. |
| 63 | \end{array} \right .$} |
| 64 | |
| 65 | \newcommand{\ext}{\xymatrix{ |
| 66 | \FF= \Fq(x)(y) \ar@{-}[d]^{<\infty} \\ \Fq(x) \ar@{-}[d] \\ \Fq} } |
| 67 | |
| 68 | \newcommand{\twoheaddownarrow}{% |
| 69 | \mathrel{\reflectbox{\rotatebox[origin=c]{-90}{$\xtwoheadrightarrow[ \; ]{ \reflectbox{\rotatebox[origin=c]{-90}{$\pi_Q \ $}} \ \ }$}}}} |
| 70 | |
| 71 | \newcommand{\longdownmapsto}{% |
| 72 | \mathrel{\reflectbox{\rotatebox[origin=c]{-90}{$\xmapsto{ \ \ \ \reflectbox{\rotatebox[origin=c]{-90}{$\pi_Q \ $}} \ \ \ }$}}}} |
| 73 | |
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| 75 | |
| 76 | \newcommand{\myubrace}[2]{\rotatebox[origin=c]{90}{$ |
| 77 | \rotatebox[origin=c]{-90}{#1} \left \{ |
| 78 | \begin{array}{l} |
| 79 | \vspace{#2} \\ |
| 80 | \end{array} |
| 81 | \right . \hspace{-1em} |
| 82 | $}} |
| 83 | |
| 84 | \newcommand{\bluebrace}{{\color{blue}\left\{}} |
| 85 | |
| 86 | |
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| 94 | \setbeamertemplate{navigation symbols}{ |
| 95 | % \insertslidenavigationsymbol |
| 96 | % \insertframenavigationsymbol |
| 97 | % \insertsubsectionnavigationsymbol |
| 98 | % \insertsectionnavigationsymbol |
| 99 | % \insertdocnavigationsymbol |
| 100 | % \insertbackfindforwardnavigationsymbol |
| 101 | } |
| 102 | |
| 103 | %\renewcommand{\item}{\item[$\bullet$]} |
| 104 | |
| 105 | |
| 106 | |
| 107 | \title[]{\LARGE{\textsc{Familles denses de courbes modulaires, nombres premiers\\ et \\rang de tenseur symétrique uniforme de la multiplication dans les corps finis}}} |
| 108 | |
| 109 | \author[Alexey {\textsc Zykin}]{\textbf{Alexey {\textsc Zykin}$^{\dag}$} \\ (\textbf{1984 - 2017}) \\Laboratoire GAATI \\Université de la Polynésie Française\\ |
| 110 | {\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} |
| 111 | |
| 112 | |
| 113 | \date[]{\\ \vspace{2em} {\bf Séminaire GAATI}\\ {\bf UPF} \\{\small Avril 2017}} |
| 114 | |
| 115 | \newtheorem{defin}{Définition} |
| 116 | \newtheorem{theoreme}{Théorème} |
| 117 | \newtheorem{lemme}{Lemme} |
| 118 | \newtheorem{corollaire}{Corollaire} |
| 119 | \newtheorem{proposition}{Proposition} |
| 120 | \newtheorem{propriete}{Propriété} |
| 121 | %\newtheorem{exemple}[definition]{Exemple} |
| 122 | |
| 123 | \newcommand{\NN}{\ensuremath{\mathbb{N}}} |
| 124 | \newcommand{\CC}{\ensuremath{\mathbb{C}}} |
| 125 | \newcommand{\ZZ}{\ensuremath{\mathbb{Z}}} |
| 126 | \newcommand{\PF}{\mathbf{P}_F} |
| 127 | \newcommand{\DF}{\mathsf{Div}(F)} |
| 128 | \newcommand{\Jac}{\ensuremath{\mathcal{J}\mathsf{ac}(F/\Fq)}} |
| 129 | \newcommand{\Fqr}[2][q]{\mathds{F}_{\!{#1}^{#2}}} |
| 130 | \newcommand{\Fq}{\Fqr{}} |
| 131 | \newcommand{\F}{\mathds{F}} |
| 132 | \newcommand{\FF}{\mathsf{F}} |
| 133 | \newcommand{\Fqn}{\Fqr{n}} |
| 134 | \newcommand{\D}[1][D]{\ensuremath{\mathcal{#1}}} |
| 135 | \newcommand{\Ld}[1][\D]{\ensuremath{\mathscr{L}\!\!\left(#1\right)}} % utilisation : \Ld ou \Ld[A] pour un diviseur A au lieu de D |
| 136 | \newcommand{\Ak}[1][k]{\ensuremath{\mathbb{A}_{#1}}} |
| 137 | \newcommand{\A}{\ensuremath{\mathsf{A}}} |
| 138 | \newcommand{\Cl}{\ensuremath{\mathsf{Cl}}} |
| 139 | \newcommand{\mus}{\ensuremath{\mu^\mathsf{sym}}} |
| 140 | \newcommand{\Ms}{\ensuremath{M^\mathsf{sym}}} |
| 141 | \newcommand{\ms}{\ensuremath{m^\mathsf{sym}}} |
| 142 | \newcommand{\chch}{{C}hudnovsky-{C}hudnovsky} |
| 143 | \newcommand{\ch}{{C}hudnovsky} |
| 144 | |
| 145 | |
| 146 | |
| 147 | \addtobeamertemplate{footline}{\texttt{\hfill\insertframenumber/{\inserttotalframenumber}}} |
| 148 | % |
| 149 | %\AtBeginSubsection[] { |
| 150 | %\begin{frame}<beamer> |
| 151 | %\frametitle{Plan} |
| 152 | %\tableofcontents[currentsection,currentsubsection] |
| 153 | %\end{frame} |
| 154 | %} |
| 155 | %\AtBeginSection[] { |
| 156 | %\begin{frame}<beamer> |
| 157 | %\frametitle{Plan} |
| 158 | %\tableofcontents[currentsection]%,currentsubsection] |
| 159 | %\end{frame} |
| 160 | %} |
| 161 | |
| 162 | \setbeamertemplate{sections/subsections in toc}[sections numbered] |
| 163 | %\setbeamertemplate{sections in toc}[sections numbered] |
| 164 | |
| 165 | \begin{document} |
| 166 | |
| 167 | % \begin{frame}[plain] |
| 168 | % |
| 169 | % \begin{center} |
| 170 | % |
| 171 | % {\bf Institut de Mathématiques de Marseille}\\ |
| 172 | % |
| 173 | % {\bf Equipe Analyse, Géométrie et Topologie (AGT) }\\ |
| 174 | % |
| 175 | % \vspace{2em} |
| 176 | % |
| 177 | % {\bf Séminaire de Géométrie Complexe}\\ |
| 178 | % Mardi 12 Juin 2018 |
| 179 | % \end{center} |
| 180 | % |
| 181 | % \begin{center} |
| 182 | % |
| 183 | % \end{center} |
| 184 | % |
| 185 | % \end{frame} |
| 186 | |
| 187 | \begin{frame}[plain] |
| 188 | |
| 189 | \titlepage |
| 190 | |
| 191 | \end{frame} |
| 192 | |
| 193 | \begin{frame}[plain]{Plan} |
| 194 | |
| 195 | \tableofcontents |
| 196 | |
| 197 | \end{frame} |
| 198 | |
| 199 | \section{Introduction} |
| 200 | |
| 201 | \subsection{Définitions} |
| 202 | |
| 203 | %%%%% SLIDE 1 |
| 204 | \begin{frame}{Définition formelle I} |
| 205 | |
| 206 | \end{frame} |
| 207 | |
| 208 | %%%%% SLIDE 2 |
| 209 | \begin{frame}{Définition formelle II} |
| 210 | |
| 211 | \end{frame} |
| 212 | |
| 213 | %%%%% SLIDE 3 |
| 214 | \begin{frame}{Définition formelle III} |
| 215 | |
| 216 | \end{frame} |
| 217 | |
| 218 | \subsection{Quantités asymptotiques} |
| 219 | |
| 220 | %%%%% SLIDE 6 |
| 221 | \begin{frame} |
| 222 | |
| 223 | \end{frame} |
| 224 | |
| 225 | \section{Algorithme de D.V. et G.V. Chudnovsky (1987)} |
| 226 | |
| 227 | \subsection{Avec des places rationnelles} |
| 228 | |
| 229 | %%%%% SLIDE 9 |
| 230 | \begin{frame}{Algorithme original de Chudnovsky et Chudnovsky} |
| 231 | |
| 232 | \end{frame} |
| 233 | |
| 234 | \subsection{Principe} |
| 235 | |
| 236 | %%%%% SLIDE 8 |
| 237 | \begin{frame}{Principe pour multiplier avec l'algorithme de Chudnovsky} |
| 238 | |
| 239 | \end{frame} |
| 240 | |
| 241 | \subsection{Avec des places de degré un et deux} |
| 242 | |
| 243 | %%%%% SLIDE 10 |
| 244 | \begin{frame}{Evaluations sur des places de degré 1 et 2} |
| 245 | |
| 246 | \end{frame} |
| 247 | |
| 248 | \section{Conditions permettant l'utilisation de l'algorithme} |
| 249 | |
| 250 | \subsection{Conditions principales} |
| 251 | |
| 252 | %%%%% SLIDE 11 |
| 253 | \begin{frame}{Conditions suffisantes pour appliquer l'algorithme} |
| 254 | |
| 255 | \end{frame} |
| 256 | |
| 257 | \subsection{Applications} |
| 258 | |
| 259 | %%%%% SLIDE 11 |
| 260 | \begin{frame}{Le cas des extensions de petits degré} |
| 261 | |
| 262 | \end{frame} |
| 263 | |
| 264 | \begin{frame}{Algorithme de Chudnovsky sur un corps de fonctions hyperelliptique de genre 2} |
| 265 | |
| 266 | \end{frame} |
| 267 | |
| 268 | |
| 269 | \begin{frame}{Exemple pour les \textit{petites} extensions $\F_{16^n}$ de $\F_{16}$} |
| 270 | |
| 271 | \end{frame} |
| 272 | |
| 273 | \setbeamercovered{transparent} |
| 274 | |
| 275 | \begin{frame} |
| 276 | |
| 277 | \end{frame} |
| 278 | |
| 279 | %%%%%%%%%%%%% T %%%%%%%%%%%%%%% |
| 280 | |
| 281 | |
| 282 | %%%%%%%%%%%%% T %%%%%%%%%%%%%%% |
| 283 | |
| 284 | |
| 285 | %%%%%%%%%%%%% T %%%%%%%%%%%%%%% |
| 286 | |
| 287 | \section{Nouveau résultats} |
| 288 | |
| 289 | \subsection{Bornes uniformes connues} |
| 290 | |
| 291 | \begin{frame} |
| 292 | |
| 293 | \end{frame} |
| 294 | |
| 295 | \subsection{Nouvelles bornes uniformes} |
| 296 | |
| 297 | \begin{frame} |
| 298 | |
| 299 | \end{frame} |
| 300 | |
| 301 | %%%%% SLIDE 14 |
| 302 | \begin{frame}{Corps de fonctions sur $\F_{p^2}$} |
| 303 | |
| 304 | \end{frame} |
| 305 | |
| 306 | \begin{frame} |
| 307 | |
| 308 | \end{frame} |
| 309 | |
| 310 | %%%%%%%%%%%%% T %%%%%%%%%%%%%%% |
| 311 | |
| 312 | \begin{frame} |
| 313 | |
| 314 | \end{frame} |
| 315 | |
| 316 | \begin{frame} |
| 317 | |
| 318 | \end{frame} |
| 319 | |
| 320 | \section{Conclusions et perspectives} |
| 321 | |
| 322 | \subsection{Problèmes et/ou travail en cours} |
| 323 | |
| 324 | %%%%% SLIDE 15 |
| 325 | |
| 326 | \begin{frame}{Conclusion} |
| 327 | |
| 328 | \end{frame} |
| 329 | |
| 330 | \begin{frame} |
| 331 | |
| 332 | \end{frame} |
| 333 | |
| 334 | %%%%% SLIDE DE FIN |
| 335 | |
| 336 | \begin{frame}[plain] |
| 337 | \begin{beamerboxesrounded}% |
| 338 | [lower=block title, % |
| 339 | upper=block title,% |
| 340 | shadow=true]{} |
| 341 | \begin{center} |
| 342 | {\Large \textbf{{\color{mycvblue}Thank you for your attention.}}}\\ |
| 343 | \vspace{3em} |
| 344 | {\Large \textbf{{\color{mycvblue}Questions?}}}\\ |
| 345 | \end{center} |
| 346 | \end{beamerboxesrounded} |
| 347 | |
| 348 | \end{frame} |
| 349 | |
| 350 | \end{document} |