talk.tex

\begin{frame}
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        \coordinate (my south west) at ($ (current page.south west)+(5pt,20pt) $);
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        \node[anchor=north west] (orthonormal bases) at (my north west) {
            \begin{tikzpicture}
                \node[align=center] at (0,0) {orthonormal\\bases};
                \node[inner sep=0pt] at (2.5,0) {\includestandalone[scale=1.2]{figures/onb}};
            \end{tikzpicture}
        };

        \onslide<2-> {
            \node[anchor=west] (finite frames) at ($ (my west) + (10pt,0) $) {
                \begin{tikzpicture}
                    \node[align=center] at (0,0) {finite\\frames};
                    \node[inner sep=0pt] at (1.5,0) {\includestandalone[scale=1]{figures/frame-52}};
                \end{tikzpicture}
            };

            \draw[decorate,decoration={snake,segment length=10pt, amplitude=1pt,post length=5pt},-{Stealth[round,scale=1.5]}] (orthonormal bases.south -| finite frames) -- (finite frames) node[midway, right, align=center, font=\scriptsize] {generalize\\to};
        }

        \onslide<3-> {
            \node[anchor=east] (eigenstep tableaux) at (my east) {
                \begin{tikzpicture}
                    \node[align=center, anchor=east] at (0,0) {eigenstep\\tableaux};
                    \node[font=\scriptsize, inner sep=0pt, anchor=west,draw=black,rounded corners] (tableau) at (4pt,0) {
                        \begin{tabular}[h]{c|cccccc}
                            & $0$ & $1$ & $2$ & $3$ & $4$ & $5$ \\ \hline
                            $2$ & $0$ & $0$ & $1.4$ & $2.4$ & $3$ & $5$ \\
                            $1$ & $0$ & $2$ & $2.6$ & $3.6$ & $5$ & $5$
                        \end{tabular}
                    };
                \end{tikzpicture}
            };

            \draw[-{Stealth[round,scale=1.5]},shorten >=5pt, shorten <=5pt] (finite frames) -- (eigenstep tableaux) node [midway, above, font=\scriptsize, align=center] {have\\associated};
        }

        \onslide <4-> {
            \node[anchor=south] (polytope of eigensteps) at (my south) {
                \begin{tikzpicture}[scale=.7]
                    \node[align=center,anchor=east] at (0,0) {polytope\\of\\eigensteps};
                    \node[anchor=west] at (4pt,0) {
                        \begin{tikzpicture}[scale=.7]
                            \draw[thin,fill=blue!20] (0,1) -- (1,1) -- (2,2) -- (1,3) -- (0,2) -- cycle;
                            \node[font=\scriptsize,anchor=center] at (.8,1.8) {$\Lambda_{5,2}$};
                            \node[inner sep=0,circle,minimum size=2pt,fill,draw,blue] (lambda) at (1.382, 2.382) {};
                        \end{tikzpicture}
                    };
                \end{tikzpicture}
            };

            \draw[decorate,decoration={snake,segment length=10pt, amplitude=1pt,post length=5pt},-{Stealth[round,scale=1.5]}] (eigenstep tableaux.195) -- (polytope of eigensteps.120) node[midway, above, sloped, font=\scriptsize] {form a};

            \draw (tableau) to[out=270,in=45] (lambda);
        }

        \onslide <5-> {
            \node[anchor=south east, align=left,fill=red!20, rounded corners, inner sep=10pt] at (my south east) {
                Q: What are the\\
                combinatorics of\\
                these polytopes?
            };
        }
    \end{tikzpicture}
\end{frame}