Ian Jauslin
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authorIan Jauslin <jauslin@ias.edu>2017-06-24 03:24:09 +0000
committerIan Jauslin <jauslin@ias.edu>2017-06-24 03:26:13 +0000
commit133934bd3e166bf03854592d22ebb8da05c7aa29 (patch)
tree052eacb824590d51b93bceea4f6b27410e883d05
As presented at GLaMP 2017 on 2017-06-24HEADv1.0master
-rw-r--r--GLaMP_2017.tex312
-rw-r--r--Makefile52
-rw-r--r--README36
l---------figs/cross_example.fig/Makefile1
-rw-r--r--figs/cross_example.fig/cross_example.tikz.tex16
-rw-r--r--figs/cross_example.fig/grid.tikz.tex10
l---------figs/cross_example.fig/libs/shapes.sty1
l---------figs/cross_packing.fig/Makefile1
-rw-r--r--figs/cross_packing.fig/cross_packing_l.tikz.tex14
-rw-r--r--figs/cross_packing.fig/cross_packing_r.tikz.tex14
l---------figs/cross_packing.fig/libs/shapes.sty1
l---------figs/cross_sliding.fig/Makefile1
-rw-r--r--figs/cross_sliding.fig/cross_sliding1.tikz.tex17
-rw-r--r--figs/cross_sliding.fig/cross_sliding2.tikz.tex18
l---------figs/cross_sliding.fig/libs/shapes.sty1
l---------figs/gaunt_fisher.fig/Makefile1
-rw-r--r--figs/gaunt_fisher.fig/gaunt_fisher2.tikz.tex30
-rw-r--r--figs/gaunt_fisher.fig/gaunt_fisher3.tikz.tex53
l---------figs/gaunt_fisher.fig/libs/shapes.sty1
l---------figs/hole_example.fig/Makefile1
-rw-r--r--figs/hole_example.fig/hole_example_cross.tikz.tex36
-rw-r--r--figs/hole_example.fig/hole_example_cross_decorrelated.tikz.tex63
-rw-r--r--figs/hole_example.fig/hole_example_square.tikz.tex24
l---------figs/hole_example.fig/libs/shapes.sty1
-rw-r--r--figs/libs/Makefile28
-rw-r--r--figs/libs/shapes.sty58
l---------figs/shapes.fig/Makefile1
-rw-r--r--figs/shapes.fig/cross.tikz.tex11
-rw-r--r--figs/shapes.fig/cross3.tikz.tex11
-rw-r--r--figs/shapes.fig/diamond.tikz.tex11
-rw-r--r--figs/shapes.fig/hexagon.tikz.tex32
l---------figs/shapes.fig/libs/shapes.sty1
l---------figs/square_packing.fig/Makefile1
l---------figs/square_packing.fig/libs/shapes.sty1
-rw-r--r--figs/square_packing.fig/square_packing.tikz.tex20
-rw-r--r--figs/square_packing.fig/square_packing_slide.tikz.tex25
l---------figs/square_sliding.fig/Makefile1
l---------figs/square_sliding.fig/libs/shapes.sty1
-rw-r--r--figs/square_sliding.fig/square_sliding.tikz.tex17
-rw-r--r--figs/square_sliding.fig/square_sliding_contra.tikz.tex25
-rw-r--r--libs/ian-presentation.cls186
41 files changed, 1135 insertions, 0 deletions
diff --git a/GLaMP_2017.tex b/GLaMP_2017.tex
new file mode 100644
index 0000000..417100a
--- /dev/null
+++ b/GLaMP_2017.tex
@@ -0,0 +1,312 @@
+\documentclass{ian-presentation}
+
+\usepackage[hidelinks]{hyperref}
+\usepackage{graphicx}
+\usepackage{amssymb}
+\usepackage{dsfont}
+
+\begin{document}
+\pagestyle{empty}
+\hbox{}\vfil
+\bf\Large
+\hfil Crystalline ordering\par
+\smallskip
+\hfil in hard-core lattice particle systems\par
+\vfil
+\large
+\hfil Ian Jauslin
+\normalsize
+\vfil
+\hfil\rm joint with {\bf Joel L. Lebowitz}\par
+\vfil
+arXiv:{\tt \href{http://arxiv.org/abs/1705.02032}{1705.02032}}\hfill{\tt \href{http://ian.jauslin.org}{http://ian.jauslin.org}}
+\eject
+
+\setcounter{page}1
+\pagestyle{plain}
+
+\title{Non-sliding HCLP}
+\begin{itemize}
+ \item Lattice in $d\geqslant 2$ dimensions.
+ \item Identical particles with pair hard-core interaction.
+ \item Finite number of perfect packings, which are periodic, and related to each other by isometries.
+ \item Non-sliding (defects are full of holes).
+\end{itemize}
+\eject
+
+\title{Lattice}
+\begin{itemize}
+ \item Lattice $\Lambda_\infty$ of dimension $d\geqslant 2$
+\end{itemize}
+\vfill
+\hfil\includegraphics[width=4.5cm]{grid.pdf}
+\vfill
+\eject
+
+\title{Particles}
+\begin{itemize}
+ \item Identical particles: shape $\omega\subset\mathbb R^d$
+\end{itemize}
+\vfill
+\hfil\includegraphics[width=4.5cm]{cross_example.pdf}
+\vfill
+\eject
+
+\title{Perfect packings}
+\begin{itemize}
+ \item Perfect packing: $\forall x\in\Lambda_\infty$, $\exists! y$ such that $x\in\omega+y$
+\end{itemize}
+\vfill
+\hfil\includegraphics[width=4cm]{cross_packing_r.pdf}
+\hfil\includegraphics[width=4cm]{cross_packing_l.pdf}
+\vfill
+\eject
+
+\title{Perfect packings}
+\begin{itemize}
+ \item Example with infinitely many perfect packings: $2\times2$ squares
+\end{itemize}
+\vfill
+\hfil\includegraphics[width=3cm]{square_packing.pdf}
+\hfil\includegraphics[width=3cm]{square_packing_slide.pdf}
+\vfill
+\eject
+
+\title{Non-sliding condition}
+\begin{itemize}
+ \item Defects have an amount of empty space that is proportional to their volume.
+ \item For every {\it connected} particle configuration $X$ that {\it cannot} be completed to a perfect packing, and for every particle configuration $Y\supset X$, at least one of the sites {\it neighboring} $X$ is empty.
+\end{itemize}
+\eject
+
+\title{Non-sliding condition}
+\begin{itemize}
+ \item Example: the red area cannot be entirely covered.
+\end{itemize}
+\vfill
+\hfil\includegraphics[width=2cm]{cross_sliding1.pdf}
+\hfil\includegraphics[width=2.4cm]{cross_sliding2.pdf}
+\vfill
+\eject
+
+\title{Non-sliding condition}
+\begin{itemize}
+ \item Counter-example: $2\times 2$ squares.
+\end{itemize}
+\vfill
+\hfil\includegraphics[width=2.5cm]{square_sliding.pdf}
+\hfil\includegraphics[width=2.5cm]{square_sliding_contra.pdf}
+\vfill
+\eject
+
+\title{Examples}
+\begin{itemize}
+ \item (thick) crosses, diamonds, hexagons...
+\end{itemize}
+\medskip
+\hfil\includegraphics[height=1.5cm]{cross.pdf}
+\hfil\includegraphics[height=1.5cm]{cross3.pdf}
+\hfil\includegraphics[height=1.5cm]{diamond.pdf}
+\hfil\includegraphics[height=1.5cm]{hexagon.pdf}
+\begin{itemize}
+ \item Conjecture: $k$-nearest neighbor exclusion on $\mathbb Z^2$ with
+ $$
+ k\in\{1,3,6,7,8,9,12,13,\cdots\}.
+ $$
+\end{itemize}
+\eject
+
+\title{Partition function}
+$$
+ \Xi^{(\nu)}_\Lambda(z)=
+ \sum_{X\subset\Lambda}
+ z^{|X|}\prod_{x\neq x'\in X}\phi(x,x')
+$$
+\begin{itemize}
+ \item $\Lambda\subset\Lambda_\infty$ is bounded.
+ \item $z$: {\it fugacity}, $z=e^{\beta\mu}$.
+ \item $\phi$: hard-core repulsion.
+ \item $|X|\leqslant N_{\mathrm{max}}$, maximal density: $\rho_m:=\frac{N_{\mathrm{max}}}{|\Lambda|}$.
+ \item Boundary condition: $\Lambda_\infty\setminus\Lambda$ is covered by a perfect covering, indexed by $\nu\in\{1,\cdots,\tau\}$.
+\end{itemize}
+\vfill
+\eject
+
+\title{Thermodynamical observables}
+\begin{itemize}
+ \item Pressure:
+ $$
+ p(z):=\lim_{\Lambda\to\Lambda_\infty}\frac1{|\Lambda|}\log\Xi_\Lambda^{(\nu)}(z)
+ $$
+ \item Correlation functions: for $\underline x\equiv\{x_1,\cdots,x_n\}\subset\Lambda_\infty$,
+ $$
+ \rho_n^{(\nu)}(\underline x)
+ :=\lim_{\Lambda\to\Lambda_\infty}
+ \frac1{\Xi_\Lambda^{(\nu)}(z)}
+ \sum_{\displaystyle\mathop{\scriptstyle X\subset\Lambda}_{X\supset\underline x}}
+ z^{|X|}\prod_{x\neq x'\in X}\phi(x,x')
+ $$
+\end{itemize}
+\eject
+
+\title{Result}
+\begin{itemize}
+ \item High fugacity regime: $y\equiv z^{-1}\ll 1$.
+ \item {\bf Analyticity}: $p(z)-\rho_m\log z$ and $\rho_n^{(\nu)}(\underline x)$ are {\it analytic} functions of $y$ in a disk in the complex $y$-plane centered at $0$.
+ \item {\bf Crystallization}: If $x$ is compatible with the $\nu$-th perfect packing, then
+ $$
+ \rho_1^{(\nu)}(x)=1+o(1)
+ $$
+ and if not, then
+ $$
+ \rho_1^{(\nu)}(x)=o(1)
+ $$
+\end{itemize}
+\eject
+
+\title{Low-fugacity expansion}
+\begin{itemize}
+ \item Formally,
+ $$
+ \frac1{|\Lambda|}\log\Xi_\Lambda^{(\nu)}(z)
+ =
+ \sum_{k=1}^\infty b_k(\Lambda)z^k
+ $$
+ where, if $Z_\Lambda(k_i)$ denotes the number of configurations with $k_i$ particles, then
+ $$
+ b_k(\Lambda):=\frac1{|\Lambda|}
+ \sum_{j=1}^k\frac{(-1)^{j+1}}j
+ \sum_{\displaystyle\mathop{\scriptstyle k_1,\cdots,k_j\geqslant 1}_{k_1+\cdots+k_j=k}}Z_\Lambda(k_1)\cdots Z_\Lambda(k_j)
+ $$
+\end{itemize}
+\eject
+
+\title{Low-fugacity expansion}
+\begin{itemize}
+ \item Second term:
+ $$
+ b_2(\Lambda)=\frac1{|\Lambda|}\left(Z_\Lambda(2)-\frac12Z_\Lambda^2(1)\right)
+ $$
+ \item $\frac12 Z_\Lambda^2(1)$: counts non-interacting particle configurations.
+ \item $Z_\Lambda(2)$: counts interacting particle configurations.
+ \item The terms of order $|\Lambda|^2$ cancel out!
+\end{itemize}
+\eject
+
+\title{Low-fugacity expansion}
+\begin{itemize}
+ \item \href{http://dx.doi.org/10.1017/S0305004100011191}{[Ursell, 1927]}, \href{http://dx.doi.org/10.1063/1.1749933}{[Mayer, 1937]}: $b_k(\Lambda)\to b_k$.
+ \item \href{http://dx.doi.org/10.1016/0031-9163(62)90198-1}{[Groeneveld, 1962]}, \href{http://dx.doi.org/10.1016/0003-4916(63)90336-1}{[Ruelle, 1963]}, \href{http://dx.doi.org/10.1063/1.1703906}{[Penrose, 1963]}:
+ $$
+ p(z)=\sum_{k=1}^\infty b_kz^k
+ $$
+ which has a positive radius of convergence.
+\end{itemize}
+\eject
+
+\title{High-fugacity expansion}
+\begin{itemize}
+ \item Inverse fugacity $y\equiv z^{-1}$:
+ $$
+ \Xi^{(\nu)}_\Lambda(z)=
+ z^{N_{\mathrm{max}}}
+ \sum_{X\subset\Lambda}
+ y^{N_{\mathrm{max}}-|X|}\prod_{x\neq x'\in X}\phi(x,x')
+ $$
+\end{itemize}
+\eject
+
+\title{High-fugacity expansion}
+\begin{itemize}
+ \item Formally,
+ $$
+ \frac1{|\Lambda|}\log\Xi_\Lambda^{(\nu)}(z)
+ =
+ \rho_m\log z
+ +
+ \sum_{k=1}^\infty c_k(\Lambda)y^k
+ +
+ o(1)
+ $$
+ where, if $Q_\Lambda(k_i)$ denotes the number of configurations with $N_{\mathrm{max}}-k_i$ particles, then
+ $$
+ c_k(\Lambda):=\frac1{|\Lambda|}
+ \sum_{j=1}^k\frac{(-1)^{j+1}}{j\tau^j}
+ \sum_{\displaystyle\mathop{\scriptstyle k_1,\cdots,k_j\geqslant 1}_{k_1+\cdots+k_j=k}}Q_\Lambda(k_1)\cdots Q_\Lambda(k_j)
+ $$
+\end{itemize}
+\eject
+
+\title{High-fugacity expansion}
+\begin{itemize}
+ \item \href{http://dx.doi.org/10.1063/1.1697217}{[Gaunt, Fisher, 1965]}: diamonds: $c_k(\Lambda)\to c_k$ for $k\leqslant 9$.
+ \item \href{http://dx.doi.org/10.1098/rsta.1988.0077}{[Joyce, 1988]}: hexagons (integrable, \href{http://dx.doi.org/10.1088/0305-4470/13/3/007}{[Baxter, 1980]}).
+ \item \href{http://dx.doi.org/10.1209/epl/i2005-10166-3}{[Eisenberg, Baram, 2005]}: crosses: $c_k(\Lambda)\to c_k$ for $k\leqslant 6$.
+ \item Cannot be done {\it systematically}: there exist counter-examples: e.g. nearest neighbor exclusion in 1 dimension:
+ $$
+ c_2(\Lambda)=-\frac1{192}|\Lambda|(|\Lambda|^2+2)
+ $$
+\end{itemize}
+\eject
+
+\title{Holes interact}
+\begin{itemize}
+ \item Total volume of holes: $\in\rho_m^{-1}\mathbb N$.
+\end{itemize}
+\vfill
+\hfil\includegraphics[height=4.5cm]{hole_example_cross.pdf}
+\hfil\includegraphics[height=4.5cm]{hole_example_square.pdf}
+\vfill
+\eject
+
+\title{Non-sliding condition}
+\begin{itemize}
+ \item Distinct defects are decorrelated.
+\end{itemize}
+\vfill
+\hfil\includegraphics[height=5cm]{hole_example_cross_decorrelated.pdf}
+\vfill
+\eject
+
+\title{Gaunt-Fisher configurations}
+\begin{itemize}
+ \item Group together empty space and neighboring particles.
+\end{itemize}
+\vfill
+\hfil\includegraphics[width=2.5cm]{gaunt_fisher2.pdf}
+\hfil\includegraphics[width=4cm]{gaunt_fisher3.pdf}
+\vfill
+\eject
+
+\title{Defect model}
+\vskip-5pt
+\begin{itemize}
+ \item Map particle system to a model of defects:
+ $$
+ \Xi_\Lambda^{(\nu)}(z)=z^{\rho_m|\Lambda|}\sum_{\underline\gamma\subset\mathfrak C_\nu(\Lambda)}
+ \left(\prod_{\gamma\neq\gamma'\in\underline\gamma}\Phi(\gamma,\gamma')\right)
+ \prod_{\gamma\in\underline\gamma}\zeta_\nu^{(z)}(\gamma)
+ $$
+ \begin{itemize}
+ \item $\Phi$: hard-core repulsion of defects.
+ \item $\zeta_\nu^{(z)}(\gamma)$: activity of defect.
+ \end{itemize}
+ \item The activity of a defect is exponentially small: $\exists\epsilon\ll 1$
+ $$
+ \zeta_\nu^{(z)}(\gamma)<\epsilon^{|\gamma|}
+ $$
+ \vskip-5pt
+ \item Low-fugacity expansion for defects.
+\end{itemize}
+\eject
+
+\title{Crystallization}
+\vfill
+\begin{itemize}
+ \item Peierls argument: in order to have a particle at $x$ that is not compatible with the $\nu$-th perfect packing, it must be part of or surrounded by a defect.
+ \vfill
+ \item Note: a naive Peierls argument requires the partition function to be independent from the boundary condition. This is not necessarily the case here, and we need elements from Pirogov-Sinai theory.
+\end{itemize}
+
+
+\end{document}
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..eb6cada
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,52 @@
+PROJECTNAME=$(basename $(wildcard *.tex))
+LIBS=$(notdir $(wildcard libs/*))
+FIGS=$(notdir $(wildcard figs/*.fig))
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME))
+
+all: $(PROJECTNAME)
+
+$(PROJECTNAME): $(LIBS) $(FIGS)
+ pdflatex -file-line-error $@.tex
+ pdflatex -synctex=1 $@.tex
+
+$(SYNCTEXS): $(LIBS) $(FIGS)
+ pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@)
+
+install: $(PROJECTNAME)
+ cp $^.pdf $(INSTALLDIR)/
+
+install-synctex: $(SYNCTEXS)
+ cp $^ $(INSTALLDIR)/
+
+
+$(LIBS):
+ ln -fs libs/$@ ./
+
+
+$(FIGS):
+ make -C figs/$@
+ ln -fs figs/$@/*.pdf ./
+
+
+clean-aux:
+ rm -f $(addsuffix .aux, $(PROJECTNAME))
+ rm -f $(addsuffix .log, $(PROJECTNAME))
+ rm -f $(addsuffix .out, $(PROJECTNAME))
+
+clean-libs:
+ rm -f $(LIBS)
+
+clean-figs:
+ $(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean; )
+ rm -f $(notdir $(wildcard figs/*.fig/*.pdf))
+
+clean-figs-aux:
+ $(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean-aux; )
+
+
+clean-tex:
+ rm -f $(PDFS) $(SYNCTEXS)
+
+clean: clean-aux clean-tex clean-libs clean-figs
diff --git a/README b/README
new file mode 100644
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--- /dev/null
+++ b/README
@@ -0,0 +1,36 @@
+This directory contains the source files to typeset the talk, and generate the
+figures. This can be accomplished by running
+ make
+
+
+This document uses a custom class file, located in the 'libs' directory, which
+defines a number of commands.
+
+
+* Dependencies:
+
+ pdflatex
+
+ TeXlive packages:
+ amsfonts
+ color
+ graphics
+ hyperref
+ latex
+ pgf
+ standalone
+
+ GNU make
+
+
+* Files:
+
+ GLaMP_2017.tex:
+ main LaTeX file
+
+ libs:
+ custom LaTeX class
+
+ figs:
+ source code for the figures
+
diff --git a/figs/cross_example.fig/Makefile b/figs/cross_example.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/cross_example.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile \ No newline at end of file
diff --git a/figs/cross_example.fig/cross_example.tikz.tex b/figs/cross_example.fig/cross_example.tikz.tex
new file mode 100644
index 0000000..8231de6
--- /dev/null
+++ b/figs/cross_example.fig/cross_example.tikz.tex
@@ -0,0 +1,16 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid{10}{10}{(-0.5,-0.5)}
+
+\cross{teal}{(5,5)}
+\cross{teal}{(4,2)}
+\cross{teal}{(7,2)}
+\cross{teal}{(3,8)}
+\cross{teal}{(1,7)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/cross_example.fig/grid.tikz.tex b/figs/cross_example.fig/grid.tikz.tex
new file mode 100644
index 0000000..4278366
--- /dev/null
+++ b/figs/cross_example.fig/grid.tikz.tex
@@ -0,0 +1,10 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid{10}{10}{(-0.5,-0.5)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/cross_example.fig/libs/shapes.sty b/figs/cross_example.fig/libs/shapes.sty
new file mode 120000
index 0000000..eaa25c7
--- /dev/null
+++ b/figs/cross_example.fig/libs/shapes.sty
@@ -0,0 +1 @@
+../../libs/shapes.sty \ No newline at end of file
diff --git a/figs/cross_packing.fig/Makefile b/figs/cross_packing.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/cross_packing.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile \ No newline at end of file
diff --git a/figs/cross_packing.fig/cross_packing_l.tikz.tex b/figs/cross_packing.fig/cross_packing_l.tikz.tex
new file mode 100644
index 0000000..b3bff46
--- /dev/null
+++ b/figs/cross_packing.fig/cross_packing_l.tikz.tex
@@ -0,0 +1,14 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+ \foreach \i in {0,...,3}{
+ \foreach \j in {0,...,3}{
+ \cross{teal}{(-2*\j,\j)++(\i,2*\i)}
+ }
+ }
+\end{tikzpicture}
+\end{document}
diff --git a/figs/cross_packing.fig/cross_packing_r.tikz.tex b/figs/cross_packing.fig/cross_packing_r.tikz.tex
new file mode 100644
index 0000000..18db92a
--- /dev/null
+++ b/figs/cross_packing.fig/cross_packing_r.tikz.tex
@@ -0,0 +1,14 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+ \foreach \i in {0,...,3}{
+ \foreach \j in {0,...,3}{
+ \cross{teal}{(-\j,2*\j)++(2*\i,\i)}
+ }
+ }
+\end{tikzpicture}
+\end{document}
diff --git a/figs/cross_packing.fig/libs/shapes.sty b/figs/cross_packing.fig/libs/shapes.sty
new file mode 120000
index 0000000..eaa25c7
--- /dev/null
+++ b/figs/cross_packing.fig/libs/shapes.sty
@@ -0,0 +1 @@
+../../libs/shapes.sty \ No newline at end of file
diff --git a/figs/cross_sliding.fig/Makefile b/figs/cross_sliding.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/cross_sliding.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile \ No newline at end of file
diff --git a/figs/cross_sliding.fig/cross_sliding1.tikz.tex b/figs/cross_sliding.fig/cross_sliding1.tikz.tex
new file mode 100644
index 0000000..a1cba3b
--- /dev/null
+++ b/figs/cross_sliding.fig/cross_sliding1.tikz.tex
@@ -0,0 +1,17 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+
+\fill[color=red](2.5,2.5)--++(1,0)--++(0,2)--++(-1,0)--cycle;
+
+\grid{5}{8}{(-0.5,-0.5)}
+
+\cross{teal}{(2,2)}
+\cross{teal}{(2,5)}
+
+\end{tikzpicture}
+\end{document}
diff --git a/figs/cross_sliding.fig/cross_sliding2.tikz.tex b/figs/cross_sliding.fig/cross_sliding2.tikz.tex
new file mode 100644
index 0000000..4fd395b
--- /dev/null
+++ b/figs/cross_sliding.fig/cross_sliding2.tikz.tex
@@ -0,0 +1,18 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+
+\fill[color=red](0.5,2.5)--++(1,0)--++(0,3)--++(-1,0)--cycle;
+
+\grid{6}{9}{(-0.5,-0.5)}
+
+\cross{teal}{(2,2)}
+\cross{teal}{(3,4)}
+\cross{teal}{(2,6)}
+
+\end{tikzpicture}
+\end{document}
diff --git a/figs/cross_sliding.fig/libs/shapes.sty b/figs/cross_sliding.fig/libs/shapes.sty
new file mode 120000
index 0000000..eaa25c7
--- /dev/null
+++ b/figs/cross_sliding.fig/libs/shapes.sty
@@ -0,0 +1 @@
+../../libs/shapes.sty \ No newline at end of file
diff --git a/figs/gaunt_fisher.fig/Makefile b/figs/gaunt_fisher.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/gaunt_fisher.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile \ No newline at end of file
diff --git a/figs/gaunt_fisher.fig/gaunt_fisher2.tikz.tex b/figs/gaunt_fisher.fig/gaunt_fisher2.tikz.tex
new file mode 100644
index 0000000..731d3f2
--- /dev/null
+++ b/figs/gaunt_fisher.fig/gaunt_fisher2.tikz.tex
@@ -0,0 +1,30 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+ \cross{teal}{(4,4)}
+ \cross{teal}{(3,6)}
+ \cross{teal}{(7,3)}
+ \cross{teal}{(9,4)}
+ \cross{teal}{(10,7)}
+ \cross{teal}{(4,9)}
+
+ \cross{teal}{(6,6)}
+ \cross{teal}{(7,8)}
+
+ \square{black}{(6,4)}
+ \square{black}{(5,5)}
+ \square{black}{(5,7)}
+ \square{black}{(4,7)}
+ \square{black}{(5,8)}
+ \square{black}{(7,5)}
+ \square{black}{(8,5)}
+ \square{black}{(8,6)}
+ \square{black}{(9,6)}
+ \square{black}{(8,7)}
+
+\end{tikzpicture}
+\end{document}
diff --git a/figs/gaunt_fisher.fig/gaunt_fisher3.tikz.tex b/figs/gaunt_fisher.fig/gaunt_fisher3.tikz.tex
new file mode 100644
index 0000000..36c9675
--- /dev/null
+++ b/figs/gaunt_fisher.fig/gaunt_fisher3.tikz.tex
@@ -0,0 +1,53 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+ \foreach\i in {2,...,4}{
+ \cross{teal}{(2*\i,\i)}
+ \cross{teal}{(5,15)++(\i,-2*\i)}
+ }
+ \foreach\i in {1,...,3}{
+ \cross{teal}{(-5,10)++(2*\i,\i)}
+ }
+ \cross{teal}{(3,5)}
+ \cross{teal}{(5,9)}
+ \cross{teal}{(-1,7)}
+ \cross{teal}{(0,9)}
+ \cross{teal}{(6,6)}
+ \cross{teal}{(1,6)}
+ \cross{teal}{(3,10)}
+ \cross{teal}{(4,12)}
+ \cross{teal}{(1,3)}
+ \cross{teal}{(-2,4)}
+ \cross{teal}{(-4,8)}
+
+ \square{black}{(3,3)}
+ \square{black}{(2,4)}
+ \square{black}{(4,4)}
+ \square{black}{(5,4)}
+ \square{black}{(5,5)}
+ \square{black}{(7,5)}
+ \square{black}{(8,6)}
+ \square{black}{(7,7)}
+ \square{black}{(7,8)}
+ \square{black}{(6,8)}
+ \square{black}{(6,10)}
+ \square{black}{(5,11)}
+ \square{black}{(2,12)}
+ \square{black}{(2,11)}
+ \square{black}{(1,11)}
+ \square{black}{(0,11)}
+ \square{black}{(1,10)}
+ \square{black}{(-1,10)}
+ \square{black}{(-2,10)}
+ \square{black}{(-2,9)}
+ \square{black}{(-3,9)}
+ \square{black}{(-2,8)}
+ \square{black}{(-1,5)}
+ \square{black}{(0,5)}
+ \square{black}{(0,4)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/gaunt_fisher.fig/libs/shapes.sty b/figs/gaunt_fisher.fig/libs/shapes.sty
new file mode 120000
index 0000000..eaa25c7
--- /dev/null
+++ b/figs/gaunt_fisher.fig/libs/shapes.sty
@@ -0,0 +1 @@
+../../libs/shapes.sty \ No newline at end of file
diff --git a/figs/hole_example.fig/Makefile b/figs/hole_example.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/hole_example.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile \ No newline at end of file
diff --git a/figs/hole_example.fig/hole_example_cross.tikz.tex b/figs/hole_example.fig/hole_example_cross.tikz.tex
new file mode 100644
index 0000000..f9208e1
--- /dev/null
+++ b/figs/hole_example.fig/hole_example_cross.tikz.tex
@@ -0,0 +1,36 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+ \cross{teal}{(5,2)}
+ \cross{teal}{(4,4)}
+ \cross{teal}{(3,6)}
+ \cross{teal}{(2,8)}
+ \cross{teal}{(7,3)}
+ \cross{teal}{(9,4)}
+ \cross{teal}{(11,5)}
+ \cross{teal}{(10,7)}
+ \cross{teal}{(9,9)}
+ \cross{teal}{(8,11)}
+ \cross{teal}{(6,10)}
+ \cross{teal}{(4,9)}
+
+ \cross{green}{(6,6)}
+ \cross{green}{(7,8)}
+
+ \square{black}{(6,4)}
+ \square{black}{(5,5)}
+ \square{black}{(5,7)}
+ \square{black}{(4,7)}
+ \square{black}{(5,8)}
+ \square{black}{(7,5)}
+ \square{black}{(8,5)}
+ \square{black}{(8,6)}
+ \square{black}{(9,6)}
+ \square{black}{(8,7)}
+
+\end{tikzpicture}
+\end{document}
diff --git a/figs/hole_example.fig/hole_example_cross_decorrelated.tikz.tex b/figs/hole_example.fig/hole_example_cross_decorrelated.tikz.tex
new file mode 100644
index 0000000..113171d
--- /dev/null
+++ b/figs/hole_example.fig/hole_example_cross_decorrelated.tikz.tex
@@ -0,0 +1,63 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+ \cross{teal}{(5,2)}
+ \cross{teal}{(4,4)}
+ \cross{teal}{(3,6)}
+ \cross{teal}{(2,8)}
+ \cross{teal}{(7,3)}
+ \cross{teal}{(9,4)}
+ \cross{teal}{(11,5)}
+ \cross{teal}{(10,7)}
+ \cross{teal}{(9,9)}
+ \cross{teal}{(8,11)}
+ \cross{teal}{(6,10)}
+ \cross{teal}{(4,9)}
+
+ \cross{green}{(6,6)}
+ \cross{green}{(7,8)}
+
+ \square{black}{(6,4)}
+ \square{black}{(5,5)}
+ \square{black}{(5,7)}
+ \square{black}{(4,7)}
+ \square{black}{(5,8)}
+ \square{black}{(7,5)}
+ \square{black}{(8,5)}
+ \square{black}{(8,6)}
+ \square{black}{(9,6)}
+ \square{black}{(8,7)}
+
+ \cross{teal}{(13, 6)}
+ \cross{teal}{(12, 8)}
+ \cross{teal}{(11,10)}
+ \cross{teal}{(10,12)}
+ \cross{teal}{(15, 7)}
+ \cross{teal}{(17, 8)}
+ \cross{teal}{(19, 9)}
+ \cross{teal}{(18,11)}
+ \cross{teal}{(17,13)}
+ \cross{teal}{(16,15)}
+ \cross{teal}{(14,14)}
+ \cross{teal}{(12,13)}
+
+ \cross{cyan}{(15,10)}
+ \cross{cyan}{(13,11)}
+
+ \square{black}{(14,8)}
+ \square{black}{(14,9)}
+ \square{black}{(13,9)}
+ \square{black}{(16,9)}
+ \square{black}{(17,10)}
+ \square{black}{(16,11)}
+ \square{black}{(16,12)}
+ \square{black}{(15,12)}
+ \square{black}{(14,12)}
+ \square{black}{(15,13)}
+
+\end{tikzpicture}
+\end{document}
diff --git a/figs/hole_example.fig/hole_example_square.tikz.tex b/figs/hole_example.fig/hole_example_square.tikz.tex
new file mode 100644
index 0000000..4b3fb7c
--- /dev/null
+++ b/figs/hole_example.fig/hole_example_square.tikz.tex
@@ -0,0 +1,24 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+ \foreach\i in {0,...,8}{
+ \ttsquare{teal}{(0,2*\i)}
+ \ttsquare{teal}{(4,2*\i)}
+ }
+ \ttsquare{teal}{(2,0)}
+ \ttsquare{teal}{(2,16)}
+ \foreach\i in {1,...,6}{
+ \ttsquare{green}{(2,2*\i+1)}
+ }
+
+ \square{black}{(1.5,1.5)}
+ \square{black}{(2.5,1.5)}
+ \square{black}{(1.5,14.5)}
+ \square{black}{(2.5,14.5)}
+
+\end{tikzpicture}
+\end{document}
diff --git a/figs/hole_example.fig/libs/shapes.sty b/figs/hole_example.fig/libs/shapes.sty
new file mode 120000
index 0000000..eaa25c7
--- /dev/null
+++ b/figs/hole_example.fig/libs/shapes.sty
@@ -0,0 +1 @@
+../../libs/shapes.sty \ No newline at end of file
diff --git a/figs/libs/Makefile b/figs/libs/Makefile
new file mode 100644
index 0000000..33b81e2
--- /dev/null
+++ b/figs/libs/Makefile
@@ -0,0 +1,28 @@
+PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex)))
+LIBS=$(notdir $(wildcard libs/*))
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+
+all: $(PDFS)
+
+$(PDFS): $(LIBS)
+ echo $(LIBS)
+ pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
+
+install: $(PDFS)
+ cp $^ $(INSTALLDIR)/
+
+$(LIBS):
+ ln -fs libs/$@ ./
+
+clean-libs:
+ rm -f $(LIBS)
+
+clean-aux:
+ rm -f $(addsuffix .aux, $(PROJECTNAME))
+ rm -f $(addsuffix .log, $(PROJECTNAME))
+
+clean-tex:
+ rm -f $(PDFS)
+
+clean: clean-libs clean-aux clean-tex
diff --git a/figs/libs/shapes.sty b/figs/libs/shapes.sty
new file mode 100644
index 0000000..dd4baae
--- /dev/null
+++ b/figs/libs/shapes.sty
@@ -0,0 +1,58 @@
+%%
+%% Various shapes and lattices
+%%
+
+%% TeX format
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+
+%% class name
+\ProvidesPackage{shapes}[2017/06/24]
+
+
+% square lattice (width #1, height #2, origin #3)
+\def\grid#1#2#3{
+ \foreach\i in {0,...,#2}{
+ \draw#3++(0,\i)--++(#1,0);
+ }
+ \foreach\i in {0,...,#1}{
+ \draw#3++(\i,0)--++(0,#2);
+ }
+}
+
+
+% cross (color #1, position #2)
+\def\cross#1#2{
+ \fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
+ \draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
+}
+
+% thick cross (color #1, position #2, size #3)
+\def\thickcross#1#2#3{
+ \fill[color=#1]#2++(#3*0.5,0.5*#3)--++(#3*0,1*#3)--++(#3*-1,0*#3)--++(#3*0,-1*#3)--++(#3*-1,0*#3)--++(#3*0,-1*#3)--++(#3*1,0*#3)--++(#3*0,-1*#3)--++(#3*1,0*#3)--++(#3*0,1*#3)--++(#3*1,0*#3)--++(#3*0,1*#3)--++(#3*-1,0*#3);
+ \draw[color=black]#2++(#3*0.5,0.5*#3)--++(#3*0,1*#3)--++(#3*-1,0*#3)--++(#3*0,-1*#3)--++(#3*-1,0*#3)--++(#3*0,-1*#3)--++(#3*1,0*#3)--++(#3*0,-1*#3)--++(#3*1,0*#3)--++(#3*0,1*#3)--++(#3*1,0*#3)--++(#3*0,1*#3)--++(#3*-1,0*#3);
+}
+
+
+% 1x1 square (color #1, position #2)
+\def\square#1#2{
+ \fill[color=#1]#2++(-0.5,-0.5)--++(0,1)--++(1,0)--++(0,-1)--cycle;
+ \draw[color=black]#2++(-0.5,-0.5)--++(0,1)--++(1,0)--++(0,-1)--cycle;
+}
+
+% 2x2 square (color #1, position #2)
+\def\ttsquare#1#2{
+ \fill[color=#1]#2++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
+ \draw[color=black]#2++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
+}
+\def\ttsquareempty#1{
+ \draw[color=black]#1++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
+}
+
+% diamond (color #1, position #2)
+\def\diamond#1#2{
+ \fill[color=#1]#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle;
+ \draw[color=black]#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle;
+}
+
+
+\endinput
diff --git a/figs/shapes.fig/Makefile b/figs/shapes.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/shapes.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile \ No newline at end of file
diff --git a/figs/shapes.fig/cross.tikz.tex b/figs/shapes.fig/cross.tikz.tex
new file mode 100644
index 0000000..fca0acc
--- /dev/null
+++ b/figs/shapes.fig/cross.tikz.tex
@@ -0,0 +1,11 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid55{(-2.5,-2.5)}
+\cross{teal}{(0,0)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/cross3.tikz.tex b/figs/shapes.fig/cross3.tikz.tex
new file mode 100644
index 0000000..8e50f19
--- /dev/null
+++ b/figs/shapes.fig/cross3.tikz.tex
@@ -0,0 +1,11 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid{15}{15}{(-7.5,-7.5)}
+\thickcross{teal}{(0,0)}3
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/diamond.tikz.tex b/figs/shapes.fig/diamond.tikz.tex
new file mode 100644
index 0000000..6d9eaa4
--- /dev/null
+++ b/figs/shapes.fig/diamond.tikz.tex
@@ -0,0 +1,11 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid44{(-2,-2)}
+\diamond{teal}{(0,0)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/hexagon.tikz.tex b/figs/shapes.fig/hexagon.tikz.tex
new file mode 100644
index 0000000..5439f67
--- /dev/null
+++ b/figs/shapes.fig/hexagon.tikz.tex
@@ -0,0 +1,32 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+
+\draw(0,0)--++(2,0);
+\draw(120:1)--++(3,0);
+\draw(120:2)--++(4,0);
+\draw(120:2)++(60:1)--++(3,0);
+\draw(120:2)++(60:2)--++(2,0);
+
+\draw(0,0)--++(60:4);
+\draw(1,0)--++(60:3);
+\draw(2,0)--++(60:2);
+\draw(120:1)--++(60:3);
+\draw(120:2)--++(60:2);
+
+\draw(0,0)--++(120:2);
+\draw(1,0)--++(120:3);
+\draw(2,0)--++(120:4);
+\draw(2,0)++(60:1)--++(120:3);
+\draw(2,0)++(60:2)--++(120:2);
+
+\fill[color=teal](60:1)--++(0:1)--++(60:1)--++(120:1)--++(180:1)--++(240:1)--++(300:1)--cycle;
+\draw(60:1)--++(0:1)--++(60:1)--++(120:1)--++(180:1)--++(240:1)--++(300:1)--cycle;
+
+
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/libs/shapes.sty b/figs/shapes.fig/libs/shapes.sty
new file mode 120000
index 0000000..eaa25c7
--- /dev/null
+++ b/figs/shapes.fig/libs/shapes.sty
@@ -0,0 +1 @@
+../../libs/shapes.sty \ No newline at end of file
diff --git a/figs/square_packing.fig/Makefile b/figs/square_packing.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/square_packing.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile \ No newline at end of file
diff --git a/figs/square_packing.fig/libs/shapes.sty b/figs/square_packing.fig/libs/shapes.sty
new file mode 120000
index 0000000..eaa25c7
--- /dev/null
+++ b/figs/square_packing.fig/libs/shapes.sty
@@ -0,0 +1 @@
+../../libs/shapes.sty \ No newline at end of file
diff --git a/figs/square_packing.fig/square_packing.tikz.tex b/figs/square_packing.fig/square_packing.tikz.tex
new file mode 100644
index 0000000..297e72e
--- /dev/null
+++ b/figs/square_packing.fig/square_packing.tikz.tex
@@ -0,0 +1,20 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\foreach \i in {0,...,3}{
+ \ttsquare{teal}{(2*\i,0)}
+ \ttsquare{teal}{(2*\i,2)}
+ \ttsquare{teal}{(2*\i,4)}
+}
+\grid86{[color=red, dashed](-1,-1)}
+\foreach \i in {0,...,3}{
+ \ttsquareempty{(2*\i,0)}
+ \ttsquareempty{(2*\i,2)}
+ \ttsquareempty{(2*\i,4)}
+}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/square_packing.fig/square_packing_slide.tikz.tex b/figs/square_packing.fig/square_packing_slide.tikz.tex
new file mode 100644
index 0000000..c02485a
--- /dev/null
+++ b/figs/square_packing.fig/square_packing_slide.tikz.tex
@@ -0,0 +1,25 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\clip(-1.01,-1.01)--(7.01,-1.01)--(7.01,5.01)--(-1.01,5.01)--cycle;
+\foreach \i in {0,...,3}{
+ \ttsquare{teal}{(2*\i,0)}
+ \ttsquare{teal}{(2*\i+1,2)}
+ \ttsquare{teal}{(2*\i,4)}
+}
+\ttsquare{teal}{(-1,2)}
+
+\grid86{[color=red, dashed](-1,-1)}
+
+\foreach \i in {0,...,3}{
+ \ttsquareempty{(2*\i,0)}
+ \ttsquareempty{(2*\i+1,2)}
+ \ttsquareempty{(2*\i,4)}
+}
+\ttsquareempty{(-1,2)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/square_sliding.fig/Makefile b/figs/square_sliding.fig/Makefile
new file mode 120000
index 0000000..704310e
--- /dev/null
+++ b/figs/square_sliding.fig/Makefile
@@ -0,0 +1 @@
+../libs/Makefile \ No newline at end of file
diff --git a/figs/square_sliding.fig/libs/shapes.sty b/figs/square_sliding.fig/libs/shapes.sty
new file mode 120000
index 0000000..eaa25c7
--- /dev/null
+++ b/figs/square_sliding.fig/libs/shapes.sty
@@ -0,0 +1 @@
+../../libs/shapes.sty \ No newline at end of file
diff --git a/figs/square_sliding.fig/square_sliding.tikz.tex b/figs/square_sliding.fig/square_sliding.tikz.tex
new file mode 100644
index 0000000..b63a58d
--- /dev/null
+++ b/figs/square_sliding.fig/square_sliding.tikz.tex
@@ -0,0 +1,17 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+
+\fill[color=red](-1,1)--++(0,5)--++(2,0)--++(0,-5)--cycle;
+
+\grid{8}{15}{(-4,-4)}
+
+\ttsquare{teal}{(0,0)}
+\ttsquare{teal}{(0,7)}
+
+\end{tikzpicture}
+\end{document}
diff --git a/figs/square_sliding.fig/square_sliding_contra.tikz.tex b/figs/square_sliding.fig/square_sliding_contra.tikz.tex
new file mode 100644
index 0000000..61ea43d
--- /dev/null
+++ b/figs/square_sliding.fig/square_sliding_contra.tikz.tex
@@ -0,0 +1,25 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+
+\grid{8}{15}{(-4,-4)}
+
+\ttsquare{teal}{(0,0)}
+\ttsquare{teal}{(0,7)}
+
+\ttsquare{cyan}{( 0, 2)}
+\ttsquare{cyan}{( 0,-2)}
+\ttsquare{cyan}{( 2, 0)}
+\ttsquare{cyan}{(-2, 0)}
+
+\ttsquare{cyan}{( 0, 9)}
+\ttsquare{cyan}{( 0, 5)}
+\ttsquare{cyan}{( 2, 7)}
+\ttsquare{cyan}{(-2, 7)}
+
+\end{tikzpicture}
+\end{document}
diff --git a/libs/ian-presentation.cls b/libs/ian-presentation.cls
new file mode 100644
index 0000000..aa65bb1
--- /dev/null
+++ b/libs/ian-presentation.cls
@@ -0,0 +1,186 @@
+%%
+%% Ian's presentation class
+%%
+
+%% TeX format
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+
+%% class name
+\ProvidesClass{ian-presentation}[2017/06/20]
+
+\def\ian@defaultoptions{
+ \pagestyle{plain}
+ \RequirePackage{color}
+}
+
+%% paper dimensions
+\setlength\paperheight{240pt}
+\setlength\paperwidth{320pt}
+
+%% fonts
+\input{size11.clo}
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+
+%% text dimensions
+\textheight=208pt
+\textwidth=272pt
+\hoffset=-1in
+\voffset=-1in
+\oddsidemargin=24pt
+\evensidemargin=24pt
+\topmargin=8pt
+\headheight=0pt
+\headsep=0pt
+\marginparsep=0pt
+\marginparwidth=0pt
+\footskip=16pt
+
+
+%% remove default skips
+\parindent=0pt
+\parskip=0pt
+\baselineskip=0pt
+
+%% something is wrong with \thepage, redefine it
+\gdef\thepage{\the\c@page}
+
+%% correct vertical alignment at the end of a document
+\AtEndDocument{
+ % save total slide count
+ \immediate\write\@auxout{\noexpand\gdef\noexpand\slidecount{\thepage}}
+ \vfill
+ \eject
+}
+
+
+%% footer
+\def\ps@plain{
+ \def\@oddhead{}
+ \def\@evenhead{\@oddhead}
+ \def\@oddfoot{\tiny\hfill\thepage/\safe\slidecount\hfill}
+ \def\@evenfoot{\@oddfoot}
+}
+\def\ps@empty{
+ \def\@oddhead{}
+ \def\@evenhead{\@oddhead}
+ \def\@oddfoot{}
+ \def\@evenfoot{\@oddfoot}
+}
+
+
+%% title of slide
+\def\title#1{
+ \hfil{\bf\large #1}\par
+ \hfil\vrule width0.75\textwidth height0.3pt\par
+ \vskip5pt
+}
+
+
+%% hyperlinks
+% hyperlinkcounter
+\newcounter{lncount}
+% hyperref anchor
+\def\hrefanchor{%
+\stepcounter{lncount}%
+\hypertarget{ln.\thelncount}{}%
+}
+
+%% define a command and write it to aux file
+\def\outdef#1#2{%
+ % define command%
+ \expandafter\xdef\csname #1\endcsname{#2}%
+ % hyperlink number%
+ \expandafter\xdef\csname #1@hl\endcsname{\thelncount}%
+ % write command to aux%
+ \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1\endcsname{\csname #1\endcsname}}%
+ \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1@hl\endcsname{\thelncount}}%
+}
+
+%% can call commands even when they are not defined
+\def\safe#1{%
+ \ifdefined#1%
+ #1%
+ \else%
+ {\color{red}\bf?}%
+ \fi%
+}
+
+
+%% itemize
+\newlength\itemizeskip
+% left margin for items
+\setlength\itemizeskip{20pt}
+\newlength\itemizeseparator
+% space between the item symbol and the text
+\setlength\itemizeseparator{5pt}
+% penalty preceding an itemize
+\def\itemizepenalty{0}
+% counter counting the itemize level
+\newcounter{itemizecount}
+
+% item symbol
+\def\itemizept#1{
+ \ifnum#1=1
+ \textbullet
+ \else
+ $\scriptstyle\blacktriangleright$
+ \fi
+}
+
+\newlength\current@itemizeskip
+\setlength\current@itemizeskip{0pt}
+\def\itemize{
+ \par\penalty\itemizepenalty\medskip\penalty\itemizepenalty
+ \addtocounter{itemizecount}{1}
+ \addtolength\current@itemizeskip{\itemizeskip}
+ \leftskip\current@itemizeskip
+}
+\def\enditemize{
+ \addtocounter{itemizecount}{-1}
+ \addtolength\current@itemizeskip{-\itemizeskip}
+ \par\leftskip\current@itemizeskip
+ \medskip
+}
+\newlength\itempt@total
+\def\item{
+ \settowidth\itempt@total{\itemizept\theitemizecount}
+ \addtolength\itempt@total{\itemizeseparator}
+ \par
+ \medskip
+ \hskip-\itempt@total\itemizept\theitemizecount\hskip\itemizeseparator
+}
+
+%% enumerate
+\newcounter{enumerate@count}
+\def\enumerate{
+ \setcounter{enumerate@count}0
+ \let\olditem\item
+ \let\olditemizept\itemizept
+ \def\item{
+ % counter
+ \stepcounter{enumerate@count}
+ % set header
+ \def\itemizept{\theenumerate@count.}
+ % hyperref anchor
+ \hrefanchor
+ % define tag (for \label)
+ \xdef\tag{\theenumerate@count}
+ \olditem
+ }
+ \itemize
+}
+\def\endenumerate{
+ \enditemize
+ \let\item\olditem
+ \let\itemizept\olditemizept
+}
+
+
+%% end
+\ian@defaultoptions
+
+\endinput