\documentclass[11pt,notitlepage]{article}
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\usepackage[all]{xy}
\usepackage[english,greek]{babel}
\usepackage{dbnsymb, amsmath, graphicx, amssymb, multicol, stmaryrd, pifont,
  amscd, colortbl, mathtools, wasysym, needspace, import, longtable, overpic,
  enumitem, bbm, pdfpages, ../picins, array, setspace}
\usepackage{tensor}
\usepackage{txfonts}	% for the likes of \coloneqq.
\usepackage{fontawesome} % for \faPlay
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{utfsym}	% for the likes of \car=\usym{1F697}
\usepackage[textwidth=8.5in,textheight=10.5in,centering]{geometry}
\parindent 0in
\usepackage[makeroom]{cancel}

% Following http://tex.stackexchange.com/a/847/22475:
\usepackage[setpagesize=false]{hyperref}
\hypersetup{colorlinks,
  linkcolor={blue!50!black},
  citecolor={blue!50!black},
  urlcolor={blue!50!black}
}

% Following http://tex.stackexchange.com/questions/59340/how-to-highlight-an-entire-paragraph
\usepackage[framemethod=tikz]{mdframed}

\usepackage[T1]{fontenc}

\def\myurl{http://www.math.toronto.edu/~drorbn}
\def\thistalk{Sydney-230327}
\def\title{Computing the Zombian of an Unfinished Columbarium}

\def\navigator{{
  \href{\myurl}{Dror Bar-Natan}:
  \href{http://drorbn.net/ap}{Academic Pensieve}:
  \href{http://drorbn.net/ap/Talks}{Talks}:
  \href{http://drorbn.net/ap/Talks/Sydney-230327}{Sydney-230327}:
}}
\def\thanks{{Thanks for inviting me to Sydney!}}
\def\webdef{{{\greektext web}$\coloneqq$\href{http://drorbn.net/syd23}{http://drorbn.net/syd23}}}
\def\web#1{{\href{\myurl/Talks/\thistalk/#1}{{\greektext web}/#1}}}
\def\titleA{{\title}}
\def\titleB{{\title}}
\def\titleC{{\title}}

\definecolor{mblue}{HTML}{E0E0FF}
\definecolor{mgray}{HTML}{B0B0B0}
\definecolor{morange}{HTML}{FFA50A}
\definecolor{mpink}{HTML}{FFE0E0}
\definecolor{myellow}{HTML}{FFFF00}
\def\blue{\color{blue}}
\def\gray{\color{gray}}
\def\mgray{\color{mgray}}
\def\morange{\color{morange}}
\def\pink{\color{pink}}
\def\magenta{\color{magenta}}
\def\red{\color{red}}
\def\yellowm#1{{\setlength{\fboxsep}{0pt}\colorbox{yellow}{$#1$}}}
\def\myellowm#1{{\setlength{\fboxsep}{0pt}\colorbox{myellow}{$#1$}}}
\def\mpinkm#1{{\setlength{\fboxsep}{0pt}\colorbox{mpink}{$#1$}}}
\def\mbluem#1{{\setlength{\fboxsep}{0pt}\colorbox{mblue}{$#1$}}}
\def\cbox#1#2{{\setlength{\fboxsep}{0pt}\colorbox{#1}{#2}}}

\def\arXiv#1{{\href{http://arxiv.org/abs/#1}{{\tiny arXiv:}\linebreak[0]{#1}}}}

\def\qed{{\linebreak[1]\null\hfill\text{$\Box$}}}

\def\act{{\hspace{-1pt}\sslash\hspace{-0.75pt}}}
\def\ad{\operatorname{ad}}
\def\Ad{\operatorname{Ad}}
\def\aft{$\overrightarrow{\text{4T}}$}
\def\AS{\mathit{AS}}
\def\bbZZ{{\mathbb Z\mathbb Z}}
\def\CW{\text{\it CW}}
\def\diag{\operatorname{diag}}
\def\eps{\epsilon}
\def\FL{\text{\it FL}}
\def\Hom{\operatorname{Hom}}
\def\IHX{\mathit{IHX}}
\def\mor{\operatorname{mor}}
\def\PvT{{\mathit P\!v\!T}}
\def\remove{\!\setminus\!}
\def\STU{\mathit{STU}}
\def\SW{\text{\it SW}}
\def\TC{\mathit{TC}}
\def\tr{\operatorname{tr}}
\def\vT{{\mathit v\!T}}

\def\bara{{\bar a}}
\def\barb{{\bar b}}
\def\barT{{\bar T}}
\def\bbE{{\mathbb E}}
\def\bbe{\mathbbm{e}}
\def\bbH{{\mathbb H}}
\def\bbN{{\mathbb N}}
\def\bbO{{\mathbb O}}
\def\bbQ{{\mathbb Q}}
\def\bbR{{\mathbb R}}
\def\bbZ{{\mathbb Z}}
\def\bcA{{\bar{\mathcal A}}}
\def\calA{{\mathcal A}}
\def\calD{{\mathcal D}}
\def\calF{{\mathcal F}}
\def\calG{{\mathcal G}}
\def\calH{{\mathcal H}}
\def\calI{{\mathcal I}}
\def\calK{{\mathcal K}}
\def\calL{{\mathcal L}}
\def\calM{{\mathcal M}}
\def\calO{{\mathcal O}}
\def\calP{{\mathcal P}}
\def\calR{{\mathcal R}}
\def\calS{{\mathcal S}}
\def\calT{{\mathcal T}}
\def\calU{{\mathcal U}}
\def\fraka{{\mathfrak a}}
\def\frakb{{\mathfrak b}}
\def\frakg{{\mathfrak g}}
\def\frakh{{\mathfrak h}}
\def\tilE{\tilde{E}}
\def\tilq{\tilde{q}}

\def\tDelta{\tilde{\Delta}}
\def\tf{\tilde{f}}
\def\tF{\tilde{F}}
\def\tg{\tilde{g}}
\def\tI{\tilde{I}}
\def\tm{\tilde{m}}
\def\tR{\tilde{R}}
\def\tsigma{\tilde{\sigma}}
\def\tS{\tilde{S}}
\def\tSW{\widetilde{\SW}}

\def\car{\reflectbox{\usym{1F697}}}
\def\rac{\usym{1F697}}

% From http://tex.stackexchange.com/questions/154672/how-to-get-a-medium-sized-otimes
\DeclareMathOperator*{\midotimes}{\text{\raisebox{0.25ex}{\scalebox{0.8}{$\bigotimes$}}}}

%%%

\def\FormulasA{{\raisebox{2mm}{\parbox[t]{3.125in}{
{\red\bf The Alexander Polynomial.} Draw an $n$-crossing knot $K$ as
a long knot as on the right, with the edges are marked with a running
index ${k\in\{1,\ldots,2n+1\}}$. Let $A$ be the $(2n+1)\times(2n+1)$
matrix constructed by starting with the identity matrix $I$, and adding
a $2\times 2$ block for each crossing:
}}}}

\def\Arules{{$\displaystyle
  \begin{array}{c|cccc}
    A &   \text{col }i\!+\!1  &  \text{col }j\!+\!1 \\
    \hline
    \text{row }i &  -T^s  & T^s-1 \\
    \text{row }j &  0  & -1
  \end{array}
$}}

\def\FormulasB{{\raisebox{0mm}{\parbox[t]{3.95in}{
For our example, it is:
\par \[
A=\left(
\begin{array}{ccccccc}
 1 & \mbluem{-T} & 0 & 0 & \mbluem{T-1} & 0 & 0 \\
 0 & 1 & \mpinkm{-1} & 0 & 0 & \mpinkm{\ 0\ } & 0 \\
 0 & 0 & 1 & \myellowm{-T} & 0 & 0 & \myellowm{T-1} \\
 0 & \mbluem{\ 0\ } & 0 & 1 & \mbluem{-1} & 0 & 0 \\
 0 & 0 & \mpinkm{T-1} & 0 & 1 & \mpinkm{-T} & 0 \\
 0 & 0 & 0 & \myellowm{\ 0\ } & 0 & 1 & \myellowm{-1} \\
 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
\end{array}
\right)
\]
{\bf\red Definition.} The Alexander polynomial, up to a power of $T$, is given by
$\Delta = \det(A)$.
}}}}

\pagestyle{empty}

\begin{document} \latintext
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\begin{center}
\input{Zombian1.pdftex_t}
\vfill
\input{Zombian1.pdftex_t}
\end{center}

\end{document}

\endinput

