
%%%%%%%%% MASTER -- compiles the 4 sections

\documentclass[12pt,letterpaper]{amsart}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pagestyle{plain}                                                      %%
%%%%%%%%%% EXACT 1in MARGINS %%%%%%%                                   %%
\setlength{\textwidth}{6.5in}     %%                                   %%
\setlength{\oddsidemargin}{0in}   %% (It is recommended that you       %%
\setlength{\evensidemargin}{0in}  %%  not change these parameters,     %%
\setlength{\textheight}{8.5in}    %%  at the risk of having your       %%
\setlength{\topmargin}{0in}       %%  proposal dismissed on the basis  %%
\setlength{\headheight}{0in}      %%  of incorrect formatting!!!)      %%
\setlength{\headsep}{0in}         %%                                   %%
\setlength{\footskip}{.5in}       %%                                   %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                                   %%
\newcommand{\required}[1]{\section*{#1}}                               %%
\renewcommand{\refname}{References Cited}                              %%
\bibliographystyle{plain}                                              %%
\renewcommand{\bibliofont}{\normalsize}                                %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%PUT YOUR MACROS HERE

\renewcommand{\thefootnote}{\fnsymbol{footnote}}


\usepackage{epsfig}
\usepackage{amscd}
\usepackage{amsmath, amssymb, amsthm}
%\renewcommand{\textfraction}{.1}
%\renewcommand{\arraystretch}{2}
%\setlength{\arrayrulewidth}{10mm}
%\documentclass{report}
%\usepackage{epsfig}
%\usepackage{amscd}
%\usepackage{amsmath, amssymb, amsthm}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{question}[theorem]{Question}
%\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
%\newtheorem{exercise}{Exercise}
\newtheorem{example}[theorem]{Example}
%\numberwithin{equation}{section}


%\def\blfootnote{\xdef\@thefnmark{}\@footnotetext}
\def\ZZ{{\mathbb Z}}
\def\reals{{\mathbb R}}
\def\cx{{\mathbb C}}
\def\LL{{\mathcal L}}
\def\JJ{{\mathcal J}}
\def\Ci{{\mathcal C}^\infty}
\def\Re{\,\mathrm{Re}\,}
\def\Im{\,\mathrm{Im}\,}
\def\tom{\widetilde{\omega}}
\def\diam{\mathrm{diam}\,}
\def\sgn{\mathrm{sgn}\,}
\def\tr{\mathrm{tr}\,}
\def\WF{\mathrm{WF}_h\,}
\def\div{\mathrm{div}\,}
\def\supp{\mathrm{supp}\,}
\def\Arg{\mathrm{Arg}\,}
\def\id{\,\mathrm{id}\,}
\def\Ph{\widehat{\varphi}}
\def\Phd{\widehat{\varphi}_{\gamma,d}}
\def\P{\varphi}
\def\Pd{\varphi_{\gamma,d}}
\def\O{{\mathcal O}}
\def\SS{{\mathbb S}}
\def\s{{\mathcal S}}
\def\OPS{{\mathrm OP} {\mathcal S}}
\def\cchar{\mathrm{char}\,}
\def\nbhd{\mathrm{neigh}\,}
\def\neigh{\mathrm{neigh}\,}
\def\Op{\mathrm{Op}\,}
\def\Opb{\mathrm{Op}_{h,b}^w}
\def\Psib{\Psi_{h,b}}
\def\esssupp{\text{ess-supp}\,}
\def\ad{\mathrm{ad}\,}
\def\neg{\mathcal{N}}
\def\hsc{{\left( \tilde{h}/h \right)}}
\def\hscnp{\frac{\tilde{h}}{h}}
\def\csh{{\left( h/\tilde{h} \right)}}
\def\phi{\varphi}
\def\half{{\frac{1}{2}}}
\def\dist{\text{dist}\,}
\def\diag{\text{diag}\,}
\def\Spec{\text{Spec}\,}
\def\l{{L^2(X)}}
\def\be{\begin{eqnarray*}}
\def\ee{\end{eqnarray*}}
\def\ben{\begin{eqnarray}}
\def\een{\end{eqnarray}}
\def\ker{\text{ker}}
\def\km{\text{ker}_{m_0(z)}(P-z)}
\def\kmm{\text{ker}_{m_1(z)}(P-z)}
\def\MM{\mathcal{M}}
\def\lll{\left\langle}
\def\rrr{\right\rangle}
\def\rqf{\right\rangle_{QF}}
\def\PP{\mathcal{P}}
\def\DD{\mathcal{D}}
\def\EE{\mathcal{E}}
\def\L2R{L_{\text{Rest}}^2}
\def\contraction{\lrcorner}
\def\11{\mathds{1}}
\def\Vol{\text{Vol}\,}
\def\AA{\mathcal{A}}

\def\thesubsection{\arabic{subsection}}

%\includeonly{NSFsumm}

\begin{document}

\include{NSFsumm}
\setcounter{page}{1}
\include{NSFdesc}
\setcounter{page}{1}
\include{NSFrefs}
\setcounter{page}{1}
\include{NSFbio}

\end{document}
