\documentclass[12pt,titlepage]{article}

\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{graphicx}
\usepackage{color}
\usepackage{ucs}
\usepackage[utf8x]{inputenc}
\usepackage{xparse}
\usepackage{hyperref}

%----Macros----------
%
% Unresolved issues:
%
%  \righttoleftarrow
%  \lefttorightarrow
%
%  \color{} with HTML colorspec
%  \bgcolor
%  \array with options (without options, it's equivalent to the matrix environment)

% Of the standard HTML named colors, white, black, red, green, blue and yellow
% are predefined in the color package. Here are the rest.
\definecolor{aqua}{rgb}{0, 1.0, 1.0}
\definecolor{fuschia}{rgb}{1.0, 0, 1.0}
\definecolor{gray}{rgb}{0.502, 0.502, 0.502}
\definecolor{lime}{rgb}{0, 1.0, 0}
\definecolor{maroon}{rgb}{0.502, 0, 0}
\definecolor{navy}{rgb}{0, 0, 0.502}
\definecolor{olive}{rgb}{0.502, 0.502, 0}
\definecolor{purple}{rgb}{0.502, 0, 0.502}
\definecolor{silver}{rgb}{0.753, 0.753, 0.753}
\definecolor{teal}{rgb}{0, 0.502, 0.502}

% Because of conflicts, \space and \mathop are converted to
% \itexspace and \operatorname during preprocessing.

% itex: \space{ht}{dp}{wd}
%
% Height and baseline depth measurements are in units of tenths of an ex while
% the width is measured in tenths of an em.
\makeatletter
\newdimen\itex@wd%
\newdimen\itex@dp%
\newdimen\itex@thd%
\def\itexspace#1#2#3{\itex@wd=#3em%
\itex@wd=0.1\itex@wd%
\itex@dp=#2ex%
\itex@dp=0.1\itex@dp%
\itex@thd=#1ex%
\itex@thd=0.1\itex@thd%
\advance\itex@thd\the\itex@dp%
\makebox[\the\itex@wd]{\rule[-\the\itex@dp]{0cm}{\the\itex@thd}}}
\makeatother

% \tensor and \multiscript
\makeatletter
\newif\if@sup
\newtoks\@sups
\def\append@sup#1{\edef\act{\noexpand\@sups={\the\@sups #1}}\act}%
\def\reset@sup{\@supfalse\@sups={}}%
\def\mk@scripts#1#2{\if #2/ \if@sup ^{\the\@sups}\fi \else%
  \ifx #1_ \if@sup ^{\the\@sups}\reset@sup \fi {}_{#2}%
  \else \append@sup#2 \@suptrue \fi%
  \expandafter\mk@scripts\fi}
\def\tensor#1#2{\reset@sup#1\mk@scripts#2_/}
\def\multiscripts#1#2#3{\reset@sup{}\mk@scripts#1_/#2%
  \reset@sup\mk@scripts#3_/}
\makeatother

% \slash
\makeatletter
\newbox\slashbox \setbox\slashbox=\hbox{$/$}
\def\itex@pslash#1{\setbox\@tempboxa=\hbox{$#1$}
  \@tempdima=0.5\wd\slashbox \advance\@tempdima 0.5\wd\@tempboxa
  \copy\slashbox \kern-\@tempdima \box\@tempboxa}
\def\slash{\protect\itex@pslash}
\makeatother

% math-mode versions of \rlap, etc
% from Alexander Perlis, "A complement to \smash, \llap, and lap"
%   http://math.arizona.edu/~aprl/publications/mathclap/
\def\clap#1{\hbox to 0pt{\hss#1\hss}}
\def\mathllap{\mathpalette\mathllapinternal}
\def\mathrlap{\mathpalette\mathrlapinternal}
\def\mathclap{\mathpalette\mathclapinternal}
\def\mathllapinternal#1#2{\llap{$\mathsurround=0pt#1{#2}$}}
\def\mathrlapinternal#1#2{\rlap{$\mathsurround=0pt#1{#2}$}}
\def\mathclapinternal#1#2{\clap{$\mathsurround=0pt#1{#2}$}}

% Renames \sqrt as \oldsqrt and redefine root to result in \sqrt[#1]{#2}
\let\oldroot\root
\def\root#1#2{\oldroot #1 \of{#2}}
\renewcommand{\sqrt}[2][]{\oldroot #1 \of{#2}}

% Manually declare the txfonts symbolsC font
\DeclareSymbolFont{symbolsC}{U}{txsyc}{m}{n}
\SetSymbolFont{symbolsC}{bold}{U}{txsyc}{bx}{n}
\DeclareFontSubstitution{U}{txsyc}{m}{n}

% Manually declare the stmaryrd font
\DeclareSymbolFont{stmry}{U}{stmry}{m}{n}
\SetSymbolFont{stmry}{bold}{U}{stmry}{b}{n}

% Manually declare the MnSymbolE font
\DeclareFontFamily{OMX}{MnSymbolE}{}
\DeclareSymbolFont{mnomx}{OMX}{MnSymbolE}{m}{n}
\SetSymbolFont{mnomx}{bold}{OMX}{MnSymbolE}{b}{n}
\DeclareFontShape{OMX}{MnSymbolE}{m}{n}{
    <-6>  MnSymbolE5
   <6-7>  MnSymbolE6
   <7-8>  MnSymbolE7
   <8-9>  MnSymbolE8
   <9-10> MnSymbolE9
  <10-12> MnSymbolE10
  <12->   MnSymbolE12}{}

% Declare specific arrows from txfonts without loading the full package
\makeatletter
\def\re@DeclareMathSymbol#1#2#3#4{%
    \let#1=\undefined
    \DeclareMathSymbol{#1}{#2}{#3}{#4}}
\re@DeclareMathSymbol{\neArrow}{\mathrel}{symbolsC}{116}
\re@DeclareMathSymbol{\neArr}{\mathrel}{symbolsC}{116}
\re@DeclareMathSymbol{\seArrow}{\mathrel}{symbolsC}{117}
\re@DeclareMathSymbol{\seArr}{\mathrel}{symbolsC}{117}
\re@DeclareMathSymbol{\nwArrow}{\mathrel}{symbolsC}{118}
\re@DeclareMathSymbol{\nwArr}{\mathrel}{symbolsC}{118}
\re@DeclareMathSymbol{\swArrow}{\mathrel}{symbolsC}{119}
\re@DeclareMathSymbol{\swArr}{\mathrel}{symbolsC}{119}
\re@DeclareMathSymbol{\nequiv}{\mathrel}{symbolsC}{46}
\re@DeclareMathSymbol{\Perp}{\mathrel}{symbolsC}{121}
\re@DeclareMathSymbol{\Vbar}{\mathrel}{symbolsC}{121}
\re@DeclareMathSymbol{\sslash}{\mathrel}{stmry}{12}
\re@DeclareMathSymbol{\bigsqcap}{\mathop}{stmry}{"64}
\re@DeclareMathSymbol{\biginterleave}{\mathop}{stmry}{"6}
\re@DeclareMathSymbol{\invamp}{\mathrel}{symbolsC}{77}
\re@DeclareMathSymbol{\parr}{\mathrel}{symbolsC}{77}
\makeatother

% \llangle, \rrangle, \lmoustache and \rmoustache from MnSymbolE
\makeatletter
\def\Decl@Mn@Delim#1#2#3#4{%
  \if\relax\noexpand#1%
    \let#1\undefined
  \fi
  \DeclareMathDelimiter{#1}{#2}{#3}{#4}{#3}{#4}}
\def\Decl@Mn@Open#1#2#3{\Decl@Mn@Delim{#1}{\mathopen}{#2}{#3}}
\def\Decl@Mn@Close#1#2#3{\Decl@Mn@Delim{#1}{\mathclose}{#2}{#3}}
\Decl@Mn@Open{\llangle}{mnomx}{'164}
\Decl@Mn@Close{\rrangle}{mnomx}{'171}
\Decl@Mn@Open{\lmoustache}{mnomx}{'245}
\Decl@Mn@Close{\rmoustache}{mnomx}{'244}
\makeatother

% Widecheck
\makeatletter
\DeclareRobustCommand\widecheck[1]{{\mathpalette\@widecheck{#1}}}
\def\@widecheck#1#2{%
    \setbox\z@\hbox{\m@th$#1#2$}%
    \setbox\tw@\hbox{\m@th$#1%
       \widehat{%
          \vrule\@width\z@\@height\ht\z@
          \vrule\@height\z@\@width\wd\z@}$}%
    \dp\tw@-\ht\z@
    \@tempdima\ht\z@ \advance\@tempdima2\ht\tw@ \divide\@tempdima\thr@@
    \setbox\tw@\hbox{%
       \raise\@tempdima\hbox{\scalebox{1}[-1]{\lower\@tempdima\box
\tw@}}}%
    {\ooalign{\box\tw@ \cr \box\z@}}}
\makeatother

% \mathraisebox{voffset}[height][depth]{something}
\makeatletter
\NewDocumentCommand\mathraisebox{moom}{%
\IfNoValueTF{#2}{\def\@temp##1##2{\raisebox{#1}{$\m@th##1##2$}}}{%
\IfNoValueTF{#3}{\def\@temp##1##2{\raisebox{#1}[#2]{$\m@th##1##2$}}%
}{\def\@temp##1##2{\raisebox{#1}[#2][#3]{$\m@th##1##2$}}}}%
\mathpalette\@temp{#4}}
\makeatletter

% udots (taken from yhmath)
\makeatletter
\def\udots{\mathinner{\mkern2mu\raise\p@\hbox{.}
\mkern2mu\raise4\p@\hbox{.}\mkern1mu
\raise7\p@\vbox{\kern7\p@\hbox{.}}\mkern1mu}}
\makeatother

%% Fix array
\newcommand{\itexarray}[1]{\begin{matrix}#1\end{matrix}}
%% \itexnum is a noop
\newcommand{\itexnum}[1]{#1}

%% Renaming existing commands
\newcommand{\underoverset}[3]{\underset{#1}{\overset{#2}{#3}}}
\newcommand{\widevec}{\overrightarrow}
\newcommand{\darr}{\downarrow}
\newcommand{\nearr}{\nearrow}
\newcommand{\nwarr}{\nwarrow}
\newcommand{\searr}{\searrow}
\newcommand{\swarr}{\swarrow}
\newcommand{\curvearrowbotright}{\curvearrowright}
\newcommand{\uparr}{\uparrow}
\newcommand{\downuparrow}{\updownarrow}
\newcommand{\duparr}{\updownarrow}
\newcommand{\updarr}{\updownarrow}
\newcommand{\gt}{>}
\newcommand{\lt}{<}
\newcommand{\map}{\mapsto}
\newcommand{\embedsin}{\hookrightarrow}
\newcommand{\Alpha}{A}
\newcommand{\Beta}{B}
\newcommand{\Zeta}{Z}
\newcommand{\Eta}{H}
\newcommand{\Iota}{I}
\newcommand{\Kappa}{K}
\newcommand{\Mu}{M}
\newcommand{\Nu}{N}
\newcommand{\Rho}{P}
\newcommand{\Tau}{T}
\newcommand{\Upsi}{\Upsilon}
\newcommand{\omicron}{o}
\newcommand{\lang}{\langle}
\newcommand{\rang}{\rangle}
\newcommand{\Union}{\bigcup}
\newcommand{\Intersection}{\bigcap}
\newcommand{\Oplus}{\bigoplus}
\newcommand{\Otimes}{\bigotimes}
\newcommand{\Wedge}{\bigwedge}
\newcommand{\Vee}{\bigvee}
\newcommand{\coproduct}{\coprod}
\newcommand{\product}{\prod}
\newcommand{\closure}{\overline}
\newcommand{\integral}{\int}
\newcommand{\doubleintegral}{\iint}
\newcommand{\tripleintegral}{\iiint}
\newcommand{\quadrupleintegral}{\iiiint}
\newcommand{\conint}{\oint}
\newcommand{\contourintegral}{\oint}
\newcommand{\infinity}{\infty}
\newcommand{\bottom}{\bot}
\newcommand{\minusb}{\boxminus}
\newcommand{\plusb}{\boxplus}
\newcommand{\timesb}{\boxtimes}
\newcommand{\intersection}{\cap}
\newcommand{\union}{\cup}
\newcommand{\Del}{\nabla}
\newcommand{\odash}{\circleddash}
\newcommand{\negspace}{\!}
\newcommand{\widebar}{\overline}
\newcommand{\textsize}{\normalsize}
\renewcommand{\scriptsize}{\scriptstyle}
\newcommand{\scriptscriptsize}{\scriptscriptstyle}
\newcommand{\mathfr}{\mathfrak}
\newcommand{\statusline}[2]{#2}
\newcommand{\tooltip}[2]{#2}
\newcommand{\toggle}[2]{#2}

% Theorem Environments
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{prop}{Proposition}
\newtheorem{cor}{Corollary}
\newtheorem*{utheorem}{Theorem}
\newtheorem*{ulemma}{Lemma}
\newtheorem*{uprop}{Proposition}
\newtheorem*{ucor}{Corollary}
\theoremstyle{definition}
\newtheorem{defn}{Definition}
\newtheorem{example}{Example}
\newtheorem*{udefn}{Definition}
\newtheorem*{uexample}{Example}
\theoremstyle{remark}
\newtheorem{remark}{Remark}
\newtheorem{note}{Note}
\newtheorem*{uremark}{Remark}
\newtheorem*{unote}{Note}

%-------------------------------------------------------------------

\begin{document}

%-------------------------------------------------------------------


\section*{Jacob Lurie}

Jacob Lurie is a mathematician at the Institute for Advanced Study.

\begin{itemize}%
\item \href{http://www.math.harvard.edu/~lurie/}{website}


\item \href{http://en.wikipedia.org/wiki/Jacob_Lurie}{Wikipedia entry}


\item \href{https://www.ias.edu/scholars/lurie}{Institute for Advanced Study entry}



\end{itemize}
After an early interest in [[formal logic]] (specifically notions of [[computability|computable]] [[surreal numbers]], see \href{http://www.ams.org/notices/199607/comm-conway.pdf}{Notices of the AMS vol 43, Number 7}) Lurie indicated in \href{http://dspace.mit.edu/handle/1721.1/30144}{his PhD thesis} how the [[moduli stack of elliptic curves]] together with the collection of [[elliptic cohomology]] [[spectra]] associated to each [[elliptic curve]] is naturally understood as a geometric object in a [[homotopy theory|homotopy theoretic]] refinement of [[algebraic geometry]] that has come to be known as [[derived algebraic geometry]]. He then embarked on a monumental work laying out detailed foundations of the subjects necessary for this statement, which is [[homotopy theory]] in its modern incarnation as [[higher category theory]], [[higher geometry]] in terms of [[higher topos theory]] and finally [[higher algebra]] in terms of [[(infinity,1)-operad|higher operads]], all in principle very much along the lines originally developed by [[Alexander Grothendieck]] and his school for ordinary [[algebraic geometry]], but now considerably further refined to the general context of [[homotopy theory]]. While some developments in these topics had been available before, Lurie's comprehensive work has arguably led these subjects to an era of reinvigorated activity with a variety of further spin-offs. Among these most notable is maybe the formalization and proof of the [[cobordism hypothesis]], which lays [[monoidal (infinity,n)-category|higher monoidal category theoretic]] foundations for ([[extended topological quantum field theory|local, topological]]) [[quantum field theory]]. In 2014 Lurie was awarded a \href{http://www.macfound.org/fellows/921/}{MacArthur Genius Grant} and the Breakthrough Prize in Mathematics.

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{references_partly_indexed_on_the_lab}{References (partly) indexed on the $n$Lab}\dotfill \pageref*{references_partly_indexed_on_the_lab} \linebreak
\noindent\hyperlink{higher_category_theory}{Higher category theory}\dotfill \pageref*{higher_category_theory} \linebreak
\noindent\hyperlink{higher_topos_theory}{Higher topos theory}\dotfill \pageref*{higher_topos_theory} \linebreak
\noindent\hyperlink{higher_algebra}{Higher algebra}\dotfill \pageref*{higher_algebra} \linebreak
\noindent\hyperlink{higher_geometry}{Higher geometry}\dotfill \pageref*{higher_geometry} \linebreak
\noindent\hyperlink{elliptic_cohomology}{Elliptic cohomology}\dotfill \pageref*{elliptic_cohomology} \linebreak
\noindent\hyperlink{publications_before_thesis}{Publications before thesis}\dotfill \pageref*{publications_before_thesis} \linebreak
\noindent\hyperlink{other_material}{Other material}\dotfill \pageref*{other_material} \linebreak


\hypertarget{references_partly_indexed_on_the_lab}{}\subsection*{{References (partly) indexed on the $n$Lab}}\label{references_partly_indexed_on_the_lab}

\hypertarget{higher_category_theory}{}\subsubsection*{{Higher category theory}}\label{higher_category_theory}

\begin{itemize}%
\item \emph{[[(∞,2)-Categories and the Goodwillie Calculus]]} (\href{http://www.math.harvard.edu/~lurie/papers/GoodwillieI.pdf}{pdf}, \href{http://arxiv.org/abs/0905.0462}{arXiv})

on [[(∞,1)-category|(∞,1)-categories]] of [[(∞,n)-category|(∞,n)-categories]], specifically on [[internal (∞,1)-categories]], and on [[Goodwillie calculus]]



\end{itemize}
on [[higher category theory]], [[internal (∞,1)-categories]]

\begin{itemize}%
\item [[On the Classification of Topological Field Theories]] (\href{http://arxiv.org/abs/0905.0465}{arXiv})

on [[FQFT|functorial]] [[extended topological quantum field theory|extended]] [[TQFT|topological]] [[quantum field theory]] classified via the [[cobordism theorem]] by [[symmetric monoidal (∞,n)-categories]]



\end{itemize}
\hypertarget{higher_topos_theory}{}\subsubsection*{{Higher topos theory}}\label{higher_topos_theory}

\begin{itemize}%
\item \emph{[[Higher Topos Theory]]} (\href{http://arxiv.org/abs/math.CT/0608040}{arXiv}, \href{http://www.math.harvard.edu/~lurie/papers/highertopoi.pdf}{published version})

on [[(∞,1)-category theory]] and [[higher topos theory]]



\end{itemize}
\hypertarget{higher_algebra}{}\subsubsection*{{Higher algebra}}\label{higher_algebra}

\begin{itemize}%
\item \emph{[[Higher Algebra]]}

on [[higher algebra]]



\end{itemize}
subsuming

\begin{itemize}%
\item [[Stable ∞-Categories]] (\href{http://arxiv.org/abs/math/0608228}{arXiv})

on [[stable (∞,1)-categories]] [[stable homotopy theory]] and [[homological algebra]]


\item [[higher algebra|Noncommutative Algebra]] (\href{http://arxiv.org/abs/math/0702299}{arXiv})

and

[[higher algebra|Commutative Algebra]] (\href{http://arxiv.org/abs/math/0703204}{arXiv}, \href{http://www.math.harvard.edu/~lurie/papers/DAG-III.pdf}{pdf})


\item \emph{$\mathbb{E}[k]$-[[Ek-Algebras|Algebras]]} (\href{http://www.math.harvard.edu/~lurie/papers/DAG-VI.pdf}{pdf})

on [[little cubes operad]]


\item [[Deformation Theory]] (\href{http://arxiv.org/abs/0709.3091}{arXiv})

on the notions of [[Kähler differential]] and [[cotangent complex]] and their generalization from the ordinary context of [[algebra]] to that of [[higher algebra]].


\item \emph{[[Moduli Problems and DG-Lie Algebras]]}

on [[∞-Lie algebra]]s as formal neighbourhoods of point in [[∞-stack]]s.



\end{itemize}
\hypertarget{higher_geometry}{}\subsubsection*{{Higher geometry}}\label{higher_geometry}

The foundations of [[higher geometry]]:

\begin{itemize}%
\item [[Structured Spaces]] (\href{http://arxiv.org/abs/0905.0459}{arXiv})

\begin{itemize}%
\item on [[structured (∞,1)-topos]]es and [[generalized schemes]]

\end{itemize}


\end{itemize}
Survey on the general program

\begin{itemize}%
\item PhD thesis, [[Derived Algebraic Geometry]]

on [[derived algebraic geometry]]



\end{itemize}
A volume on [[E-∞ geometry]] ([[spectral algebraic geometry]])

\begin{itemize}%
\item [[Jacob Lurie]], \emph{[[Spectral Algebraic Geometry]]}

\end{itemize}
The basic definitions are in

\begin{itemize}%
\item [[Jacob Lurie]], \emph{[[Spectral Schemes]]}

\end{itemize}
Fundamental properties of $E_\infty$-geometry are discussed in

\begin{itemize}%
\item [[Jacob Lurie]], \emph{[[Quasi-Coherent Sheaves and Tannaka Duality Theorems]]}


\item [[Jacob Lurie]], \emph{[[Closed Immersions]]}


\item [[Jacob Lurie]], \emph{[[Descent Theorems]]}


\item [[Jacob Lurie]], \emph{[[Proper Morphisms, Completions, and the Grothendieck Existence Theorem]]}


\item [[Jacob Lurie]], \emph{[[Representability Theorems]]}


\item [[Jacob Lurie]], \emph{[[Rational and p-adic Homotopy Theory]]}



\end{itemize}
Application to [[moduli stack of elliptic curves]]:

\begin{itemize}%
\item [[A Survey of Elliptic Cohomology]] (\href{http://www.math.harvard.edu/~lurie/papers/survey.pdf}{pdf})

on the [[generalized (Eilenberg-Steenrod) cohomology]] theory [[tmf]], the gluing of all [[elliptic cohomology]] theories



\end{itemize}
\hypertarget{elliptic_cohomology}{}\subsubsection*{{Elliptic cohomology}}\label{elliptic_cohomology}

\begin{itemize}%
\item \emph{Elliptic cohomology I: Spectral abelian varieties} (\href{http://www.math.harvard.edu/~lurie/papers/Elliptic-I.pdf}{pdf})


\item \emph{Elliptic cohomology II: Orientations} (\href{http://www.math.harvard.edu/~lurie/papers/Elliptic-II.pdf}{pdf})


\item \emph{Elliptic cohomology III: Tempered Cohomology} (\href{http://www.math.harvard.edu/~lurie/papers/Elliptic-III-Tempered.pdf}{pdf})


\item \emph{Elliptic cohomology IV: Equivariant elliptic cohomology}, (announced)



\end{itemize}
\hypertarget{publications_before_thesis}{}\subsubsection*{{Publications before thesis}}\label{publications_before_thesis}

\begin{itemize}%
\item M H Freedman, A Kitaev, J Lurie, \emph{Diameters of homogeneous spaces}, Math. res. lett. 10:1, 11-20 (2003)


\item J. Lurie, \emph{Anti-admissible sets}, J Symb Logic 64:2, 408-435 (1999)


\item J. Lurie, \emph{On a conjecture of Conway}, Illinois J. Math. 46:2, 497-506 (2002)


\item J. Lurie, \emph{On simply laced Lie algebras and their minuscule representations}, Comment. Math. Helv. 76:3, 515-575 (2001) \href{http://dx.doi.org/10.1007/PL00013217}{doi}



\end{itemize}
\hypertarget{other_material}{}\subsection*{{Other material}}\label{other_material}

\begin{itemize}%
\item \href{http://www.math.harvard.edu/~lurie/FF.html}{Informal notes} on the [[Fargues-Fontaine curve]] with [[Dennis Gaitsgory]].


\item [[Kerodon]] is an online textbook on [[Categorical Homotopy Theory|categorical homotopy theory]] and related mathematics.



\end{itemize}
category: people

[[!redirects J. Lurie]]



\end{document}