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\begin{document}

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\section*{Edward Witten}

Edward Witten is a theoretical physicist at the Institute for Advanced Study.

\begin{itemize}%
\item \href{http://www.sns.ias.edu/~witten/}{website}


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


\item interview by [[Hirosi Ooguri]], Notices Amer. Math. Soc, May 2015 p491 (\href{http://www.ams.org/notices/201505/rnoti-p491.pdf}{pdf})


\item \emph{Adventures in Physics and Math}, \href{http://www.kyotoprize.org/en/laureates/commemorative_lectures/}{Kyoto Prize lecture} 2014 (\href{http://www.kyotoprize.org/wp/wp-content/uploads/2016/02/30kB_lct_EN.pdf}{pdf}, [[WittenKyotoPrizeLecture.pdf:file]])



\end{itemize}
Witten's work originates in theoretical [[quantum field theory]] and stands out as making numerous and deep connections between that and mathematical [[geometry]] and [[cohomology]]. In the course of the 1980s Witten became the central and leading figure in [[string theory]].

Insight gained from the study of quantum field theories and specifically those relevant in [[string theory]] led Witten to mathematical results deep enough to gain him a [[Fields medal]], see \hyperlink{FieldMedalWork}{below}. Indeed, a whole list of sub-fields in mathematics originate in aspects of Witten's work in QFT/string theory and carry his name, such as [[Chern-Simons theory]] which many people call ``Chern-Simons-Witten theory'', [[Wess-Zumino-Witten theory]], the [[Witten genus]], [[Gromov-Witten theory]], [[Seiberg-Witten theory]], [[Rozansky-Witten invariant]], the [[Witten conjecture]]. Other parts are still waiting to be absorbed into the mathematical literature such as [[Horava-Witten theory]], [[Diaconescu-Moore-Witten anomaly]] etc..

Despite the deeply theoretical and abstract mathematical aspects of his work, Witten has visibly always been motivated by fundamental questions in the [[phenomenology]] of the [[standard model of particle physics]] [[standard model of cosmology|and cosmology]]. (Indeed, some of his work on [[scattering amplitudes]] crucially enters into the [[experiment|experimental]] detection of the [[Higgs particle]], for more on this see at \emph{[[string theory results applied elsewhere]]}. ) He prominently argued that specifically [[heterotic string theory]] is a plausible candidate for a fundamental [[GUT|grand unified gauge field theory]] including [[quantum gravity]].

Since about the turn of the millennium Witten has tended to more esoteric mathematical aspects of string theory, such as its relation to [[Khovanov homology]] and [[geometric Langlands duality]] which apparently the string theory community at large is following less enthusiastically than it was the case during the excited 1990s.

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

\noindent\hyperlink{quotes}{Quotes}\dotfill \pageref*{quotes} \linebreak
\noindent\hyperlink{FieldMedalWork}{Fields medal work}\dotfill \pageref*{FieldMedalWork} \linebreak
\noindent\hyperlink{related_lab_entries}{Related $n$Lab entries}\dotfill \pageref*{related_lab_entries} \linebreak


\hypertarget{quotes}{}\subsection*{{Quotes}}\label{quotes}

In \href{http://www.pbs.org/wgbh/nova/elegant/view-witten.html}{Nova interview 2003}, also \href{http://www.sns.ias.edu/~witten/papers/string.pdf}{American Scientist Astronomy Issue 2002}:

\begin{quote}%
 Back in the early '70s, the Italian physicist, [[Daniele Amati]] reportedly said that string theory was part of 21st-century physics that fell by chance into the 20th century. I think it was a very wise remark.


\end{quote}
$\backslash$linebreak

[[Edward Witten]] in interview with Graham Farmelo, \href{https://grahamfarmelo.com/the-universe-speaks-in-numbers-interview-5}{``The Universe Speaks in Numbers'', interview 5}, 2019 (quote from 21:15 - 21:46):

\begin{quote}%
 I actually believe that string/M-theory is on the right track toward a deeper explanation. But at a very fundamental level it’s not well understood. And I’m not even confident that we have a good concept of what sort of thing is missing or where to find it. The reason I am not is that in hindsight it is clear the view given in the 1980s of what is missing was too narrow. Instead of discovering what we thought was missing, we broadened the picture in the 90s, in unexpected directions.


\end{quote}
$\backslash$linebreak

\hypertarget{FieldMedalWork}{}\subsection*{{Fields medal work}}\label{FieldMedalWork}

In

\begin{itemize}%
\item [[Michael Atiyah]], \emph{On the work of Edward Witten}, Proceedings of the International Congress of Mathematics, Kyoto 1990 (\href{http://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0031.0036.ocr.pdf}{pdf})

\end{itemize}
the following ``influential papers'' are listed as relevant for Edward Witten receiving the \href{http://159.226.47.99:8080/general/prize/medal/1990.htm}{Fields Medal in 1990}.

First of all

\begin{itemize}%
\item \emph{Supersymmetry and Morse theory}, J. Differential Geom. Volume 17, Number 4 (1982), 661-692. (\href{http://projecteuclid.org/euclid.jdg/1214437492}{Euclid})

This discusses deformations of [[supersymmetric quantum mechanics]] on a [[Riemannian manifold]] and how its supersymmetric ground states are related to the [[Morse theory]] of a deformation function. The way this supersymmetric quantum mechanics appears as the point-[[particle]] limit of the [[type II superstring]] is explained at the end of


\item \emph{Global anomalies in string theory}, in W. Bardeen and A. White (eds.) \emph{Symposium on Anomalies, Geometry}, Topology, pp. 61--99. World Scientific, 1985



\end{itemize}
which otherwise is on [[quantum anomalies]] in string theory, such as the [[Green-Schwarz anomaly]], etc.

Finally Atiyah's section 2 mentions

\begin{itemize}%
\item (with [[Cumrun Vafa]]), \emph{Eigenvalue inequalities for Fermions in gauge theories}, Comm. Math. Phys. 95 (1984) 257 (\href{http://projecteuclid.org/euclid.cmp/1103941573}{Euclid})

\end{itemize}
Then

\begin{itemize}%
\item \emph{Elliptic genera and quantum field theory}, Comm. Math. Phys. 109 (1987)

on the [[elliptic genus]]/[[Witten genus]] as the [[partition function]] of the [[type II superstring]]/[[heterotic superstring]]



\end{itemize}
And various articles on the foundations of [[topological field theory]] such as

\begin{itemize}%
\item \emph{Topological quantum field theory}, Comm. Math. Phys. Volume 117, Number 3 (1988), 353-386 (\href{http://projecteuclid.org/euclid.cmp/1104161738}{Euclid})

on [[topologically twisted D=4 super Yang-Mills theory]] and the corresponding twists of the [[superstring]] which yield the [[A-model]] and [[B-model]] [[topological string]] 2d [[TQFTs]];


\item \emph{On the structure of the topological phase of two dimensional gravity} Nuclear Phys, B 340 (1990) 281 (\href{http://ccdb5fs.kek.jp/cgi-bin/img_index?200033155}{scans})

on the [[topological string]] limit of the [[worldsheet]] [[2d quantum gravity]] theory of the string, including the [[A-model]] and [[B-model]] [[topological twists]] of the [[type II superstring]];



\end{itemize}
and

\begin{itemize}%
\item \emph{Quantum field theory and the Jones polynomial}, Comm, Math, Phys, 121 (1989) 351

on the [[quantization]] of 3d [[Chern-Simons theory]], its [[Jones polynomial]] [[knot invariant]] [[quantum observables]] and its [[holographic principle|holographic]] relation to the quantization of the [[WZW model]] (the [[string]] propagating on a suitable [[Lie group]] [[manifold]]).



\end{itemize}
\hypertarget{related_lab_entries}{}\subsection*{{Related $n$Lab entries}}\label{related_lab_entries}

\begin{itemize}%
\item [[string theory]], [[M-theory]]


\item [[M-theory on G2-manifolds]]


\item [[Gromov-Witten invariants]], [[Rozansky-Witten invariant]]


\item [[Seiberg-Witten theory]]


\item [[supersymmetric quantum mechanics]]


\item [[fuzzy dark matter]]



\end{itemize}
(\ldots{})

\begin{quote}%
clearly, this list deserves be further expanded\ldots{}


\end{quote}
category: people

[[!redirects E. Witten]] [[!redirects Witten]]



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