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\section*{Joseph Bernstein}

\textbf{Joseph Bernstein} is an Israeli mathematician, born and educated in Russia (his Russian name iss   , transliterated as Josif/Iosif Naumovi Bern\v{s}tejn); his teacher there was [[Israel Gel'fand]]. His numerous works (especically with [[Alexander Beilinson]]) brought to proliferation of sheaf-theoretic and algebro-geometric methods in representation theory (D-modules, perverse sheaves, Beilinson-Bernstein localization theory), and are now cornerstones of [[geometric representation theory]]. With [[V. Lunts]] he introduced the appropriate definition of [[equivariant derived category]] (in general not equivalent to the (naive) derived category of equivariant sheaves).

\begin{itemize}%
\item \href{http://en.wikipedia.org/wiki/Joseph_Bernstein}{wikipedia}


\item homepage at TelAviv: \href{http://www.math.tau.ac.il/~bernstei}{web}, publication \href{http://www.math.tau.ac.il/~bernstei/Publication_list/Publication_list.html}{list}


\item webpage at MathNet.ru: \href{http://www.mathnet.ru/php/person.phtml?option_lang=rus&personid=18576}{Russian}\emph{, \href{http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=18576}{English}; list of publications at mathnet.ru: \href{http://www.mathnet.ru/PersLogos/18576/Publication_list.pdf}{pdf}}



\end{itemize}
\hypertarget{selected_writings}{}\subsection*{{Selected writings}}\label{selected_writings}

\begin{itemize}%
\item I. N. Bern\v{s}ten, I. M. Gelfand, V. A. Ponomarev, Coxeter functors, and Gabriel's theorem. (Russian) Uspehi Mat. Nauk \textbf{28} (1973), no. 2(170), 19--33.


\item J. N. Bernstein, I. M. Gel'fand, S. I. Gel'fand, \emph{   $P^n$    }, .    ., 12:3 (1978), 66--67, \href{http://www.mathnet.ru/php/getFT.phtml?jrnid=faa&paperid=2008&volume=12&year=1978&issue=3&fpage=66&what=fullt&option_lang=eng}{pdf} (Russian); Engl. transl. \emph{Algebraic bundles over $P^n$ and problems of linear algebra}, Funct. Anal. and its Appl. 1978, 12:3, 212--214


\item A. Beilinson, J. Bernstein, \emph{Localisations de $\mathfrak{g}$--modules}, C. R. Acad. Sci. Paris \textbf{292} (1981), 15--18.


\item [[A. A. Beilinson]], J. Bernstein, P. Deligne, \emph{Faisceaux pervers}, Ast\'e{}risque \textbf{100} (1983).


\item J. Bernstein, [[V. Lunts]], \emph{On nonholonomic irreducible D-modules}, Invent. Math. \textbf{94)), (1988), no. 2, 223--243.}


\item J. Bernstein, [[V. Lunts]], \emph{Equivariant sheaves and functors, Springer Lecture Notes in Math. \textbf{1578} (1994). \href{http://www.ams.org/mathscinet-getitem?mr=95k:55012}{MR95k:55012}}


\item [[A. Beĭlinson]], J. Bernstein, \emph{A proof of Jantzen conjectures}, I. M. Gelfand Seminar, 1--50, Adv. Soviet Math. \textbf{16}, Part 1, Amer. Math. Soc. 1993, \href{http://www.math.harvard.edu/~gaitsgde/grad_2009/BB%20-%20Jantzen.pdf}{pdf}


\item Joseph Bernstein's notes on [[D-module]]s: \href{http://www.math.uchicago.edu/~arinkin/langlands/Bernstein/Bernstein-dmod.pdf}{pdf}



\end{itemize}
On the [[Langlands program]]:

\begin{itemize}%
\item [[Joseph Bernstein]], [[Stephen Gelbart]] (eds.), \emph{An Introduction to the Langlands Program}, Springer 2018 (\href{https://link.springer.com/book/10.1007/978-0-8176-8226-2}{doi:10.1007/978-0-8176-8226-2})

\end{itemize}
[[!redirects J. Bernstein]] [[!redirects I. N. Bernšteĭn]]



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