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\section*{Nikolai Durov}

\textbf{Nikolai Durov} (  ) is a Russian mathematician from St. Petersburg with main current interests in [[arithmetic geometry]], currently employed at St. Petersburg Department of the Steklov Institute of Mathematics.

\begin{itemize}%
\item \href{http://www.pdmi.ras.ru/eng/perso/durov.php}{homepage} at Steklov
\item \href{http://www.mathnet.ru/php/person.phtml?&personid=34084&option_lang=eng}{mathnet.ru} entry
\item wikipedia: \href{http://en.wikipedia.org/wiki/Nikolai_Durov}{Nikolai Durov}

\end{itemize}
Durov obtained his Ph.D. in 2007 in Bonn under \href{http://en.wikipedia.org/wiki/Gerd_Faltings}{Gerd Faltings}:

\begin{itemize}%
\item \emph{New approach to Arakelov geometry}, \href{http://arxiv.org/abs/0704.2030}{arxiv/0704.2030}

\end{itemize}
Durov's mathematical work preceding his study in Bonn includes his work on classical [[Galois theory]] of polynomial equations; it provides essentially the third historically available method to compute algorithmically a Galois group of a given equation. His method is however statistical and some random data are included in input. The algorithm terminates with probability $1$ for all equations iff the [[Riemann hypothesis]] is true. The exposition of these results is in

\begin{itemize}%
\item N. V. Durov, \emph{Computation of the Galois group of a polynomial with rational coefficients. I.} (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 319 (2004), Vopr.Teor. Predst. Algebr. i Grupp. 11, 117--198, 301; English translation in J. Math. Sci. (N. Y.) 134 (2006), no. 6, 2511--2548 (MR2006b:12006)
\item N. V. Durov, \emph{Computation of the Galois group of a polynomial with rational coefficients. II.} (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 321 (2005), Vopr. Teor. Predst. Algebr. i Grupp. 12, 90--135, 298; English translation in J. Math. Sci. (N. Y.) 136 (2006), no. 3, 3880--3907 (MR2006e:12004)

\end{itemize}
Nikolai Durov is also an experienced computer programmer. He was a member of a St Petersburg State University student team winning a student \href{http://www.cs.northwestern.edu/~agupta/_projects/acm_ibm/acm2001.htm}{world tournament} in programming. His high school education was in Italy. His younger brother \href{http://durov.vkontakte.ru}{Pavel V. Durov} is a professional programmer and main constructor behind \href{http://Vkontakte.ru}{one of the most popular internet sites} in Russia. The company is not any more in their control. Nikolai and Pavel together established communication platform and company \href{https://telegram.org}{Telegram} (see \href{https://telegram.org/faq}{FAQ} and \href{https://en.wikipedia.org/wiki/Telegram_(messaging_service}{wikipedia}) where they work on Nikolai's envisioned [[zoranskoda:Telegram Open Network]] (TON) which he classifies as a 5th generation [[blockchain]] project enhanced with additional DNS, proxy and (torrent-like) storage infrastructure.

\begin{itemize}%
\item TON whitepaper, 23 page \href{https://cdn.crowdfundinsider.com/wp-content/uploads/2018/03/TON-White-Paper-Telegram-ICO.pdf}{pdf}, mirrors \href{https://drive.google.com/file/d/1ucUeKg_NiR8RxNAonb8Q55jZha03WC0O/view}{pdf} \href{https://icorating.com/upload/whitepaper/gNQ7e9z3lCGi519Wz8mmC0Kg8aA0goeZKAQ802vo.pdf}{pdf}
\item Nikolai Durov, \emph{Telegram Open Network}, technical overview, Dec 2017, 132 pp. \href{https://toncoin.tech/TON-official-whitepaper.pdf}{pdf}, mirror \href{https://www.kriptovaluta.hr/wp-content/uploads/2018/03/TON-Technology.pdf}{pdf}; \emph{Telegram Open Network Blockchain}, Sep 2018, 121 pp. \href{https://www.docdroid.net/qY4sQEv/telegram-open-network-blockchain-september-5-2018.pdf}{pdf}; \emph{Telegram Open Network Virtual Machine}, Sep. 2018, 148 pp. \href{https://www.docdroid.net/R3vEKBY/telegram-open-network-virtual-machine-september-5-2018.pdf}{pdf}; \emph{Fift: a brief introduction} (about his new Forth-like stack based programming language on TON), May 23, 2019, 87 pp. pdf is at channel \href{https://t.me/Tgram/170}{t.me/Tgram/170}

\end{itemize}
The technical overview sporadically uses the notation from [[type theory]].

Durov's earlier publications also include

\begin{itemize}%
\item N. Durov, S. Meljanac, A. Samsarov, [[Z. Škoda]], \emph{A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra}, Journal of Algebra 309, n. 1, 318--359 (2007) (\href{http://dx.doi.org/10.1016/j.jalgebra.2006.08.025}{doi:jalgebra}) (\href{http://front.math.ucdavis.edu/math.RT/0604096}{math.RT/0604096}).

\end{itemize}
where in chapters 7--9 Durov presented a flexible theory of a class of functors which can be viewed as representing generalizations of \href{http://en.wikipedia.org/wiki/Formal_scheme}{formal schemes} but over an arbitrary ring, and with weaker assumptions. This theory is then applied to a problem in Lie theory and deformation theory; an interesting chapter on symplectic Weyl algebras is included. In chapter 10 an alternative method using [[Hopf algebras]] rather than geometry is presented.

Recently he introduced the notion of a [[vectoid]] and the related notion of an [[algebrad]] which is a generalization of the notions of a symmetric and a non-symmetric operad:

\begin{itemize}%
\item Nikolai Durov, \emph{Classifying vectoids and generalisations of operads}, \href{http://arxiv.org/abs/1105.3114}{arxiv/1105.3114}, the translation of ``    '', Trudy MIAN, vol. 273
\item \emph{Classifying vectoids and generalizations of operads}, talk at The International Conference ``Contemporary Mathematics'' June 12, 2009, video: \href{http://www.mathnet.ru/php/presentation.phtml?option_lang=eng&presentid=345}{link}

\end{itemize}
Other sources:

\begin{itemize}%
\item \emph{Computation of derived absolute tensor square of the ring of integers}, talk at 2nd annual conference-meeting MIAN--POMI ``Algebra and Algebraic Geometry'', St. Petersburg, December 25, 2008, \href{http://www.mathnet.ru/php/presentation.phtml?option_lang=eng&presentid=267}{link}
\item \emph{Arithmetic intersection theory and homotopical algebra}, seminar 2007
\item N. V. Durov, \emph{    (Topological realizations of algebraic varieties)}, preprint POMI 13/2012 (in Russian) \href{http://www.pdmi.ras.ru/preprint/2012/12-13.html}{abstract}, \href{ftp://ftp.pdmi.ras.ru/pub/publicat/preprint/2012/13-12_rus.pdf.gz}{pdf.gz}
\item N. V. Durov, \emph{  ${\mathbb{F}}_p$-      }, (Multiplicative monoids of ${\mathbb{F}}_p$-algebras and absolute tensor products of finite fields), preprint POMI 12/2012 (in Russian) \href{http://www.pdmi.ras.ru/preprint/2012/12-12.html}{abstract} \href{ftp://ftp.pdmi.ras.ru/pub/publicat/preprint/2012/12-12_rus.pdf.gz}{pdf.gz}
\item N. V. Durov, \emph{Homotopy theory of normed sets I. Basic constructions}, Algebra i Analiz, 29:6 (2017), 35–98 \href{http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=aa&paperid=1562&option_lang=eng}{mathnet.ru}; \emph{Homotopy theory of normed sets II. Model categories}, Algebra i Analiz, 30:1 (2018) 32–95 \href{http://mi.mathnet.ru/eng/aa1571}{mathnet.ru}

\end{itemize}
His paper on normed sets above (part 1 out of 3) is partly extending ideas from

\begin{itemize}%
\item [[Frederic Paugam]], \emph{Overconvergent global analytic geometry}, 2015, \href{https://arxiv.org/abs/1410.7971}{arXiv:1410.7971v2}

\end{itemize}
[[!redirects Nikolai Durov]] [[!redirects Николай Дуров]] [[!redirects Николай Валерьевич Дуров]]



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