Nikolai Durov

**Nikolai Durov** (Николай Валерьевич Дуров) 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.

- homepage at Steklov
- mathnet.ru entry
- wikipedia: Nikolai Durov

Durov obtained his Ph.D. in 2007 in Bonn under Gerd Faltings:

*A new approach to Arakelov geometry*, arxiv/0704.2030

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

- N. V. Durov,
*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) - N. V. Durov,
*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)

Nikolai Durov is also an experienced computer programmer. He was a member of a St Petersburg State University student team winning a student world tournament in programming. His high school education was in Italy. His younger brother Pavel V. Durov is a professional programmer and main constructor behind one of the most popular internet sites in Russia.

Nikolai Durov is currently working on his habilitation thesis. His earlier publications also include

- N. Durov, S. Meljanac, A. Samsarov, Z. Škoda,
*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) (doi:jalgebra) (math.RT/0604096).

where in chapters 7–9 Durov presented a flexible theory of a class of functors which can be viewed as representing generalizations of 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:

- Nikolai Durov,
*Classifying vectoids and generalisations of operads*, arxiv/1105.3114, the translation of “Классифицирующие вектоиды и классы операд”, Trudy MIAN, vol. 273 *Classifying vectoids and generalizations of operads*, talk at The International Conference “Contemporary Mathematics” June 12, 2009, video: link

Other sources:

*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, link*Arithmetic intersection theory and homotopical algebra*, seminar 2007- N. V. Durov,
*Топологические реализации алгебраических многообразий (Topological realizations of algebraic varieties)*, preprint POMI 13/2012 (in Russian) abstract, pdf.gz - N. V. Durov,
*МУЛЬТИПЛИКАТИВНЫЕ МОНОИДЫ ${\mathbb{F}}_p$-АЛГЕБР И АБСОЛЮТНЫЕ ТЕНЗОРНЫЕ ПРОИЗВЕДЕНИЯ КОНЕЧНЫХ ПОЛЕЙ*, (Multiplicative monoids of ${\mathbb{F}}_p$-algebras and absolute tensor products of finite fields), preprint POMI /2012 (in Russian) abstract

Revised on September 24, 2012 18:22:56
by Zoran Škoda
(109.227.8.56)