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.

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

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 11 for all equations iff the Riemann hypothesis is true. The exposition of these results is in

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. The company is not any more in their control. Nikolai and Pavel together established communication platform and company Telegram (see FAQ and wikipedia) where they worked on Nikolai’s envisioned Telegram Open Network (TON) which he classifies as a 5th generation blockchain project enhanced with additional DNS, proxy and (torrent-like) storage infrastructure.

The technical overview sporadically uses the notation from type theory.

Durov’s earlier publications also include

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:

Other sources:

His paper on normed sets above (part 1 out of 3) is partly extending ideas from