Laboratory for Complex Analysis and Differential Equations

• We have detected existence of hierarchy over a set of singular strata of cuspidal type for all A-discriminants. 
• Our researchers have produced rational expressions for multiple roots of systems of algebraic equations.
• The Laboratory has obtained an integral formula for solving a general algebraic system of n equations with n variables.
• We have proven the criterion of maximum reducibility of representations of monodromy of two-dimensional hypergeometric systems. 
• In the theory of Riemann surfaces we have created a discrete version of the classical Woman theorem on the maximum possible order of cyclic groups of automorphisms of a Riemann surface with genus over one.
• We have proven the theorem on open representation of Navier-Stokes equations in weighted spaces of Hölder type smooth functions.

Education and career development:

• We have reviewed the bachelors program in the specialization «Substantial, complex and functional analysis» and the masters program «Computer analysis» at the Siberian Federal University, we have developed and implemented 25 educational programs.
• We have held 5 international scientific conferences, 1 scientific school for young researchers, 1 international scientific seminar.
• 2 doctoral dissertation and 8 candidate dissertations have been defended.

Organizational and structural changes: We are conducting negotiations for the Laboratory to be accepted to the European Several Complex Variables Consortium that unites leading research centers

Other results:

• We held the 5th School-conference in algebraic geometry and complex analysis for young mathematicians (Koryazhma, 17–22 August 2015, in collaboration with the V. A. Steklov Mathematical Institute of the Russian Academy of Science and the Higher School of Economics).
• We conducted the conference «Complex analysis and differential equations» (Saint Petersburg, 05 ‑ 09 October 2015, in collaboration with the V. A. Steklov Mathematical Institute of the Russian Academy of Science).
• We have held the International conference on algebraic geometry, complex analysis and computer algebra (Koryazhma, 03 – 09 August 2016, in collaboration with the V. A. Steklov Mathematical Institute of the Russian Academy of Science and the Higher School of Economics).
• We have held the 3rd Russian-Chinese scientific conference in complex analysis, algebra, algebraic geometry and mathematical physics (Moscow, 10 – 16 May 2016, in collaboration with the V. A. Steklov Mathematical Institute of the Russian Academy of Sciences).
• The Laboratory held the conference «Several Complex Variables» (Krasnoyarsk, 11 – 15 September 2017, in collaboration with the V. A. Steklov Mathematical Institute of the Russian Academy of Sciences).
• The Laboratory has achieved quantitative and qualitative level of scientific with, recognition of the Krasnoyarsk school of complex analysis. This has lead to increase in numbers of grants of different levels, the number of students involved in scientific work including those from other regions of Russia and from other countries.

Collaborations:

• University of Potsdam (Germany): joint research
• V. A. Steklov Steklov Mathematical Institute of the Russian Academy of Sciences (Russia), Higher School of Economics (Russia): joint scientific conference and schools