Guests of the laboratory

Yurii Mikhailovich Vorobiev

The well-known Russian mathematician Yurii Mikhailovich Vorobiev visited the laboratory since July 01 to July 18, 2016.
 Yu.M. Vorobiev graduated from the Chair of Applied Mathematics at MIEM (he was a student in the famous «advanced group», his teachers were, in particular, V.I.Arnold and Yu.I.Manin). He defended his thesis in the field of geometrical methods in the theory of semiclassical approximation, and then the Doctoral dissertation, in the theory of deformations in the Poisson geometry. His research is well known abroad. At present, he is Professor at University of Sonora (Mexico) and actively works in the field of applications of methods of Poisson geometry to the theory of adiabatic approximation.

J. F. Colombeau

The outstanding French mathematician J. F. Colombeau visited the laboratory 'Mathematical methods of natural science' since September 22 to October 2, 2015
J.F.Colombeau made a large contribution to the functional analysis, and the theory of nonlinear differential equations; his results found applications in different fields of physics, geophysics, general theory of relativity, and different fields of technology. The main objects related to J.F.Colombeau’s name are the so-called Colombeau algebras of generalized functions.  

Almost from the very beginning, in the theory of generalized functions opened by S.L.Sobolev and L.Schwartz, it was clear that no associative and commutative operation of multiplication can be defined for these functions (that is, the generalized functions cannot be multiplied, for example, cannot be squared), and this fact greatly restricted the application of these functions in the theory of nonlinear waves. 

The object introduced by J.F.Colombeau, i.e., the Colombeau algebra of generalized functions, contains all standard generalized functions and admits multiplication of its elements; and at the same time, the algebra of smooth functions is isomorphically embedded in the Colombeau algebra. This expansion of the set of generalized functions   allowed significant advance in solving a series of important applied problems and simultaneously raised many new mathematical questions which still remain open.

Lectures by Professor J. F. Colombeau