Until 2007 the laboratory was called the Laboratory of Mathematical Methods in Mechanics. Up to 1987 the laboratory was headed by Academician P.Ya.Kochina, and from 1987 to 2007, by Academician V.P.Maslov. Since 2007 it is headed by S.Yu.Dobrokhotov. The personnel of the laboratory are engaged in deep research work in a wide range of problems in mathematical and theoretical physics, hydromechanics, thermodynamics, and probability theory. This research is carried out by V.P.Maslov, L.A.Bagirov, S.Yu.Dobrokhotov, S.Ya.Sekerzh-Zenkovich, A.I.Shafarevich, A.B.Sossinsky, V.E.Nazaikinskii, and others.

People previously affiliated with the laboratory include V.A.Borovikov (1932–2008), M.I.Vishik, O.V.Golubeva, P.N.Zhevandrov, R.V.Isakov, V.V.Kozlov, V.B.Lidskii (1924–2008), L.M.Markhashov, O.A.Oleinik (1925-2001), M.P.Poteryakhin, E.S.Semenov, O.L.Tolstova, T.Ya.Tudorovskii, and V.I.Khlebnikov.

The regular scientific seminar "Asymptotic Methods in Mathematical Physics" is held at the Laboratory.

Asymptotic methods for the constructive calculation of wave fields and vortices in nonhomogeneous media taking into account focusing effects have been developed. These methods are applied to the computation of surface and internal waves and vortices (in fluids and in the atmosphere) generated by various sources. On the basis of these methods, analytic and numerical algorithms for calculating the propagation of tsunami waves and mesoscale vortices in the atmosphere have been constructed.

Approaches to the analysis of the cooling regimes of the destroyed reactor No. 4 of the Chernobyl nuclear power plant have been proposed.

A generalized adiabatic principle (algorithm) yielding an efficient and sufficiently unified method for describing motion in low-dimensional problems of quantum and wave mechanics has been put forward. This algorithm, based on the theory of pseudodifferential operators and the Maslov canonical operator has led, in particular, to the description of quantum and classical motion in diverse nanostructures for a wide range of energies and frequencies.

For a broad class of quantum-mechanical and wave-theoretic spectral problems (in finite-dimensional as well as infinite-dimensional situations), the theory of quasiclassial asymptotics with complex phase has been constructed. The relationship between these asymptotics and various objects and notions of classical Hamiltonian mechanics have been established. Quasiclassical asymptotics with complex phase have been applied, in particular, to a series of problems of superconductivity and superfluidity.

Asymptotic geometric methods for finding rapidly varying and singular solutions of linear and nonlinear equations of mathematical physics, including the equations of hydrodynamics, have been obtained.

The laboratory is closely connected to the Faculty of Nanotechnologies and Informatics (FNTI) of Moscow Physical-Technical Institute. Several researchers affiliated with the laboratory hold part-time positions at the Department of Mathematics and Mathematical Methods of FNTI (chaired by S.Yu.Dobrokhotov), lecture and conduct exercise classes at FNTI in general and special mathematical subjects. In recent years, most of the graduate students at the laboratory have been graduates from that department.