The Dr. Iskin will undertake theoretical research in condensed atomic and molecular physics. He will investigate quantum phases of two-species Fermi-Fermi, Bose-Bose and Bose-Fermi mixtures of atomic gases at ultracold temperatures. There are four main problems in this proposal. The first problem is about creating and observing a spatially modulated superfluid phase with characteristics of an Fulde-Ferrell and Larkin-Ovchinnikov (FFLO) type superfluidity in trapped atomic Fermi-Fermi mixtures. The second problem is about the phase diagram of the two-species Bose-Hubbard model, and their observation in atomic Bose-Bose mixtures. Both of these problems are highly popular in the field, and Dr. Iskin has already made a great progress on them. The third problem is about the limiting case of light-atom--heavy-atom mixtures, particularly those which can be described by light-heavy (Fermi-Fermi, Bose-Bose, Bose-Fermi and Fermi-Bose) Falicov-Kimball models. Dr. Iskin will apply the renormalization group theory to all 4 of these models. Finally, the last problem is about heteronuclear molecules, and creation and observation of a new phase of matter, i.e. ferroelectric superfluidity.