The main results:
Quantization of Hall conductivity of two dimensional electron gas was proved within the drift approximation, using the topological properties of the edge trajectories. Anapole moment of the hydrogen atom was calculated. An epsilon-expansion was developed for the estimate of the critical value of the coupling constant at which a bound state first appears in a potential well. A general expression was obtained for the preexponential factor in the formula for the energy of the weakly bound state in two dimensions. Interaction of a magnetic monopole with condensed matter was analyzed and the relation was clarified between the response of the medium to the monopole fields and the 'tail' of magnetization that remains in the medium after the monopole has passed. Semi-quantitative formula was obtained for the superfluid transition temperature T_c in arbitrary bose liquid, which relates Tc to the mean kinetic energy per particle in the normal phase. An estimate was obtained for T_c in molecular liquid hydrogen.