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International Conference “Modern Trends in Condensed Matter Physics” is focused on recent progress in the condensed matter physics. The event is dedicated to the memory of Lev Gor`kov who was one of the creators of this general area of physics in its modern form. The conference covers a number of topical sections of condensed matter physics: quantum phase transitions superconductor-insulator transitions Kondo insulators electronic transport in the presence of inhomogeneities and electron-electron interaction topological properties of low-dimensional systems theory of high-temperature superconductivity theory of spin superfluidity physics of mesoscopic structures