Conductor Valery Gergiev is on a mission. “When I meet [Putin] I tell him, ‘Do we have a chance to improve dramatically the situation of the provincial orchestras in Russia?’ ” He asks ‘What is the situation?’, and I tell him we lost, in the 1980s and 1990s especially, many great teachers, many great musicians, not only famous ones but also . . . thousands of teachers and tens of thousands of professional musicians.”