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We consider two types of contour dynamics in parallel. One is related to physical Hele-Shaw problem (or Laplacian growth). The other one is the Loewner evolution. Harmonic momenta are conserved for the first evolution and Virasoro generators are conserved for the second one. We discuss differences and similarities of these two constructions, deduce generating functions, reveal relations with Conformal Field Theory. Host: Razvan Teodorescu |