L\"owner equations and dispersionless hierarchies
  Using the Hirota representation of dispersionless dKP and dToda hierarchies, we show that the chordal L\"owner equations and radial L\"owner equations respectively serve as consistency conditions for one variable reductions of these integrable hierarchies. We also clarify the geometric meaning of this result by relating it to the eigenvalue distribution of normal random matrices in the large N limit. 
Takashi Takebe, Lee-Peng Teo and Anton Zabrodin