Singular elastic interfaces

Soft elastic interfaces exhibit intriguing similarities to liquid interfaces: they possess a surface tension and are susceptible to interfacial instabilities. The first part of this talk addresses how soft solids behave when exposed to liquid drops, which provide a singular forcing. It is shown that such "soft wetting" fundamentally differs from the usual wetting on rigid surfaces. In the second part we discuss the formation of cusps and creases at elastic interfaces -- and point out striking similarities with cusps at viscous interfaces.