Robert Lipton works on the multi-scale analysis of heterogeneous media. Lipton's research includes the following areas: Identification of new wave phenomena due to sub-wavelength resonances and multiple scattering. Accurate multi-scale analysis of heterogeneous media with non well separated length scales. Non-local modeling for understanding the fracture process and the creation of interface. Chacterizing the macroscopic effect of the microstructure on strength. Identifying the macroscopic effect of microscopic interfaces. Extraction of the effect of microstructure on extreme elastic properties.