Professor Lippner’s current research interests are in discrete mathematics with an emphasis on using methods from analysis, geometry, and topology. He has worked on the theory of graph limits and with his collaborators has developed general methods  to translate measure theoretic results into statements about finite graphs. He has worked with Shing-Tung Yau on spectral graph theory motivated by ideas from geometry and topology. These various research topics have found applications in numerical methods, Computer Science and Physics.

Professor Zhou’s research focuses on PDE Theory and analysis of  inverse problems arising in various imaging and tomography methods, as well as theoretical design of invisibility cloaks. Both of these aspects amount to a rigorous mathematical understanding of the dependence of the underlying differential operator, linear or nonlinear, on partial knowledge of its solutions. She is interested in applying tools from PDE’s, Fourier and real analysis, mathematical physics and microlocal analysis to important inverse problems, usually highly non linear, which arise in physical processes including various wave propagation phenomena in electromagnetism, elasticity, acoustics, and also in general relativity for potential applications to astronomy and astrophysics.