Robert Berman works mainly on analytical aspects of complex algebraic and differential geometry. His research focuses on connections between these fields and probability, statistical mechanics and mathematical physics and also arithmetic (Arakelov) geometry, as well as convex geometry and analysis.
In broad terms his research concerns, among other things, the problem of describing the emergence of coherent structures in large scale complex systems from a geometric and analytic point of view. His work reveals that similar mathematical tools and structures can be used to understand seemingly unrelated areas, ranging from the geometric structure of the universe to signal processing and metrology, as well as the complexity of algebraic equations.
He is (since 2013) a Knut and Alice Wallenberg Academy Fellow (see http://www.wallenbergacademyfellows.se/en/List-of-scientists/BermanRobert/ for a popular account of some of his work).