Professor Spielberg's research project centers on certain boundary actions of a Fuchsian group, related to the action of the group on its limit set. The fundamental example is that of the modular group PSL(2,Z) acting on a Cantor set obtained by disconnecting the extended real line at the points of a countable invariant set. In this case the crossed product C*-algebra is isomorphic to a certain Cuntz algebra. The objects of study here are more general Fuchsian groups which give rise in an analogous fashion to other algebras of Cuntz and Krieger. Professor Spielberg's research is in the area of C*-algebras. These algebras consist of families of operators (infinite matrices of complex numbers) with a certain reality property: the algebra is generated by elements whose value in any state of the system is a real number. The study of these algebras was originally motivated by physics, and they are still of major interest in this area and in other branches of pure mathematics.
