The research in the Alavi group is at present largely concerned with the following question: how can one best use a given (finite) amount of parallel computing power in trying to solve electronic (many-particle) Schrodinger equations? We are particularly interested in physical systems in which the electronic wave functions exhibit much irreducible entanglement, in other words cannot be expressed as single configurations (or Slater determinants) in any one-particle basis. As well as being a question of enormous basic significance to theoretical physics and chemistry, the answer to this question impinges on a broad swathe of knowledge: ranging from many-body theory, through to the mathematics of graph theory, optimization and stochastic processes, through to algorithm design and computer science.
As well as, of course, the questions of application. As a graduate student, you will embark on a rigorous course of work which will bring you in contact with each of these areas. Ideal background for this type of work is a good first degree in theoretical physics or chemistry, applied mathematics, or computer science.