My research concerns the development of mathematical methods to control quantum systems. A physical system has often an infinite-dimensional spectrum of energies (unbounded energies!), so that approximation techniques are convenient for studying the whole system, in order to reduce its complexity.  Important examples of systems which show unbounded energies range from atoms in a cavity to molecules and their rotational dynamics. Crucial approximations to reduce the complexity of the system are the adiabatic one, used to control slowly varying systems, and the Galerkin one, used to break degeneracies. As the development of quantum devices faces the problem of a quantum system interacting with the environment, I am also interested in translating the currently available techniques into the open quantum systems framework.

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