Exercising a working control over high-temperature, and ultimately room temperature superconductivity, is deemed the dream-technology of the 21^st century. This has turned into a realistic goal since the discovery of high temperature superconductivity (HTSC) in cuprate oxide materials in 1986. 

These materials have taught us to think in terms of electrons in strong correlation with each other, which is the opposite extreme from the free electron picture which has been instrumental in the development of today's semiconductor industry.

The new picture is that of Mott insulators, electrons which are immobilized on account of their mutual repulsions. Due to this strong tendency to localize, the internal degrees of freedom of individual electrons, most notably the spin, will surface up in the material properties. That these entities will count raises the possibility for there to arise a considerably richer variety of state of matters than were previously anticipated.

Our principal aim, through theoretical modeling and large scale numerical calculations of these strongly correlated electrons, is to unearth and contribute paradigmatic concepts which will lead us to new electron technologies, e.g., spintronics and quantum computing based on electron correlations.

Holes doped into a Mott insulator, is the basic ingredient for the superconductivity in the cuprates. A hole attempting to make an excursion within this system will suffer a quantum mechanical interference from the background spin configurations of the localized electrons. This is most efficiently cast in the language of quantal phases, one of the key concepts that underlie our research.