Biology and medicine provide many challenging problems that can be addressed efficiently only with adequately developed mathematical tools. As these disciplines are becoming increasingly quantitative, there is a need in the development of mathematical models for a vast variety of processes and phenomena, most of which have (spatial and/or temporal) multiscale characteristics.

Our interests here lie primarily with low dimensional nanostructures where the motion of electrons can be confined from one, two, and even three spatial dimensions. The respective structures are known as quantum wells, quantum wires, and quantum dots. Such structures will continue transforming our lives as they will be used as parts of environmental, chemical, and biological sensors, in transportation industries, energy saving technologies, biomedicine, communications, and information technology.

We are interested in non-trivial dynamic processes, including but not limited to nonlocal and those that are far from their equilibrium, as well as in the associated phenomena and systems, and their modeling. Such processes occur frequently in systems ranging from semiconductor plasma to chemical and biological networks, and from tiny man-made nano-objects to living cell cycles.

In modeling many phenomena and processes in Nature as well as in man-made systems there is often some indeterminacy in the future evolution of such systems, phenomena, and processes that, by the language of mathematics, can be described by probability distributions.

As it stands now, humanity depletes its resources with an astronomical speed, much faster than they can be replenished. It is important to understand that the only way for our further development could be a balance between our needs and preserving the environment. We are interested in the development of mathematical foundations for and mathematical modeling of alternative and renewable sources of energy.