Subgroups of simple rings/theory of coagulation

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The first half of this project deals with the structure and properties of simple rings, mathematical objects that are of fundamental importance in many branches of pure mathematics, as well as in applications to other areas of science. One of the goals of this project, for example, is to gain a precise understanding of projective representations of groups - important tools in such areas of science as the study of the structure of atoms and crystals, and solid-state physics.  The second half of this project deals with the theory of coagulation/fragmentation. This theory was discovered almost a century ago as a result of the chemical study of the formation of polymers. It has found numerous practical practical applications in science and engineering, ranging from oil extraction, manufacture of plastics, dispersion of hazardous materials, and hematology, to theories of planet and galaxy formation. Our group has been investigating the behavior of systems of particles which grow and decline by clustering or splitting apart (such as radioactive dust inside a damaged reactor, or gas bubbles forming in underground oil tables). The way such systems develop over time, and in particular the way external factors influence their evolution, is the focus of our research. The practical applications include the ability not only to predict the behavior of such systems, but to control that behavior.