Subgroups of simple rings/theory of coagulation

该项目的前半部分涉及简单环的结构和性质，这些数学对象在纯数学的许多分支中具有根本的重要性，以及在其他科学领域的应用。例如，该项目的目标之一是精确理解群的投影表示--这是研究原子和晶体结构以及固态物理学等科学领域的重要工具。 本项目的后半部分涉及凝聚/破碎理论。这一理论是在几乎世纪前通过对聚合物形成的化学研究而发现的。它在科学和工程中有许多实际的应用，从石油开采，塑料制造，危险物质的分散，血液学，到行星和星系形成的理论。我们小组一直在研究通过聚集或分裂而增长和下降的粒子系统的行为（例如受损反应堆内的放射性尘埃，或地下油表中形成的气泡）。这些系统随着时间的推移而发展的方式，特别是外部因素影响其演变的方式，是我们研究的重点。实际应用包括不仅能够预测这种系统的行为，而且能够控制这种行为。

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.