Mathematical Sciences: Rings and Modules

本研究将集中于环论和表示论中的一些问题。关于仿射代数的问题，与它们的增长和它们的单模有关。此外，还将讨论半单李代数的表示理论，特别是最高权模，以及一些相关的有限维结合代数的模理论。本研究属于环论和表示论的一般领域。这些领域目前非常活跃，有一个人能够在这些主题之间架起桥梁是很有价值的。人们可以期待对数学界具有重要意义的结果。

This research will focus on some problems in ring theory and representation theory. Questions on affine algebras, related to their growth and their simple modules will be examined. Further the representation theory of semisimple Lie algebras, with special attention to highest weight modules will be considered, as well as, the module theory of some related finite-dimensional associative algebras. This research is in the general area of ring theory and representation theory. These areas are currently very active and it is valuable to have someone who can bridge these subjects. One can expect results of significance to the mathematical community.