Mathematical Sciences: Cohomology of G/P and Representation Theory of G, for Real Reductive Lie Groups and Generalizations

Casian将利用群的表示理论研究实约李群、杯积和Weyl群作用的旗变的上同调问题。他将研究确定哪些舒伯特细胞对同源性中的非扭转部分有贡献的问题。他还将调查Kac-Moody环境中的类似问题。李群理论是为了纪念挪威数学家索夫斯·李而命名的，它一直是20世纪数学的主要主题之一。作为利用系统中固有对称性的数学工具，李群表示理论对数学本身，特别是分析和数论，以及理论物理，特别是量子力学和基本粒子物理产生了深远的影响。

Casian will study the problem of computing the cohomology of the flag variety for real reductive Lie groups, the cup product and Weyl group action, using the representation theory of the group. He will investigate the problem of determining which Schubert cells contribute to the non torsion part in homology. He will also investigate similar problems in the Kac-Moody setting. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.