Geometry and Representations of Reductive Groups

EvensEvens将继续他在几何和表示论之间的关系的工作。在他与卢的工作中，他将试图推广他们之前的定理，将泊松几何的新领域与19世纪计算交集重数的经典问题联系起来。特别是，他希望找到一种泊松结构来帮助计算旗形的量子上同调。在他与Grojnowski的合作中，他将继续研究实半单群表示的限制的多重性，目的是解决某些多重性问题。他将研究幂零轨道的特征循环及其与表示论中某些问题的关系。对称性在几何问题的研究中的使用一直是现代数学的伟大统一主题之一。基于对称性考虑的思想对算术和物理学中的基本问题产生了深远的影响，特别是对量子力学。有一些拓扑结构类似于有限集合中的点计数问题。这位研究人员计划将这些结构应用于数论和理论物理引发的问题。

AbstractEvensEvens will continue his work on the relation between geometry and representation theory. In his work with Lu, he will attempt to generalize their previous theorem relating the new field of Poisson geometry to the classical 19th century problem of computing intersection multiplicities. In particular, he hopes to find a Poisson structure to help compute quantum cohomology of the flag manifold. In his work with Grojnowski, he will continue his study of multiplicities of restrictions of representations of real semisimple groups, with the goal of solving certain multiplicity one problems. He will study characteristic cycles for nilpotent orbits and their relation to certain problems in representation theory.The use of symmetry in the study of geometrical problems has been one of the great unifying themes of modern mathematics. Ideas based on considerations of symmetry have had a profound impact on elementary questions in arithmetic and on physics, especially to quantum mechanics. There are certain topological constructions which are analogous to the problem of counting points in a finite set. The investigator plans to apply these constructions to problems motivated by number theory and theoretical physics.