Mathematical Sciences: Representation Theory and AutomorphicForms

斯佩教授将继续她的研究与J. Rohlfs 关于算术群自同构的Lefschetz数。 她计划找到一个稳定（在朗兰兹的意义上）， 莱夫谢茨数，然后用它来找到 使用Arthur-Selberg迹公式的Lefschetz数。 Barbasch教授将继续他在幂幺方面的工作 真实的约化群的表示，它们的特征标理论， 以及它们在酉对偶分类中的作用。 他将 参与几个项目：（i）与J.亚当斯，他将研究 幂幺情形的对偶约化对对应 （二）与A。我将研究酉对偶 对于非分歧表示，和（iii）与S。Evens他会 研究轨道几何学之间的关系，类似舒伯特 多样性和有限维的多重性 表示。 群论基本上是对称性理论。 采取 一个简单的例子，当所讨论的系统在一个 空间原点位置的变化， 翻译自然会出现。 虽然组是抽象对象， 具体情况需要具体实现， 对称群的“表示”。教授的项目 Speh和Barbasch将有助于我们理解群体 表示。

Professor Speh will continue her research with J. Rohlfs concerning Lefschetz numbers of automorphisms of arithmetic groups. She plans to find a stabilization (in the sense of Langlands) of the Lefschetz numbers and then use this to find an expression for the Lefschetz number using the Arthur-Selberg trace formulas. Professor Barbasch will continue his work on unipotent representations of real reductive groups, their character theory, and their role in the classification of the unitary dual. He will be involved in several projects: (i) with J. Adams he will study the dual reductive pair correspondence for the case of unipotent representations, (ii) with A. Moy he will study the unitary dual for unramified representations, and (iii) with S. Evens he will study relations between the geometry of orbits, similar Shubert varieties, and multiplicities in finite dimensional representations. Group theory is basically the theory of symmetry. To take a simple example, when the system in question is invariant under a change in the position of the origin of space, the group of translations naturally arises. While groups are abstract objects, particular situations demand concrete realizations or "representations" of the symmetry group. The projects of Professors Speh and Barbasch will contribute to our understanding of group representations.