Mathematical Sciences: Analysis Over Loop Spaces

格罗斯将研究自然狄利克雷形式算子 环空间上的布朗桥测度。 的 特别感兴趣的是证明存在性和唯一性， 相关薛定谔算符的基态， 同伦类 这是格罗斯近期工作的延续 循环群上的对数Sobolev不等式 李群表示论的含义。 李群理论，以挪威人的荣誉命名 数学家Sophus Lie，一直是 世纪数学。 作为数学工具， 利用系统中固有的对称性， 李群的表示理论对 数学本身和理论物理学，特别是 量子力学和基本粒子物理学。

Gross will investigate the natural Dirichlet form operator over loop spaces associated to Brownian bridge measure. The particular interest is in proving existence and uniqueness of ground states of the associated Schroedinger operators over homotopy classes. This is a continuation of Gross's recent work on logarithmic Sobolev inequalities on loop groups which has many implications for the representation theory of Lie groups. 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 and theoretical physics, especially quantum mechanics and elementary particle physics.