Mathematical Sciences: Topics in Analysis on Symmetric Spaces and Antomorphic Forms

Katok教授将研究与自同构形式有关的几个问题。特别是，她将研究非全纯质量形式的傅里叶系数。她还将通过发展双曲动力系统的高上同调理论来研究Livshitz理论的推广。自同构形式产生于19世纪中期的非欧几里得几何。因此，数学家和物理学家很早就认识到，许多具有根本重要性的物体在其基本性质上是非欧几里得的。这个领域主要关注关于整数的问题，但在使用几何和分析时，它保留了与历史根源的联系，因此与理论物理中的规范理论和信息论中的编码理论等领域的问题联系在一起。

Professor Katok will work on several problems connected with automorphic forms. In particular, she will study the Fourier coefficients of non-holomorphic Maass forms. She will also study a generalization of Livshitz theory through the development of a higher cohomology theory for hyperbolic dynamical systems. Automorphic forms arose out of non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.