Mathematical Sciences: Zeta Functions and Transfer Operators

Efrat教授将研究几个与自同构形式有关的问题。特别是，他将研究单位区间上的动力系统与附加在黎曼曲面上的ζ函数之间的相互作用。特别地，探索模曲面的ζ函数与相应动力系统的传递算子的行列式之间的联系的结果。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 Efrat will work on several problems connected with automorphic forms. In particular, he will study the interplay between dynamical systems on the unit interval and zeta functions attached to Riemann surfaces. In particular, to explore consequences of the connection between zeta functions of modular surfaces and the determinant of the transfer operator for the corresponding dynamical system. 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.