Mathematical Sciences: Two Problems in Modular Surfaces

Sheingorn教授将研究与自同构形式相关的几个问题。特别是，他将研究某些数论对象等同于高度对称空间上测地线的几何特征这一见解的后果。自同构形起源于19世纪中叶的非欧几里德几何。因此，数学家和物理学家都早已认识到，许多具有根本重要性的物体本质上都是非欧几里得的。这个领域主要涉及关于整数的问题，但在使用几何和分析时，它保留了与其历史根源的联系，从而与理论物理中的规范理论和信息论中的编码理论等不同领域的问题有关。

Professor Sheingorn will work on several problems connected with automorphic forms. In particular, he will study the consequences of the insight that certain number theoretic objects are equivalent to geometric traits of geodesics on highly symmetric spaces. 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.