Mathematical Sciences: The Theory of Automorphic Forms

亨特利教授将研究与自同构形式有关的几个问题。特别是，他将研究高阶约化群上的非全纯尖点形式。他希望为这类群体证明韦尔定律的类比。他还将研究小本征值及其与拉马努詹猜想的关系。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 Huntley will work on several problems connected with automorphic forms. In particular, he will study non-holomorphic cusp forms on higher rank reductive groups. He hopes to prove an analogue of Weyl's law for such groups. He will also study small eigenvalues and their relation to the Ramanujan conjecture. 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.