Automorphic forms - computational and p-adic aspects

自同构形式是一种特殊的数学函数，它具有许多显著的对称性，自19世纪伟大的雅可比、魏尔斯特拉斯和戴德金以来，就一直吸引着数学家。在赫克、艾希勒、韦尔和志村的深刻见解的推动下，由这些著名人物发起的理论在20世纪继续迅速发展，这些见解表明了与数论和几何的深刻联系。自同构形式和这些其他领域之间的崇高相互作用是著名的朗兰兹猜想的缩影，由罗伯特·朗兰兹在20世纪60年代提出。从那时起，这些猜想指导了许多领域的数学研究。朗兰兹猜想背后的哲学强烈地影响了我自己的研究。

Automorphic forms, special mathematical functions possessing many remarkable symmetries, have fascinated mathematicians since the times of 19th century greats Jacobi, Weierstrass and Dedekind. The theories initiated by these eminent names continued to develop rapidly in the 20th century, spurred on by deep insights of Hecke, Eichler, Weil and Shimura suggesting deep connections with number theory and geometry. The sublime interactions between automorphic forms and these other fields are epitomized by the famous Langlands conjectures, formulated by Robert Langlands in the 1960s. Since then, these conjectures have guided mathematical research in many fields. The philosophy underlying the Langlands conjectures strongly influences my own research.