Automorphic forms - computational and p-adic aspects

自守形式 - 计算和 p-adic 方面

• 批准号: 355600-2011
• 负责人: Greenberg, Matthew
• 金额: $ 1.89万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=482773
• 关键词: Automorphic; forms; computational; adic; aspects

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.

自守形式是一种特殊的数学函数，具有许多显著的对称性，自19世纪世纪以来，数学家们一直对自守形式感兴趣。这些著名的理论开始继续发展迅速，在世纪，刺激了深刻的见解赫克，艾希勒，韦尔和志村建议深刻的联系与数论和几何。自守形式和其他这些场之间的崇高相互作用，可以用著名的朗兰兹图来概括，这是罗伯特·朗兰兹在20世纪60年代提出的。 从那时起，这些理论指导了许多领域的数学研究。 朗兰兹哲学的哲学基础强烈地影响了我自己的研究。