Diophantine problems : modern and classical perspectives

丢番图问题：现代与古典的观点

• 批准号: 250160-2012
• 负责人: Bennett, Michael
• 金额: $ 2.55万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=547524
• 关键词: Diophantine; problems; modern; classical; perspectives

Diophantine problems have a classical appeal that reaches beyond research mathematics, in some cases such as Fermat's Last Theorem, even as far as popular culture. For a practising mathematician, they provide test-cases for the latest theorems and conjectures from Arithmetic and, indeed, Algebraic Geometry, for understanding the arithmetic of curves and surfaces, and for observing the interplay between analytic and algebraic techniques, between the theoretical and the computational.

丢番图问题具有经典的吸引力，其影响力超出了研究数学的范畴，在某些情况下，例如费马大定理，甚至影响到了流行文化。对于实践数学家来说，它们提供了来自算术乃至代数几何的最新定理和猜想的测试用例，用于理解曲线和曲面的算术，并观察分析和代数技术之间、理论和实际之间的相互作用。计算性的。