WORKSHOP: Non-Commutative Constructions in Arithmetic and Geometry

研讨会：算术和几何中的非交换构造

• 批准号: EP/G001278/1
• 负责人: Minhyong Kim
• 金额: $ 0.39万
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2008
• 资助国家: 英国
• 起止时间: 2008 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FG001278%2F1
• 关键词: WORKSHOP; Non; Commutative; Constructions; Arithmetic

It is little exaggeration to state that the mathematics of the twentieth century has made great advances through the study of commutative structures and linearization. This has been true both in the study of geometric structures and arithmetic ones. Meanwhile, partly through the intervention of ideas from physics, an increasing number of mathematicians have been struggling to extend the insights gained from commutative constructions to non-commutative structures, including non-abelian Galois theory and non-commutative differential and algebraic geometry. Such developments have been gradually coming to the fore over the last two decades in several regions of the world, including the UK, France, and Japan, partly in response to a grand research program proposed by the French mathematician Alexandre Grothendieck in the 80's. The time is then just right to plan ahead for a coherent vision of future research, where significant advances will depend on a sharing of vision and resources that cut across the boundary of disciplines and of nations. This workshop is a preliminary attempt to bring together world leaders in non-commutative constructions for in-depth discussion on future possibilities for collaboration, research, and the dissemination of ideas.

毫不夸张地说，二十世纪的数学通过交换结构和线性化的研究取得了巨大的进步。在几何结构和算术结构的研究中都是如此。与此同时，部分通过物理学思想的介入，越来越多的数学家一直在努力将从交换构造中获得的见解扩展到非交换结构，包括非交换伽罗瓦理论以及非交换微分和代数几何。过去二十年来，此类进展在包括英国、法国和日本在内的世界多个地区逐渐崭露头角，部分原因是法国数学家亚历山大·格洛腾迪克 (Alexandre Grothendieck) 在 80 年代提出的一项宏伟研究计划。现在正是提前规划未来研究的连贯愿景的最佳时机，其中的重大进展将取决于跨越学科和国家边界的愿景和资源共享。本次研讨会是一次初步尝试，旨在将非交换构造领域的世界领导人聚集在一起，深入讨论未来合作、研究和思想传播的可能性。