WORKSHOP: Non-Commutative Constructions in Arithmetic and Geometry

可以毫不夸张地说，20世纪的数学通过对交换结构和线性化的研究取得了巨大的进步。这在几何结构和算术结构的研究中都是正确的。同时，部分由于物理学思想的介入，越来越多的数学家一直在努力将从交换结构中获得的见解扩展到非交换结构，包括非阿贝尔伽罗瓦理论和非交换微分几何和代数几何。在过去的二十年里，这种发展在世界上的一些地区逐渐脱颖而出，包括英国、法国和日本，部分是为了响应法国数学家亚历山大·格罗滕迪克在80年代提出的一项重大研究计划。现在正是为未来研究的一个连贯愿景提前计划的好时机，在这个愿景中，重大进展将依赖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，旨在将非交换结构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。

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.