Support of US Participants in the Research Program: K-Theory, Algebraic Cycles and Motivic Homotopy Theory, Cambridge, UK.

该奖项为将在艾萨克·牛顿数学科学研究所举行的K理论、代数循环和动机同伦理论研究计划的美国参与者提供支持。该项目可能会有180-250人参加，其中包括只参加研讨会的人，我们预计其中约有50人来自美国，包括相当数量的初级参与者(即来自美国各大学的初级教师、博士后候选人和高级研究生)。该项目希望让世界上大多数专注领域的专家参与进来，其中包括一些来自美国、欧洲和全球其他地区的专家。此外，位于剑桥大学校园的艾萨克·牛顿研究所提供了极好的额外资源。我们预计，这一计划将为交流关键科学思想提供一个极好的机会，并为这些领域的进一步进展提供刺激，因为参与这一计划可能会为美国参与者提供进一步进展和突破的刺激和机会。该计划的一个重要方面是针对初级参与者：除了为期一周的入门研讨会外，三个主题研讨会的每一次都将在几次介绍性讲座之前进行。这是一个令人兴奋的领域，应用于几个领域，如算术几何、霍奇理论和数学物理。本课程的一个主题是探索下列领域之间的联系：*代数K-理论，动机上同调和动机同伦理论*霍奇理论，周期，调节器和算术几何*数学物理K-理论，代数圈和动机同伦理论是从上同调的角度研究代数簇(包括相关学科，如阿拉克洛夫几何)的交汇点。这是一个广阔的领域，有着许多深刻的相互联系。近年来，这一领域也取得了一些令人瞩目的进展，该地区仍然存在的几个重要问题最终得到了积极的解决：例如，Milnor猜想和Bloch-Kato猜想以及Lichtenbaum-Quillen猜想在过去15年中得到了解决，后两者在过去7-8年中得到了解决。为研究这些猜想而开发的技术已经刺激并提供了对相关猜想的可能的攻击。该计划的一个主要目标是将研究这一广泛领域的不同方面的数学家们聚集在一起，在更长的一段时间内，以促进思想交流和刺激进一步的进步。更多细节可在项目网站上获得：https://www.newton.ac.uk/event/kahThis奖反映了国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award provides support for US based participants to the K-Theory, Algebraic cycles and Motivic Homotopy Theory research program which will be held at the Isaac Newton Institute for Mathematical Sciences. The program will likely involve 180-250 participants including the ones participating only in the workshops, of which we expect around 50 to be from the US, including a significant number of junior participants (i.e., junior faculty, post-doctoral candidates and advanced graduate students from across US universities). The program hopes to involve as participants most of the world's experts in the focused areas, including some from the US, as well as Europe and other parts of the globe. Moreover, the Isaac Newton Institute located on the campus of Cambridge University provides excellent additional resources. We expect this program will provide an excellent opportunity for exchange of key scientific ideas and provide stimulus for further progress in these areas, as such participation in this program is likely to provide stimulus and opportunities for further progress and breakthroughs to the US participants. A significant aspect of the program is targeted toward junior participants: in addition to a week-long introductory workshop, each of the three themed workshops will be preceded by several talks of an introductory nature. This is an exciting area with applications to several fields like Arithmetic Geometry, Hodge theory and Mathematical Physics. A theme of this program is to explore connections between the following areas:* Algebraic K-theory, Motivic Cohomology and Motivic Homotopy Theory* Hodge Theory, Periods, Regulators and Arithmetic Geometry* Mathematical PhysicsK-theory, Algebraic cycles and Motivic homotopy theory are fields at the confluence of studying algebraic varieties (including related subjects such as Arakelov geometry) from a cohomological point of view. This is a broad area with numerous deep inter-connections. This area has also seen some spectacular advances in recent years with several of the important problems that remained conjectures in the area finally resolved positively: for example, the Milnor and the Bloch-Kato conjectures as well as the Lichtenbaum-Quillen conjectures have been solved during the past 15 years, with the latter two solved during the past 7-8 years. The techniques developed for work on these conjectures have stimulated and provided possible attacks on related conjectures. One primary goal of this program is to bring together mathematicians working on different aspects of this broad area for an extended period so as to promote an exchange of ideas and stimulate further progress. Further details are available at the program website: https://www.newton.ac.uk/event/kahThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.