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

该奖项为美国的参与者提供支持K理论，代数循环和动机同伦理论研究计划，该计划将在艾萨克·牛顿数学科学研究所举行。该计划可能涉及180-250名参与者，包括仅参加研讨会的参与者，我们预计其中约有50人来自美国，包括大量初级参与者（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）。 该计划希望吸引世界上大多数重点领域的专家参与，包括来自美国、欧洲和地球仪其他地区的专家。 而且，位于剑桥大学校园内的艾萨克·牛顿研究所提供了极好的额外资源。我们希望该计划将为关键科学思想的交流提供一个极好的机会，并为这些领域的进一步进展提供动力，因为参与该计划可能会为美国参与者提供进一步进步和突破的动力和机会。 该计划的一个重要方面是针对初级参与者：除了为期一周的介绍性研讨会外，三个主题研讨会中的每一个都将有几个介绍性的讲座。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。该计划的主题是探索以下领域之间的联系：* 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，代数循环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Arakelov几何）的汇合点。这是一个广泛的领域，有许多深刻的相互联系。近年来，该地区也取得了一些惊人的进展，该地区仍然存在的一些重要问题最终得到了积极的解决：例如，Milnor和Bloch-Kato以及Lichtenbaum-Quillen在过去15年中已经解决，后两个在过去7-8年中得到解决。为这些攻击而开发的技术刺激并提供了对相关攻击的可能性。该计划的一个主要目标是汇集数学家在这一广泛领域的不同方面工作了很长一段时间，以促进思想交流和刺激进一步的进展。更多细节可在该计划的网站：https://www.newton.ac.uk/event/kahThis奖项反映了NSF的法定使命，并已被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估的支持。

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.