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

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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.