Conference: Arithmetic, K-theory, and Algebraic Cycles

This award supports participation in the conference "Arithmetic, K-theory and Algebraic Cycles" to take place May 26-31, 2025 at the Ohio State University. In recent years, there have been several major advances in the field of Arithmetic Geometry, Algebraic K-theory and Algebraic Cycles. Arithmetic Geometry is the study of spaces from the point of view of number theory and is largely concerned with the solutions of polynomial equations, especially over the integers.

Algebraic K-Theory and Algebraic Cycles are certain special techniques that can understand the geometric nature of a problem, one that is again defined in terms of polynomial equations. In recent years there have been a number of important developments in this area and the purpose of the week-long workshop and conference is to bring together established experts in these areas along with early-career researchers with the goal of stimulating further progress.

In more detail, in recent years there have been major developments in Arithmetic Geometry, Algebraic K-theory and Algebraic Cycles, leading up to the solution of the Milnor, Bloch-Kato and Lichtenbaum-Quillen conjectures, as well as the conjectures of Thomason and Morel concerned with equivariant phenomena for actions of linear algebraic groups. The powerful techniques introduced for the solution of the above conjectures have stimulated work on several outstanding remaining problems in the area, which are often arithmetic in nature, but use sophisticated tools from Algebraic K-theory and Algebraic cycles.

The goal of the program is to focus on several of the outstanding problems in the area, surveying the progress made and planning strategies for further advancement. The conference website is https://people.math.osu.edu/joshua.1/AKC_conf_2025.html.

This 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.