Conference: Motivic and non-commutative aspects of enumerative geometry, Homotopy theory, K-theory, and trace methods

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This award provides support for the travel and local expenses of early-career U.S.-based mathematicians to attend the conferences "Motivic and non-commutative aspects of enumerative geometry" and "Homotopy theory, K-theory, and trace methods" in Nijmegen, the Netherlands, held from July 3-7th, 2023. The conferences focuses on exciting, interconnected areas of mathematics which broadly study foundational questions in algebraic K-theory. The events aim to connect U.S.-based mathematicians with European researchers and provide opportunities to build new collaborations. In addition to the interaction with more established researchers in the field, sessions of short presentations are designed to allow graduate students, postdoctoral researchers, and early career faculty to share their own work.Algebraic K-theory records important and subtle invariants of a ring or scheme. Unfortunately, computing these K-groups outside of a handful of examples is notoriously difficult. Two dominant approaches have arisen to tackle this problem: motivic homotopy, which builds in algebraic geometry many classical constructions from stable homotopy theory, and trace methods, which approximate the algebraic K-groups by constructions in classical and equivariant stable homotopy. These conferences will bring together experts representing all of these areas and several related fields in mathematics, building on exciting recent developments and providing a forum to expose early-career mathematicians in algebraic geometry and homotopy theory to these areas.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.