During NMC 2025, the three-yearly N.G. de Bruijn Prize will be awarded to Markus Land, Akhil Mathew, Lennart Meier and Georg Tamme for their excellent mathematical work published in a peer-reviewed journal between 2022 and 2024. Their article, "Purity in chromatically localized algebraic K-theory" (J. Amer. Math. Soc. 37 (2024), nr. 4, 1011 The work contains a significant Dutch contribution by Lennart Meier (Utrecht University). Lennart Meier will give a plenary lecture on the work done.

Algebraic K theory and higher algebraic localizations

Algebraic K theory is a fundamental invariant of rings. Although at first glance it appears to be a classic algebraic invariant, its construction uses higher algebra, a form of algebra in which sets are replaced by spaces and abilities by coherent homotopies. As a result, algebraic K theory can most naturally be seen as an invariant of higher algebraic rings, resulting in higher algebraic abelian groups. Although it has long been known how algebraic K theory behaves in relation to p-local equivalents for a prime number p, higher algebra allows higher versions of prime numbers and associated localizations.

In my article "Purity in chromatically localized algebraic K-theory," together with M. Land, A. Mathew and G. Tamme, I have proven a general statement on how algebraic K-theory behaves in relation to such higher-algebraic localizations. The aim of the lecture is to explain this thesis and, if time permits, to discuss how it contributed to the evidence of Rogne's redshift-conjucture and the rebuttal of Ravenel's telescope-conjucture.

Biography

Lennart Meier studied mathematics and philosophy in Bielefeld and Bonn and graduated in 2009 with a Diplom thesis on stringtopology under the supervision of Matthias Kreck. He stayed in Bonn to promote in 2012 in the stable homotope theory accompanied by Stefan Schwede. He then became Whyburn Instructor at the University of Virginia, where he worked for two years. After a two-month stay at the Hausdorff Institute, he returned to Bonn as a postdoctoral researcher with a scholarship from the DFG (Deutsche Forschungsgemeinschaft). In 2018, he joined the Mathematical Institute of Utrecht University as assistant professor, where he gained tenure in 2020.