De Bruijn lecture

Day 1 (Tuesday 22 April) @ 16:30 – 17:30

Lennart Meier (Utrecht University)

During NMC 2025), the triennial N.G. de Bruijn Prize will be awarded to Markus Land, Akhil Mathew, Lennart Meier, and Georg Tamme for their outstanding mathematical work published in a peer-reviewed journal between 2022 and 2024. Their paper, “Purity in chromatically localized algebraic K-theory”  (J. Amer. Math. Soc. 37 (2024), no. 4, 1011-1040), has already led to spectacular applications, including the resolution of two major, long-standing conjectures. The work includes significant Dutch contributions from Lennart Meier (Utrecht University). Lennart Meier will give a plenary lecture about the work performed.

Algebraic K-theory and higher-algebraic localizations

Algebraic K-theory is a fundamental invariant of rings.  While seemingly a classical algebraic invariant, its construction involves *higher algebra*, a form of algebra where sets get replaced by spaces and equalities are replaced by coherent homotopies. Thus, algebraic K-theory is most naturally seen as an invariant of higher-algebraic rings producing higher-algebraic abelian groups as output. While it has long been known how algebraic K-theory behaves for p-local equivalences for a prime p, higher algebra allows for higher versions of primes and the corresponding localizations.

In my paper “Purity in chromatically localized algebraic K-theory” with M. Land, A. Mathew and G. Tamme, I have shown a general statement how algebraic K-theory behaves with respect to such higher-algebraic localizations. The goal of the talk is to explain this theorem and, if time remains, say how it has helped in proving Rognes’s redshift conjecture and disproving Ravenel’s telescope conjecture.

Biography

Lennart Meier studied Mathematics and Philosophy in Bielefeld and Bonn and graduated in 2009 with a Diplom thesis about string topology under the supervision of Matthias Kreck. He stayed in Bonn to obtain his PhD in stable homotopy theory under the supervision of Stefan Schwede in 2012. Subsequently he became Whyburn Instructor at the University of Virginia, where he worked for two years. After a two-months stay at the Hausdorff Institute, he returned 2015 with a grant from the DFG (German Research Foundation) to Bonn as a postdoctoral researcher, until joining the Mathematical Institute at Utrecht University as Assistant Professor in 2018 and obtaining tenure in 2020.