News: “Frontiers of Science Award” for UR Mathematician Prof. Kings

The article, "Eisenstein-Kronecker classes, integrality of critical values of Hecke L-functions and p-adic interpolation", which is forthcoming in the Annals of Mathematics, resolves a nearly 50-year-old conjecture on L-functions of abelian varieties with complex multiplication, originally formulated by N. Katz and P. Deligne in 1977.

L-functions are fundamental invariants of systems of equations, encoding key arithmetic properties such as the number of integer solutions. The conjecture states that these L-functions take integral values, leading to surprising congruences between them. While partial results were previously established by N. Katz (1977) and D. Blasius (1983) for significant cases, Prof. Kings and Prof. Sprang have now completed the proof for all remaining cases. Their breakthrough introduces a novel construction, Eisenstein-Kronecker classes, which is expected to have further applications in the field. “I am very pleased about this award, which impressively confirms the research strength and international visibility of the CRC Higher Invariants in Regensburg”, says Prof. Kings. 

Prof. Dr. Guido Kings studied mathematics and philosophy at the Universities of Bonn and Princeton. He obtained his PhD in 1994 at the University of Münster, where he also completed his habilitation in the year 2000. In 2001, he was appointed a research professor at the Max Planck Institute for Mathematics in Bonn before accepting a professorship at the University of Regensburg later that year. Since 2014, he has served as the spokesperson of the Collaborative Research Center 1085 "Higher Invariants" in Regensburg. For his contributions to mathematics, he has received multiple honors, including an invited lecture at the International Congress of Mathematicians (ICM) in 2002. Since 2012, he has also been a Fellow of the American Mathematical Society (AMS) (inaugural class).

Prof. Dr. Johannes Sprang completed his PhD and habilitation in Regensburg. Since 2021, he has been a tenure-track professor at the University of Duisburg-Essen and a Principal Investigator in the Collaborative Research Center 1085 "Higher Invariants".