The Bôcher Memorial Prize 2026 recognises the joint work of Komvos’ Corresponding Member and Jonathan Luk on fundamental questions in general relativity.
Mihalis Dafermos, Professor of Mathematics at Princeton and a Corresponding Member of Komvos, received the Bôcher Memorial Prize 2026 from the American Mathematical Society, jointly with Jonathan Luk of Stanford. The award recognises their collaborative research on the interiors of rotating black holes and the ability of Einstein’s equations to determine the evolution of spacetime.
The Bôcher Memorial Prize is the oldest award of the American Mathematical Society (AMS). It is awarded every three years for outstanding research in mathematical analysis published in a recognised peer-reviewed outlet during the preceding six years.
Princeton’s announcement, dated 2 December 2025, links the award to their study of the stability of the Cauchy horizon in Kerr black holes. It notes that the result addresses the fundamental question of the uniqueness of solutions to the equations of general relativity and overturns earlier expectations.
The question concerns the predictive power of the theory itself: is knowledge of the initial state of spacetime sufficient to determine a unique future evolution?
What does the research reveal about black holes?
Dafermos and Luk’s work examines the geometry inside rotating black holes. It focuses on the Cauchy horizon, an internal boundary associated with the ability to predict the evolution of spacetime from initial data. This region tests the expectation that Einstein’s equations determine a unique evolution.
The Kerr solution to Einstein’s equations describes the geometry of a rotating black hole. The two mathematicians investigate what happens to its internal structure when that geometry is perturbed.
For the class of initial data they consider, they prove that spacetime can be extended beyond a portion of the Cauchy horizon with a continuous metric. The metric is the mathematical structure that describes the geometry of spacetime. This continuity is reflected in the term “C⁰-stability”, which appears in the paper’s title.
The result has implications for Roger Penrose’s strong cosmic censorship conjecture, which concerns the predictability of spacetime. The study identifies the conditions under which a particular formulation of the conjecture — inextendibility with a continuous metric — is false. It also points to the presence of singularities at the inner horizons, contributing to the search for a more precise mathematical formulation.
The publication and the standing of the award
The award-winning paper was published in Annals of Mathematics in 2025, following many years of research. The prize recognises a contribution at the intersection of mathematical analysis and general relativity, where the study of equations allows researchers to examine the behaviour of spacetime under extreme conditions.
The paper is entitled “The interior of dynamical vacuum black holes I: The C⁰-stability of the Kerr Cauchy horizon”. It spans 322 pages in volume 202 of the journal and was published online on 26 September 2025. Its first version was posted on arXiv in October 2017.
Stanford describes the Bôcher Memorial Prize as the AMS’s highest honour in mathematical analysis. Previous recipients include Norbert Wiener, Norman Levinson and Isadore Singer, as noted by MIT’s Department of Mathematics.
Semyon Dyatlov of MIT was also honoured in the 2026 award cycle for a separate body of research: his results on the control of eigenfunctions of the Laplace operator on surfaces with Anosov geodesic flows.
Mihalis Dafermos’ academic career
Mihalis Dafermos is the Henry Burchard Fine Professor of Mathematics at Princeton and the Lowndean Professor of Astronomy and Geometry at Cambridge. His research focuses on mathematical physics and general relativity, particularly the formation, stability and internal structure of black holes.
He graduated from Harvard in 1997 with the highest distinction, summa cum laude. He completed his PhD at Princeton in 2001 under the supervision of Demetrios Christodoulou.
His previous honours include the Adams Prize in 2004, the Bodossaki Prize in 2008, and the Whitehead Prize and IAMP Early Career Award in 2009. He has also been elected a Fellow of the American Mathematical Society and the International Society on General Relativity and Gravitation.
For Komvos, the recognition of Mihalis Dafermos, one of its Corresponding Members, has particular significance within the “Space Science, Technology and Industry” initiative. His work highlights the contribution of mathematical research to our understanding of the Universe and the international presence of Greek scientists in this field.
