Prix Piaget 2025 - Corentin Bodart
We are pleased to announce that Corentin Bodart has been awarded the 2025 Piaget Prize, which is presented in rotation each year in astronomy, mathematics, or physics and recognises the best doctoral thesis in the discipline concerned.
His doctoral thesis in mathematics, entitled Geometric and algorithmic aspects of nilpotent groups, was defended on 31 October 2024 under the supervision of Tatiana Nagnibeda. This year, the prize acknowledges the quality of this doctoral work. We warmly congratulate him on this distinction.
Abstract: Nilpotent groups are among the best understood classes of groups in geometric group theory. This thesis highlights that nilpotent groups also behave in surprising ways. First, we prove that the growth of the number of geodesics in some virtually nilpotent groups is intermediate, these are the first groups presenting this property. Next, we study the horofunction boundary of some groups, highlighting important differences between nilpotent groups of class 2 and 3, both regarding the action of a group on its boundary, or the number of Busemann points. The second half of the thesis takes an algorithmic direction, studying the membership problems to submonoids and rational subsets. We show that these two problems are not equivalent even within nilpotent groups of class 2, and solve the second problem in the Heisenberg group. Finally, the last two chapters investigate complete growth series and Green series.
Following the completion of his PhD, Corentin Bodart began a postdoctoral position at the AV短视频 of Oxford in January 2025, funded by the SNSF. His current research continues along the lines of his thesis, with recent work focusing on on membership problems but looking at other groups (metabelian groups, permutations groups, Grigorchuk's group) and from different perspectives (decidability but also languages, distortion, separability). He is also working toward a deeper understanding of Thompson’s groups, a task he notes may well be the work of a lifetime.