Piet LammersJunior Professor
Piet Lammers holds a CNRS junior professorship. He is a member of the Laboratory of Probability, Statistics, and Modeling1. After studying at Utrecht University, he completed his Ph.D. at the University of Cambridge under the supervision of James Norris, followed by a postdoctoral fellowship at the IHES in Hugo Duminil-Copin’s research group. In 2023, he was invited to give a Peccot Lecture at the Collège de France for his work in statistical physics.
His research lies at the intersection of probability, combinatorics, and statistical physics. It focuses on phase transitions in lattice models, with a particular interest in the XY and Heisenberg models, for which he is developing new probabilistic and combinatorial approaches based on random paths and loops. More recently, in collaboration with Hugo Duminil-Copin and several co-authors, he has also contributed to advances in the six-vertex model, highlighting new links between integrable models and critical phenomena. His ERC project will help strengthen the research momentum at the LPSM by supporting the recruitment of postdoctoral researchers and hosting international visitors.
- 1
CNRS/SORBONNE UNIVERSITÉ/UNIVERSITÉ PARIS CITÉ
GeStruct (Geometric Structure of Lattice Spin O(N) models)
Why does a magnet suddenly become magnetic when cooled? Why do some materials become superconductors while others remain mere conductors? These phenomena arise from the collective behavior of a very large number of interacting particles and are among the fundamental questions of mathematical physics.
A major breakthrough for simpler models, such as the Ising model, involved translating particle interactions into random geometric structures derived from percolation theory. This approach has profoundly revitalized the available mathematical tools and enabled decisive progress in understanding phase transitions. However, for continuous-spin models, such as the XY and Heisenberg models, methods of comparable effectiveness are still lacking.
This project aims to develop new mathematical tools based on random paths and loops. Rather than directly studying particle interactions, this approach highlights hidden structures that make certain questions more accessible. By combining probability, combinatorics, and statistical physics, the project aims to advance our understanding of phase transitions and critical phenomena, while developing methods that may find applications in other areas of mathematical physics.