Welcome to my webpage! My name is Piet Lammers, I am a CNRS researcher in probability theory and mathematical physics, currently based at Sorbonne Université (Jussieu), in the Laboratory of Probability, Statistics, and Modeling (LPSM). With my research group, we are mostly interested in the mathematics of phase transitions.
- 🇬🇧 An introduction to our research
- 🇳🇱 Een inleiding tot ons onderzoek
- 🇫🇷 Une introduction à nos recherches
Research overview for specialists. Together with members of my research group and our collaborators, we study phase transitions in lattice models, with a focus on two-dimensional discrete height functions, their localisation and delocalisation, and their scaling limits. We study these questions in connection with the XY model and its Berezinskii–Kosterlitz–Thouless transition, the six-vertex model, and the random-cluster model, including Bernoulli percolation.
Funding. My research group acknowledges the following funding.
- ANR: grant ANR-23-CPJ1-0150-01, 2023–2028.
- ERC Starting Grant: GeStruct (101302988), 2027–2032.
- Two members of our research group receive support from FSMP.
- One member of our research group receives support from ENS.
A simulation of the square ice model
News and announcements
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Junior workshop on statistical mechanics at CIRM
2–6 August 2027, Marseille, FranceTogether with Lucas D'Alimonte, Franco Severo, and Diederik van Engelenburg, we are organising a junior workshop on statistical mechanics at CIRM in Marseille. The workshop brings together early-career researchers to discuss recent developments and open problems in statistical mechanics. See the workshop website for the programme and registration details.
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Two new preprints: conformal invariance of the six-vertex and four-state Potts models
5/6 October 2026Emile Averous, Hugo Duminil-Copin, Tiancheng He, Ioan Manolescu, and I have completed two new papers: “Conformal invariance of the six-vertex model’s height function” and “Conformal invariance of the planar four-state Potts model and its random-cluster representation”. The papers mix exact techniques (transfer matrix formalism) and percolation theory in a new way, in order to turn the recent result on six-vertex GFF convergence on the full-plane, in a result in finite domains.
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Preprint “Gaussian free field convergence of the six-vertex model with Delta between -1 and -1/2”
6 March 2026Hugo Duminil-Copin, Ioan Manolescu, Karol Kozlowski, and I uploaded a manuscript of our project “Gaussian free field convergence of the six-vertex model with Delta between -1 and -1/2” to arXiv. This work already has important applications in the context of two-dimensional percolation, for example, it was used to derive the value of one- and two-arm exponents in the random-cluster model (including Bernoulli bond percolation) at criticality; a longstanding open problem in the field.
Meeting Geometric Methods in Percolation and Spin Models
2-13 March 2026, ICTS, Bengaluru, India
Subhajit Goswami, Trishen Gunaratnam, and I organised a spring school and workshop on Geometric Methods in Percolation and Spin Models at the ICTS in Bengaluru, India. See the website for more details.
Preprint “The BKT transition and surface tension differentiability”
27 May 2026Thibault Durand and I uploaded a manuscript of our project on the mass of the 2D XY model, the mass of the dual height function, and the free energy at a slope to arXiv. We prove that the mass in the XY model is precisely the right derivative of the free energy at zero slope. In particular, the BKT transition is characterised by the differentiability of the free energy at zero slope.
Preprint “Free energy analyticity of the disordered XY model and Debye screening in the 2D Coulomb gas”
27 March 2026Lucas D'Alimonte and I uploaded a manuscript of our project on the 2D XY and Villain models and the relationship with the Coulomb gas to arXiv. We prove that the XY and Villain models are finite factors of i.i.d. with exponential volume tails in the disordered phase, which implies a strong form of Debey screening.
Inhomogeneous Random Systems conference at IHP (Paris)
27-28 January 2026Two-day conference organised by Christian Maes, Kirone Mallick, and Ellen Saada. I moderated the first day.
Cours Peccot
I recently taught a Cours Peccot at Collège de France (see the videos below).
Upcoming talks
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Tuesday 10 November 2026, 10:30–11:30, Université Paris-Dauphine – PSL, room A711.
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Séminaire Analyse–Probabilités
Conformal invariance of the six-vertex model's height function
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Thursday 12 November 2026, 11:00, LPTHE library, Jussieu campus, tower 13–14, fourth floor.
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Séminaire Darboux
Conformal invariance of the six-vertex model's height function
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Monday 10 May 2027, Individual lecture dates and times TBA, École de Physique des Houches, Les Houches, France.
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Mathematical Statistical Physics School (10–21 May 2027)
Berezinskii-Kosterlitz-Thouless transition: links between the XY model and height functions
Recent talks
One World Mathematical Physics Seminar of the IAMP (Apr 2026, One World IAMP Mathematical Physics Seminar)
Workshop on Topological Phase Transition and Localization of Random Fields (Dec 2025, Center for Mathematical Modeling, University of Chile)
Probability seminar, University of Bath (Sep 2025, University of Bath)
Trimester Program: Probabilistic methods in quantum field theory (Jul 2025, Hausdorff Research Institute for Mathematics, Bonn)
Probability Seminar (Jun 2025, Beijing International Center for Mathematical Research)
Workshop on mathematical physics (Feb 2025, SwissMAP Research Station)
Workshop on statistical mechanics at UNIGE (Jan 2025, University of Geneva)
Mini-Workshop: Critical Phenomena of the XY Model (Nov 2024, Oberwolfach)
Bangalore Probability Seminar (Oct 2024, Online)
Séminaire de probabilités (Oct 2024, Aix Marseille Université)Contact details
- Visiting address
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Office 16-26.108
LPSM, Sorbonne Université
Campus Pierre et Marie Curie
4, place Jussieu
75005 Paris
France - Mail address
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LPSM, Sorbonne Université
Campus Pierre et Marie Curie
Case courrier 158
4, place Jussieu
75252 Paris CEDEX 05
France - Email address
- piet.lammers@cnrs.fr