Probability Seminar—Towards GFF convergence for the six-vertex model
报告人：Piet Lammers（Sorbonne Université）
时间：2025-06-16 14:00-15:00
地点：智化楼-四元厅
Abstract
The six-vertex model is a height function model that serves as a unifying framework for several two-dimensional statistical mechanics systems. In this talk, I will present a proof of a long-standing conjecture asserting that the height function converges, in a certain parameter regime, to the Gaussian Free Field (GFF). The proof combines techniques from different areas of mathematics: at its core is a soft analysis of the transfer matrix, which notably avoids reliance on the Bethe Ansatz. This analysis is made rigorous through probabilistic tools, including the Fortuin-Kasteleyn-Ginibre (FKG) inequality and Russo-Seymour-Welsh (RSW) theory. This is joint work with Hugo Duminil-Copin, Karol Kozlowski, and Ioan Manolescu. I will also discuss a closely related conjecture—that the Fortuin-Kasteleyn percolation associated with the six-vertex model converges in the scaling limit to a Conformal Loop Ensemble, CLE(κ).
Bio
Piet Lammers began his academic career at Utrecht University, before moving to the University of Cambridge for his master's and PhD in mathematics under the supervision of James Norris. From 2020 to 2023, he was a member of Hugo Duminil-Copin’s research group, working on height function models and the XY model in two dimensions. He is currently a junior professor at CNRS and Sorbonne Université. In 2023, he was awarded a Cours Peccot lecture series at the Collège de France.
