Scientists / Open questions

Hugo Duminil-Copin

Probability; statistical physics; phase transitions

2022 Fields Medal

8 questions

Geometry and statistics of simultaneous-arrival clouds in the monotone coupling of the planar FK-Ising model
Benjamini's conjecture: the limiting shape of intrinsic-metric balls in the supercritical percolation infinite cluster becomes round as p approaches p_c
Conformal invariance of the critical self-avoiding walk on the hexagonal lattice: convergence to chordal SLE(8/3)
Fourth and higher-order correction terms for two-dimensional anisotropic bootstrap percolation, and the unproved $(1,b)$ -family expansion
The Batchelor–Yung critical surface fugacity $y_c(n)=1+2/\sqrt{2-n}$ of the honeycomb half-plane $O(n)$ loop model, and the sharp $T^{-1/4}$ decay of critical bridges
Open problems in the continuum bridge decomposition of restriction measures (Alberts-Duminil-Copin, 2010)
Recovery from forest fires (self-destructive percolation) on $\mathbb{Z}^d$ in low dimensions
Percolation thresholds for critical bootstrap models with axis-contained update rules: sharp constants in two dimensions, coarse thresholds in higher dimensions

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