Scientists / Open questions

Giorgio Parisi

Statistical physics; disordered and complex systems

2021 Nobel Prize in Physics

166 questions

Finite-clause-density corrections to the full-replica-symmetry-breaking ground-state theory of random K-SAT
Equilibrium determination of the thermodynamic glass transition in the 50:50 binary soft-sphere mixture: large-N equilibration through the Γ ≈ 1.65–1.7 specific-heat anomaly and finite-size scaling
Quantitative verification of constrained-potential (Franz-Parisi) predictions for dynamical correlations in finite-dimensional supercooled liquids: rounding below $T_c$ , the fate of the spinodal exponent $\gamma = 1/2$ , and the curvature-to-length mapping
Cutoff-localized non-convergence of subgrid closures for the Sabra shell model: mechanism, convergent approximation of the optimal conditional closure, and the LES feedback question
Hausdorff dimension of the strong-coupling random surfaces of lattice gauge theories and the resulting critical dimensions
Molecular arrangements of liquids under static negative pressure and the unexplained fracture signatures of stretched liquids: surviving open issues from the Berthelot-tube experiments of Richards and Trevena (1976)
Nonperturbative completion of the one-dimensional discretized string (c=1 matrix model / two-dimensional string theory): the non-Borel-summable genus expansion and the barrier boundary-condition ambiguity
Open completion problems for the Parisi-Zhang modified (quenched) Eguchi-Kawai reduction of large- $N$ gauge theory
Quenched Eguchi-Kawai volume independence: control of $1/N$ corrections and exact planar results for the reduced model
Finite-dimensional fate of the Dimensional Random Energy Model: lower critical dimension, transition order, and correlation-length crossover in spatial dimensions $d \ge 2$
Rotation-group structure, color-gauge invariance, and spin-statistics consistency in the Parisi-Zhang scalar formulation of staggered fermions
Glass transition, ordered phases, and the asymptotic maximal density of hard spheres on the Hamming hypercube: is the Varshamov–Gilbert bound tight?
Large-time statistics of diffusion-limited aggregation: turbulent deterministic growth versus fluctuations, and the controlled derivation of DLA scaling exponents
Individual-level interaction rules of natural bird flocks: form, the mechanism fixing the topological range, and generality across species and contexts
Dynamical structure factor of topologically disordered systems: high-frequency sound attenuation with realistic particle correlations and vector displacements
Entanglement-spectrum statistics of ergodic eigenstates and the entanglement critical length at the many-body localization transition: analytical theory and critical scaling
Replica symmetry breaking and activated hopping in the constrained Boltzmann-Gibbs effective-potential theory of the glass transition for three-dimensional simple liquids
Field-theoretic origin of the double power-law critical correlation function and the universality-class structure of the long-range-to-short-range crossover in the two-dimensional long-range Ising model
A predictive diagnostic for random-number-generator-induced bias in Monte Carlo simulations of critical systems (the surviving Parisi-Rapuano generator problem)
Large-order asymptotics of perturbation theory in the Yukawa model: fermionic Green functions, controlled fermion-determinant treatment, and the four-dimensional case
Reformulating mean-field glass theory beyond the Gaussian cage: consistent statics and dynamics of high-dimensional hard spheres, and the finite-dimensional fluctuation regime it enables
Subleading instanton asymptotics of the $O(N)$ quartic (N-vector) model beyond two loops in one dimension: the $1/K^{2}$ (four-loop) correction, two-loop correlation functions in $D\ge2$ , and the large-order behavior of renormalization constants and RG functions
Universality of human response to a deadline: validating the registration and payment dynamics of Alfi, Parisi and Pietronero across events and mechanisms
Nonperturbative completion of Parisi's infrared-counterterm program: uniqueness of multilocal infrared counterterms, the nonperturbative remainder, and renormalon-shielded instanton effects

Back to open problems

Finite-clause-density corrections to the full-replica-symmetry-breaking ground-state theory of random K-SAT

Equilibrium determination of the thermodynamic glass transition in the 50:50 binary soft-sphere mixture: large-N equilibration through the Γ ≈ 1.65–1.7 specific-heat anomaly and finite-size scaling

Quantitative verification of constrained-potential (Franz-Parisi) predictions for dynamical correlations in finite-dimensional supercooled liquids: rounding below TcT_cTc​, the fate of the spinodal exponent γ=1/2\gamma = 1/2γ=1/2, and the curvature-to-length mapping

Cutoff-localized non-convergence of subgrid closures for the Sabra shell model: mechanism, convergent approximation of the optimal conditional closure, and the LES feedback question

Hausdorff dimension of the strong-coupling random surfaces of lattice gauge theories and the resulting critical dimensions

Molecular arrangements of liquids under static negative pressure and the unexplained fracture signatures of stretched liquids: surviving open issues from the Berthelot-tube experiments of Richards and Trevena (1976)

Nonperturbative completion of the one-dimensional discretized string (c=1 matrix model / two-dimensional string theory): the non-Borel-summable genus expansion and the barrier boundary-condition ambiguity

Open completion problems for the Parisi-Zhang modified (quenched) Eguchi-Kawai reduction of large-NNN gauge theory

Quenched Eguchi-Kawai volume independence: control of 1/N1/N1/N corrections and exact planar results for the reduced model

Finite-dimensional fate of the Dimensional Random Energy Model: lower critical dimension, transition order, and correlation-length crossover in spatial dimensions d≥2d \ge 2d≥2

Rotation-group structure, color-gauge invariance, and spin-statistics consistency in the Parisi-Zhang scalar formulation of staggered fermions

Glass transition, ordered phases, and the asymptotic maximal density of hard spheres on the Hamming hypercube: is the Varshamov–Gilbert bound tight?

Large-time statistics of diffusion-limited aggregation: turbulent deterministic growth versus fluctuations, and the controlled derivation of DLA scaling exponents

Individual-level interaction rules of natural bird flocks: form, the mechanism fixing the topological range, and generality across species and contexts

Dynamical structure factor of topologically disordered systems: high-frequency sound attenuation with realistic particle correlations and vector displacements

Entanglement-spectrum statistics of ergodic eigenstates and the entanglement critical length at the many-body localization transition: analytical theory and critical scaling

Replica symmetry breaking and activated hopping in the constrained Boltzmann-Gibbs effective-potential theory of the glass transition for three-dimensional simple liquids

Field-theoretic origin of the double power-law critical correlation function and the universality-class structure of the long-range-to-short-range crossover in the two-dimensional long-range Ising model

A predictive diagnostic for random-number-generator-induced bias in Monte Carlo simulations of critical systems (the surviving Parisi-Rapuano generator problem)

Large-order asymptotics of perturbation theory in the Yukawa model: fermionic Green functions, controlled fermion-determinant treatment, and the four-dimensional case

Reformulating mean-field glass theory beyond the Gaussian cage: consistent statics and dynamics of high-dimensional hard spheres, and the finite-dimensional fluctuation regime it enables

Subleading instanton asymptotics of the O(N)O(N)O(N) quartic (N-vector) model beyond two loops in one dimension: the 1/K21/K^{2}1/K2 (four-loop) correction, two-loop correlation functions in D≥2D\ge2D≥2, and the large-order behavior of renormalization constants and RG functions

Universality of human response to a deadline: validating the registration and payment dynamics of Alfi, Parisi and Pietronero across events and mechanisms

Nonperturbative completion of Parisi's infrared-counterterm program: uniqueness of multilocal infrared counterterms, the nonperturbative remainder, and renormalon-shielded instanton effects

Quantitative verification of constrained-potential (Franz-Parisi) predictions for dynamical correlations in finite-dimensional supercooled liquids: rounding below $T_c$ , the fate of the spinodal exponent $\gamma = 1/2$ , and the curvature-to-length mapping

Open completion problems for the Parisi-Zhang modified (quenched) Eguchi-Kawai reduction of large- $N$ gauge theory

Quenched Eguchi-Kawai volume independence: control of $1/N$ corrections and exact planar results for the reduced model

Finite-dimensional fate of the Dimensional Random Energy Model: lower critical dimension, transition order, and correlation-length crossover in spatial dimensions $d \ge 2$

Subleading instanton asymptotics of the $O(N)$ quartic (N-vector) model beyond two loops in one dimension: the $1/K^{2}$ (four-loop) correction, two-loop correlation functions in $D\ge2$ , and the large-order behavior of renormalization constants and RG functions