• Fluxes, Laplacians and Kasteleyn's Theorem

• Uniform Density Theorem for the Hubbard Model

• There are No Unfilled Shells in Hartree-Fock Theory

• Stability of Matter in Magnetic Fields

• Stability of Relativistic Matter via Thomas-Fermi Theory

• On the Laplace Operator penalized by mean curvature

• Optimal eigenvalues for some Laplacians and Schrödinger operators depending on curvature

• Self-energy of electrons in non-perturbative QED

        2000

• A simple proof of a theorem of Laptev and Weidl

• Diamagnetic behavior of sums of Dirichlet eigenvalues

• Many-Body aspects of approach to equilibrium

       2001

• Ground States in Non-relativistic Quantum Electrodynamics

       2002

• Stability of a model of relativistic Quantum Electrodynamics

• A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics

•  Commentaries of Michael Loss and Mary-Beth Ruskai to the `Selecta Elliott Lieb' on Inequalities.

       2003

• Determination of the spectral gap for Kac's master equation and related stochastic evolutions

• Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics

       2004

• An analytical proof of Hardy-like inequalities related to the Dirac operator

• A Note on Polarization Vectors in Quantum Electrodynamics

• Connection between the Lieb-Thirring conjecture for Schroedinger operators and an isoperimetric problem for ovals in the plane

• A Sharp analog of Young's Inequality on S^N and Related Entropy Inequalities

• Logarithmic Sobolev inequalities and Spectral Gaps

       2005

• The thermodynamic limit for matter ineracting with Coulomb forces and with the quantized electromagnetic field: I.  The lower bound

       2006

• Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems

• An Inequality of Hadamard Type for Permanents

• Inequalities for means of chords, with applications to isoperimetric problems

       2007

• Stability of Matter (review for the Young Researchers Symposium in Lissabon 2003)

• Lowest energy in non-relativistic QED: atoms and ions in motion

• Relativistic hydrogen atoms in strong magnetic fields

• Selfadjointness of Dirac Operators via Hardy-Dirac inequalities

       2008

• The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space

• Determination of the spectral gap in the Kac model for physical momentum and energy conserving collisions

• Validity of the Brunet-Derrida formula for the speed of pulled fronts with a cutoff

• Lieb-Thirring inequalities with improved constants

• Minimizing the ground state energy of an electron in a randomly deformed lattice

• Stability of atoms and molecules in an ultrarelativistic Thomas-Fermi-Weizsaecker model

• Characterization of the critical magnetic field in the Dirac-Coulomb equation

• Self-adjointness via partial Hardy-like inequalities

       2009

• Polya's conjecture in the presence of a constant magnetic field

• Low energy properties of the random displacement model

• Kramers degeneracy theorem in nonrelativistic QED

• On the symmetry of extremals for the Caffarelli-Kohn-Nirenberg inequalities

       2010

• Entropy and chaos in the Kac model

• Hardy inequalities for fractional integrals on general domain

• Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows

       2011

• On the Markov sequence problem for Jacobi polynomials

• Rigorous results for the speed of Kolmogorov--Petrovskii--Piscounov fronts with a cutoff

• Kinetic theory and the Kac master equation  

• Localization for the random displacement model (a short review for qmath 11)

       2012

• Hardy-Sobolev-Mazy'a inequalities for arbitrary domains

• Localization for the random displacement model

• A new estimate on the indirect Coulomb energy

• Sharp trace inequalities for fractional Laplacians

• Understanding  the random displacement model: From ground-state properties to localization
  

• Symmetry of extremals of functional inequalities via spectral estimates for linear operators 
  

      2013

• Sharp interpolation inequalities on the sphere : new methods and consequences

• Spectral gap for the Kac model with hard sphere collisions

• Spectral properties of Schrödinger operators on compact manifolds, flows, interpolation and spectral estimates

• Entropic Chaoticity for the Steady State of a Current Carrying System

      2014

• Nonlinear flows and rigidity results on compact manifolds

• One-dimensional Gagliardo-Nirenberg-Sobolev inequalities: Remarks on duality and flows

• The Kac model coupled to a thermostat

• Improved interpolation inequalities on the sphere

      2015

• Keller-Lieb-Thirring inequalities for Schrödinger operators on cylinders

     
      2016

• One-dimensional interpolation inequalities, Carlson--Landau inequalities and magnetic Schrödinger operators

• Monotonicity of the period of a non-linear oscillator

• On a quantum entropy power inequality of Audenaert, Datta and Ozols

• Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces

• Interpolation inequalities, nonlinear flows, boundary terms, optimality and linearization

       2017

• Symmetry for extremal functions in subcritical Caffarelli-Kohn-Nirenberg inequalities

• Uniform approximation of a Maxwellian thermostat by finite reservoirs

• Interpolation inequalities on the sphere: linear vs. nonlinear flow

• General pairing mechanism in the BCS-theory of superconductivity

      2018

• Interpolation inequalities and spectral estimates for magnetic operators

• Persistence of translational symmetry in the BCS model with radial pair interaction

•  Symmetry and symmetry breaking: rigidity and flows in elliptic PDEs

•  Entropy decay for the Kac evolution

•  Magnetic Rings  

       2019

• Symmetry of optimizers of the Caffarelli-Kohn-Nirenberg inequalities

•  Chaos, ergodicity and equilibria in a quantum Kac model

      
       2020

• Spectral gaps for reversible Markov processes with chaotic invariant measures: The Kac process with Hard Sphere Collisions in Three Dimensions
  

•  Symmetry results in two dimensional inequalities for Aharonov-Bohm magnetic fields

      
       2021

• On the convolution inequality f > f star f

• Non-linear Schrödinger equation in a uniform magnetic field

• Critical magnetic fields for 2d magnetic Dirac-Coulomb operators and Hardy inequalities

• Decay of information for the Kac evolution

• Inequalities involving Aharonov-Bohm magnetic potentials in dimensions 2 and 3
  

      
       2022

• A remark on a paper by Hundertmark and Simon

• Existence of optimizer in a Sobolev inequality for vector fields

• Which magnetic fields support a zero mode?

      
       2024

• On an inequality of Lin, Kim and Hsieh and Strong Subadditivity

      
       2025

• Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence

• A short review on improvements and stability for some interpolation inequalities

      
       2026

• A sharp criterion for zero modes of the Dirac equation

      
       Recent papers

• Spectrum for some Quantum Markov semigroups describing N-particle systems evolving under a binary collision mechanism

• The CKN inequality for spinors: symmetry and symmetry breaking

• A Kac system interacting with two heat reservoirs