Michael Loss's Home Page

Talks and Papers

• On the Laplace Operator penalized by mean curvature

• Self-energy of electrons in non-perturbative QED

• A simple proof of a theorem of Laptev and Weidl

• Diamagnetic behavior of sums of Dirichlet eigenvalues

• Many-Body aspects of approach to equilibrium

• Ground States in Non-relativistic Quantum Electrodynamics

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

• 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.

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

• 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

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

• Logarithmic Sobolev inequalities and Spectral Gaps

• 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

• 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

• 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

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

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

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

• On the Markov sequence problem for Jacobi polynomials

• Self-adjointness via partial Hardy-like inequalities

• Low energy properties of the random displacement model

• Entropy and chaos in the Kac model

• Kramers degeneracy theorem in nonrelativistic QED

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

• Hardy inequalities for fractional integrals on general domains

Educational links

• Analysis  by Elliott Lieb and Michael Loss.

• Math 2605, J1, J2, Calculus for Computer Science Majors

• Math 4317, Analysis
  

• Math 1502 M1-M3, Calculus 2

• Math 6341, Partial Differential Equations

• Math 6342, Partial Differential Equations II
  

• Calculus Resou rces Online
• First-Year Calculus (Univ. of Toronto)
• The Geometry Center
• Maple
• Mathematica
• mathematical art
• computer art

Scientific links

• AAAS, American Association for the Advancement of Science
• AMS, American Mathematical Society
• APS, American Physical Society
• AIR, improbable research
• ESI, the Erwin Schrödinger Institut in Vienna
• Forum on Physics and Society
• mp-arc , a preprint archive for mathematical physics
• Los Alamos Archive another preprint archive for mathematical physics
• SIAM, Society for Industrial and Applied Mathematics