Twelve Tales in Mathematical Physics: An Expanded Heinemann Prize Lecture
arXiv:2011.12335 · doi:10.1063/5.0056008
Abstract
This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in non-relativistic quantum mechanics, constructive quantum field theory and statistical mechanics.
arXiv commentThis is the final presubmission version which has been submitted to J. Math. Phys
References in corpus (34)
- Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators
- Charge Deficiency, Charge Transport and Comparison of Dimensions
- Schrödinger Operators with Dynamically Defined Potentials: A Survey
- Marginal triviality of the scaling limits of critical 4D Ising and models
- Sharp Phase transitions for the almost Mathieu operator
- Dynamics and spectral theory of quasi-periodic Schrödinger-type operators
- On the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2
- Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two Pictures
- On Local Borg-Marchenko Uniqueness Results
- The absolutely continuous spectrum of the almost Mathieu operator
- The Origins of Lattice Gauge Theory
- Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line
- Analytic continuation of eigenvalues of a quartic oscillator
- Spectral theory of extended Harper's model and a question by Erdős and Szekeres
- Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics
- Asymptotics of Chebyshev Polynomials, I. Subsets of
- Asymptotics of Chebyshev Polynomials, II. DCT Subsets of
- A general resonance theory based on Mourre's inequality
- Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem
- Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States
- Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase
- Equality of the Spectral and Dynamical Definitions of Reflection
- Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices
- Schrodinger Operators with Purely Discrete Spectrum
- The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities
- Critical almost Mathieu operator: hidden singularity, gap continuity, and the Hausdorff dimension of the spectrum
- Large Deviations and the Lukic Conjecture
- Existence of Hartree-Fock excited states for atoms and molecules
- Proof of the Strong Scott Conjecture for Chandrasekhar Atoms
- Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian
- Critical Lieb-Thirring Bounds in Gaps and the Generalized Nevai Conjecture for Finite Gap Jacobi Matrices
- Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schrödinger Operators
- Topics in the theory of positive solutions of second-order elliptic and parabolic partial differential equations
- Remarks on Periodic Jacobi Matrices on Trees