Erwin Schrödinger International Institute for Mathematics and Physics (ESI) Courses

The Spectrum of Self-Adjoint Extensions Associated with Exceptional Laguerre Differential Expressions

Explore self-adjoint extensions of exceptional Laguerre-type differential expressions using boundary triples, Darboux transformations, and Maya diagrams to derive Weyl-Titchmarsh m-functions.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Schrödinger Operators with Delta-Potentials on Unbounded Lipschitz Surfaces

Explore Schrödinger operators with delta-potentials on unbounded Lipschitz surfaces, focusing on ground state uniqueness, essential spectrum, and Birman-Schwinger principle applications.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Continuum Limits for Discrete Dirac Operators on 2D Square Lattices

Explore continuum limits of discrete Dirac operators on 2D square lattices, focusing on convergence in strong resolvent sense and implications for complex analysis and quantum theory.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Three-Body Hamiltonians with Zero Range Interactions - ESI Workshop 2022

Explore quantum Hamiltonians for N-particle systems with zero range interactions, focusing on mathematical construction and regularization techniques for three-body systems.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

Geometrically Induced Discrete Eigenvalues of Dirac Operators with Lorentz Scalar Delta-Shell Interactions

Explore geometrically induced discrete eigenvalues of Dirac operators with Lorentz scalar δ-shell interactions on broken lines, revealing novel spectral properties in quantum theory.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Approximation of Dirac Operators with Delta-Shell Potentials

Explore approximation of 2D Dirac operators with δ-shell potentials using squeezed potentials. Analyze convergence in norm resolvent sense for specific interaction strengths.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Laminated Metamaterials - Divergence Form Equations and Homogenisation

Explore divergence form equations with sign-indefinite coefficients, solution criteria, and homogenization methods for oscillatory ill-posed problems in quantum theory.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Schrödinger Operators with Oblique Transmission Conditions in R2

Explore Schrödinger operators with oblique transmission conditions, examining self-adjointness, spectral properties, and connections to Dirac operators with delta-potentials in quantum theory.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Some Recent Developments in Generalised Norm Resolvent Convergence

Explore recent developments in generalised norm resolvent convergence, focusing on operators in different Hilbert spaces with illustrative examples.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

On the Class of Canonical Systems Corresponding to Matrix String Equations

Explore canonical systems with 2p×2p Hamiltonians, solving direct and inverse problems using Titchmarsh-Weyl functions and S-nodes. Learn construction procedures and high energy asymptotics of Weyl functions.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Inverse Spectral Theory for Strings and the Conservative Camassa-Holm Flow

Explore inverse spectral theory for generalized indefinite strings and its application to the conservative Camassa-Holm flow, focusing on characterizing spectral measures and Weyl-Titchmarsh functions.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Absence of Excited Eigenvalues for Fröhlich Type Polaron Models at Weak Coupling

Explore polaron models at weak coupling, focusing on the absence of excited eigenvalues below the essential spectrum in Fröhlich-type systems at zero total momentum.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

The Casimir Energy as a Trace

Explore the Casimir effect's connection to spectral geometry and microlocal analysis. Learn to define Casimir energy as an operator trace and compute it using boundary layer operator determinants.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Relative Oscillation Theory and Essential Spectra of Sturm-Liouville Operators

Explore relative oscillation theory for Sturm-Liouville operators, examining perturbation results and essential spectra invariance in terms of real coefficients p, q, and r.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Improved Lieb-Thirring Type Inequalities for Non-Selfadjoint Schroedinger Operators

Explore improved Lieb-Thirring inequalities for complex-valued Schroedinger operators, focusing on eigenvalue analysis and sharpness in one-dimensional cases.

• YouTube
• 41 minutes
• Self-Paced
• Free Video