Spectral Theory Courses and Certifications

Institute for Advanced Study

Ellipses of Small Eccentricity Are Determined by Their Dirichlet - Steven Morris Zelditch

Explore the spectral analysis of ellipses with small eccentricity, focusing on Dirichlet and Neumann spectra, caustic billiard tables, and periodic orbits in nearly circular domains.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

Fields Institute

Convergence of Scattering Data and Non-Linear Fourier Transform - Part 1

Explore canonical systems, spectral problems, and Hilbert spaces of entire functions in this advanced mathematical analysis lecture on scattering data and non-linear Fourier transform.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Outliers in Sparse Wigner Matrices

Explore the impact of sparsity on extreme eigenvalues in Wigner matrices, including phase transitions and outlier emergence in the semi-circular law. Joint work with Konstantin Tikhomirov.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Maria Esteban - Spectral Results and Open Problems for Dirac-Coulomb Operators With Charge Distributions

Explore spectral results and open problems for Dirac-Coulomb operators with general charge distributions, focusing on self-adjoint extensions, eigenvalue characterizations, and electron stability conditions.

• YouTube
• 49 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

On Non-Commensurable Isospectral Locally Symmetric Spaces by C.S. Rajan

Explore non-commensurable isospectral locally symmetric spaces with C.S. Rajan. Delve into advanced mathematical concepts and their applications in geometry and number theory.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

Spectral Mapping Theorem for Normal Operators - Continuous Functions

Explore the spectral mapping theorem for normal operators and its applications to continuous functions in operator theory.

• YouTube
• 19 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Spectral Perturbation Formulae for Quenched Random Dynamics with Applications - Lecture

Explore spectral perturbation formulae for quenched random dynamics and their applications in this mathematical conference talk by Gary Froyland.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Spectra of Laplace and Dirac Operators on Noncompact Manifolds

Explore spectra of Laplace and Dirac operators on complete manifolds, including types of spectra, results for special behaviors at infinity, and effects of additional potentials.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

On the L^p Spectrum of the Laplacian on Riemannian Manifolds

Explore the $L^p$ spectrum of the Laplacian on manifolds, including resolvent sets, Weyl criterion, and hyperbolic space, with insights on conformally compact manifolds.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Computing Nodal Deficiency with a Refined Spectral Flow

Explore connections between Dirichlet-to-Neumann map, spectral flow, and nodal deficiency in Laplacian eigenfunctions. Discover improved bounds and applications to spectral minimal partitions.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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
• On-Demand
• Free Video