Dirac Operator Courses and Certifications

Centre de recherches mathématiques - CRM

Curvature Contribution to the Essential Spectrum of Dirac Operators with Critical Shell Interactions

Explore the essential spectrum of 3D Dirac operators with critical shell interactions, examining how surface geometry influences spectral properties in quantum mechanics.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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
• On-Demand
• Free Video

Prague Mathematical Physics Seminar

Cubic and Non-cubic Dirac Operators - Applications in Algebraic and Differential Geometry

Explore algebraic Dirac operators, their cohomology, and applications in differential geometry. Delve into Vogan's construction and its generalizations.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

The Topological Dirac Operator and the Dynamics of Topological Signals

Explore topological signals, higher-order Laplacians, and the Dirac operator in network science. Learn about spectral properties, diffusion dynamics, and topological synchronization in simplicial complexes and multiplex networks.

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

Prague Mathematical Physics Seminar

Cubic Dirac Operator for U_q(sl_2)

Explore quantum group theory and cubic Dirac operators, focusing on U_q(sl_2) generalization. Gain insights into special linear algebra sl(2) and its quantum counterparts.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Topology Shapes Dynamics of Higher-order Networks

Exploring how higher-order network interactions influence non-linear dynamics, synchronization, and percolation in complex systems like brain networks and climate patterns.

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

ICTP Mathematics

Frontiers in Geometry and Topology Summer School

Explore advanced topics in geometry and topology including Heegaard Floer homology, Dirac operators, pseudoholomorphic curves, and Seiberg-Witten equations through expert lectures.

• YouTube
• 15 hours 34 minutes
• On-Demand
• Free Video

Fields Institute

Homological Methods in Random Noncommutative Geometry

Explore homological methods in random noncommutative geometry, covering fuzzy spectral triples, Dirac operators, and connections to random matrix theory and BV formalism.

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

ICTP Mathematics

Families of Dirac Operators and Applications

Explore advanced concepts in geometry and topology, focusing on families of Dirac operators and their applications in mathematical physics and differential geometry.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

ICTP Mathematics

Families of Dirac Operators and Applications

Explore Dirac operators and their applications in geometry and topology, focusing on families and their mathematical significance in advanced theoretical frameworks.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

Fields Institute

A Fixed-Point Formula for Dirac Operators on Lie Groupoids

Explore fixed-point formulas for Dirac operators on Lie groupoids, delving into advanced mathematical concepts and their applications in geometric analysis.

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

Hausdorff Center for Mathematics

Dirac Operators Built from Quantum Riemannian Geometries

Explore quantum Riemannian geometries and their application in constructing Dirac operators, delving into advanced mathematical concepts at the intersection of quantum theory and geometry.

• YouTube
• 1 hour 6 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

Hausdorff Center for Mathematics

Curvature of the Determinant Line Bundle for Noncommutative Tori

Explore differential geometry of curved noncommutative tori, including spectral invariants and curvature of determinant line bundle for Dirac operators on noncommutative two tori.

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