Centre International de Rencontres Mathématiques Courses

Nairian Models - Axiom of Determinacy and Forcing the Axiom of Choice

Explore Nairian Models under the Axiom of Determinacy, forcing techniques for the Axiom of Choice, and combinatorial principles in generic extensions with insights from set theory research.

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

Big Ramsey Degrees and Forcing

Explore advanced mathematical concepts connecting Big Ramsey degrees with forcing techniques in set theory through expert analysis and recent research developments.

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

The Tree Property on Long Intervals

Explore advanced set theory by examining the tree property across regular cardinals in the interval [ω₂, ℵ_{ω²+3}], featuring groundbreaking research on singular strong limits.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Two Complexity Results in Descriptive Set Theory - Hyperfinite and Hyper-Hyperfinite Equivalence Relations

Explore connections between hyperfinite equivalence relations and Borel amenability in descriptive set theory through two major complexity results.

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

Edge States in Periodic and Aperiodic Structures

Explore edge states in honeycomb structures like graphene, covering rational and irrational line defects with energy-conserving wave equations and localization phenomena.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Dimension Reduction in Thin Domains - Lecture 2

Explore dimension reduction techniques for thin domains, focusing on Dirichlet Laplacian behavior in 2D and 3D strips with varying geometries and boundary conditions.

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

Quantum Tunneling in Magnetic Systems

Explore quantum tunneling phenomena in magnetic systems, examining eigenvalue splitting elimination and ground state transitions in double well potentials under strong magnetic fields.

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

Dimension Reduction in Thin Domains - Lecture 1

Explore dimension reduction techniques for thin domains, examining Dirichlet Laplacian behavior on strips and how geometry affects eigenvalue asymptotics as width approaches zero.

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

An Introduction to Electromagnetic Waveguides - Lecture 1

Discover the mathematical foundations of electromagnetic waveguides, exploring guided modes, eigenvalue problems, and Maxwell equations through scalar and vector field analysis.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Local Decay and Asymptotic Profile for the Damped Wave Equation in Asymptotically Euclidean Settings

Explore advanced mathematical analysis of energy decay for damped wave equations in asymptotically Euclidean settings, covering optimal decay rates and asymptotic profiles.

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

An Introduction to Electromagnetic Waveguides - Lecture 2

Explore quadratic eigenvalue problems in electromagnetic waveguides, examining non-selfadjoint characteristics, spectral properties, and inverse modes using augmented Maxwell formulations.

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

Dynamical Systems and Ordinary Differential Equations

Explore advanced mathematical concepts in dynamical systems, differential equations, ergodic theory, and their applications across geometry, number theory, and physics.

• YouTube
• 2 weeks 15 hours 30 minutes
• Self-Paced
• Free Video

Descriptive Graph Combinatorics and Advanced Topics in Combinatorial Mathematics

Explore advanced mathematical topics through expert lectures on graph theory, random structures, algebraic combinatorics, and their applications in modern mathematics.

• YouTube
• 1 week 2 days 20 hours 33 minutes
• Self-Paced
• Free Video

Mathematical Physics - Lectures and Research Seminars

Explore advanced mathematical physics through expert lectures on plasma modeling, quantum systems, statistical mechanics, and cutting-edge research from leading international mathematicians.

• YouTube
• 2 weeks 1 hour 45 minutes
• Self-Paced
• Free Video

Numerical Analysis and Scientific Computing

Explore advanced computational methods, numerical algorithms, and mathematical modeling techniques for solving complex scientific problems across multiple disciplines.

• YouTube
• 1 week 2 days 23 hours 43 minutes
• Self-Paced
• Free Video