Centre International de Rencontres Mathématiques Courses

Artin Approximation and Singularity Theory

Explore advanced mathematical concepts in Artin approximation, singularity theory, and algebraic geometry through expert lectures on formal power series and algebraic equations.

• YouTube
• 8 hours 20 minutes
• Self-Paced
• Free Video

Computational Time-Frequency and Coorbit Theory

Explore advanced mathematical analysis through computational time-frequency methods, coorbit theory, and function spaces with applications to wavelets, Gabor frames, and operator theory.

• YouTube
• 12 hours 20 minutes
• Self-Paced
• Free Video

Number Theory and its Applications to Cryptography

Explore advanced number theory applications to cryptography through elliptic curves, Frobenius distributions, and pseudorandom generators in this comprehensive mathematical semester.

• YouTube
• 20 hours 5 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

Dendric and Eventually Dendric Words - Lecture 1

Explore dendric sequences, their combinatorial properties, and connections to interval exchange transformations and episturmian sequences in this mathematical lecture.

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

Dendric and Eventually Dendric Words - Lecture 2

Explore dendric sequences and their combinatorial properties, focusing on return words and factor complexity in mathematical word theory.

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

On Expansions of Monadic Second-Order Logic with Power Predicates - Lecture 1

Explore the decidability of monadic second-order logic expanded with arithmetic predicates, connecting logic and automata theory through classical and modern techniques.

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

SBCW-Complexes and n-Cost

Explore advanced mathematical concepts connecting measure-preserving standard Borel groupoids, CW complexes, and n-dimensional cost theory for countable groups.

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

Towards Synthetic Locale Theory

Explore synthetic approaches to locale theory using type theory to build "synthetic mathematics for synthetic mathematics" inspired by Blechschmidt's duality axiom and large sheaves.

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