Centre de recherches mathématiques - CRM Courses

Spectral Analysis of Dirac Operators with a Purely Imaginary Dislocation

Explore spectral analysis of Dirac operators with imaginary dislocation, covering Green functions, pseudospectra, and effects of matrix potentials on essential and discrete spectra.

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

Dirichlet-to-Neumann Map for the p-Laplacian on Metric Measure Spaces

Explore the Dirichlet-to-Neumann map for p-Laplacian on metric measure spaces. Delve into Newton-Sobolev spaces, trace classes, and Besov functions in the context of Dirichlet and Neumann problems.

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

A Panorama of Singular Sub-Laplacians and Their Spectra

Explore exotic properties of Laplace-Beltrami operators on rank-varying sub-Riemannian structures. Delve into self-adjointness, spectral properties, and sub-Riemannian Weyl laws. Discover open questions in this fascinating field.

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

The Moduli Space of Twisted Laplacians and Random Matrix Theory

Explore the convergence of spectral number variance for twisted Laplacians to random matrix theory ensembles, extending Rudnick's work to break time-reversal symmetry and include Dirac operators.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Two-sided Lieb-Thirring Bounds for Semi-bounded Schrödinger Operators

Explore upper and lower bounds for eigenvalues of semi-bounded Schrödinger operators, focusing on atomic Hamiltonians with Kato potentials and the landscape function in all spatial dimensions.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Computer-Assisted Global Analysis of Non-Smooth Impact Dynamics Inspired by Energy Harvesting

Delve into advanced mathematical analysis of vibro-impact dynamics, exploring computational methods for energy harvesting systems and non-smooth impact phenomena through novel return map approaches.

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

Is the World Smooth or Non-smooth? Mathematical Models in Dynamic Systems

Explore mathematical modeling approaches examining smooth vs non-smooth dynamics across climate, energy transfer, and neural systems, revealing insights into complex real-world phenomena.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Critical Metrics of Eigenvalue Functionals via Subdifferential

Explore critical metrics of eigenvalue functionals using subdifferential, covering Laplace and Steklov eigenvalues and offering new perspectives on Riemannian geometry.

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

Large Steklov Eigenvalues Under Geometric Constraints

Explore large Steklov eigenvalues in compact Riemannian manifolds, examining geometric constraints and constructing metrics with fixed volume and boundary conditions.

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

Extremely Amenable Automorphism Groups of Countable Structures

Explore extreme amenability in topological groups, focusing on automorphism groups of countable structures. Discover the abundance of non-isomorphic extremely amenable Polish groups.

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

On the Critical Points of Steklov Eigenfunctions

Explore critical points of Steklov eigenfunctions on Riemannian manifolds, examining relationships between eigenfunction indexes, boundary behavior, and Euler characteristics.

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

An Overdetermined Eigenvalue Problem and the Critical Catenoid Conjecture

Explore an overdetermined eigenvalue problem on the two-sphere and its implications for characterizing the critical catenoid as a unique embedded free boundary minimal annulus.

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

A Weighted Reilly Formula for Differential Forms and Sharp Steklov Eigenvalue Estimates - Lecture

Explore weighted Reilly formula for differential forms and its applications in sharp Steklov eigenvalue estimates. Gain insights into spectral geometry and related open problems.

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

New Minimal Surfaces via Equivariant Eigenvalue Optimization - Part II

Explore equivariant optimization of Laplace and Steklov eigenvalues on surfaces to construct embedded minimal surfaces in 3-sphere and 3-ball. Discover new insights into geometric analysis and topology.

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

New Minimal Surfaces via Equivariant Eigenvalue Optimization - Part I

Explore new embedded minimal surfaces in S³ and free boundary minimal surfaces in B³ through intrinsic shape optimization of Laplace and Steklov eigenvalues, considering symmetries and analytical challenges.

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