Lectures related to Hyperbolic 3-manifold

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Invariant Integral Operators

Explores invariant integral operators and their spectral properties on hyperbolic surfaces.

Spectrum of Hyperbolic Surfaces

Explores the spectrum of hyperbolic surfaces, discussing thin C-principle, grad, normalized functions, minimum volume, and embedding properties.

Dynamics of Steady Euler Flows: New Results

Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.

Fractal Uncertainty Principle and Spectral Gaps

Explores Schottky groups, spectral gaps, and the Fractal Uncertainty Principle.

Möbius Transformations: Properties and Applications

By the instructor Malo Jézéquel explores Möbius transformations and bounded distortion in SL(2, R).

Spectrum of Hyperbolic Surfaces

Explores the Laplacian, Riemannian metric, and invariant operators in hyperbolic surfaces.

Ruelle resonances for geodesic flow

Explores Ruelle resonances for geodesic flows on non-compact manifolds, emphasizing the role of smoothness and eigenvalues in the dynamics.

Bifurcation and fractals in complex dynamical systems

Explores bifurcation, fractals, Julia sets, Mandelbrot set, and self-similarity in complex dynamical systems.

Spectrum of Hyperbolic Surfaces

Explores the spectrum of hyperbolic surfaces, focusing on Fuchsian groups and their actions.

3-dimensional Anosov flows: Stable Manifolds and Foliations

Explores stability properties of 3-dimensional Anosov flows, focusing on manifolds and foliations.

Fractal Uncertainty Principle and Spectral Gaps

Explores transfer operators, Patterson-Sullivan measure, FUP, spectral gaps, and resonances in Schottky groups.

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Unit Tangent Bundle of Hyperbolic Spaces

Covers the unit tangent bundle of hyperbolic spaces and geodesic flows.

Extreme Problems in Diophantine Approximation and Dynamics

Explores the Logarithmic Law, geodesic flows, hyperbolic surfaces, and rare events in probability.

From embedded to general manifolds: upgrading our foundations

Explores the transition from embedded to general manifolds, upgrading foundational concepts and discussing mathematical reasons for both approaches.

Distance, geodesics and complete manifolds: Complete manifolds

Explores distance, geodesics, and complete manifolds, emphasizing the existence of minimizing geodesics and the concept of metric completeness.

Spectral Expansion: Eisenstein Series

Covers the spectral expansion of Eisenstein series and the properties of hyperbolic surfaces.

Periodic Orbits of Hamiltonian Systems

Covers the theory of periodic orbits of Hamiltonian systems and the Conley-Zehnder index.