Lectures related to Hyperbolic manifold

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.

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

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

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

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

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

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

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

Explores linear response for chaotic systems, discussing SRB states, Lyapunov exponents, and convergence of the response formula.

Explores the dynamics of singular Riemann surface foliations and their intricate behavior.

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

Covers ODE RK schemes, including explicit RK stages and accuracy computation.

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

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

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

Covers dynamical approaches to the spectral theory of operators.

Covers the spatial response of systems, including the calculation of the center of mass and convolution.

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

Discusses stability analysis of equilibrium points in dynamical systems.