Lectures related to Hyperbolic 3-manifold

Bird's-eye view and aims

Covers optimization on manifolds, smoothness, tools needed for optimization, and advanced algorithms using Hessians and Riemannian connections.

Small Scale Stability: Equilibrium Point

Discusses stability analysis of equilibrium points in dynamical systems.

Riemannian distance, geodesically convex sets

Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.

Gauge Theories: Chiral Transformations and Path Integrals

Covers the gauged Wess-Zumino-Witten model and its applications in conformal field theory.

Phase Portrait and Non-linear Systems

Covers phase portraits, eigenvalue decomposition, Jordan decomposition, and stable nodes in non-linear systems.

Spectral Analysis: Hyperbolic Surfaces

Explores the spectral analysis of hyperbolic surfaces through the trace formula and its applications in understanding geometric and spectral properties.