Lectures related to Curvature of Riemannian manifolds

Curvature and Inflection Points

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Riemannian Hessians: Definition and Example

Covers the definition and computation of Riemannian Hessians on manifolds.

Plates II: Föppl-von Kármán Equations

Covers the framework for plates, bending and stretching energies, and Föppl-von Kármán Equations, exploring mean and Gaussian curvatures.

Gaussian Curvature in Plates

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.

Mean and Gaussian Curvature

Explores mean and Gaussian curvature, emphasizing their calculation for different bases and surfaces.

Curvature and Osculating Circle

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

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.

Plates II: Mechanics of Slender Structures

Explores the mechanics of slender structures, discussing plate evaluation, bending energy, and curvature tensors.

Riemannian connections

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Mechanics of Kirchhoff Rods: Finite Strain and Rotation Theory

Explores the theory of finite strain and rotation in Kirchhoff rods, covering inextensible strains, finite rotations, and equilibrium.

Minimal Surfaces and Discrete Differential Geometry

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Shells I: Mechanics of Slender Structures

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Geometric Quantities in Parameterized Curves

Explores parameterized curves, regularity, and geometric quantities like the carbide vector and curvature.

Optimality Conditions: First Order

Covers optimality conditions in optimization on manifolds, focusing on global and local minimum points.

Plates II: Föppl-von Kármán Equations

Explores the theory of plates, including bending and stretching energies, and the Föppl-von Kármán Equations.

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Understanding Chaos in Quantum Field Theories

Explores chaos in quantum field theories, focusing on conformal symmetry, OPE coefficients, and random matrix universality.

Brown-York Stress Tensor

Covers the Brown-York stress tensor and its relation to AdS/CFT correspondence.

Geometric Principles in Architecture: Hyperboloids and Paraboloids

Discusses geometric principles in architecture, focusing on hyperboloids and paraboloids and their applications in design and structural engineering.