Geometry and Symmetry in Non-Convex Optimization

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Riemannian connections: What they are and why we care

Covers Riemannian connections, emphasizing their properties and significance in geometry.

Smooth Manifolds: Setup

Introduces smooth manifolds, emphasizing the importance of submanifolds of linear spaces.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Affinity and Ellipses in Descriptive Geometry

Explores affinity in geometry, segment construction, ellipses, and circle projections.

Symmetry in Geometry

Emphasizes the importance of maintaining a dedicated time for geometry in the weekly schedule.

Inversion & Family of Orthogonal Circles

Explores inversion, orthogonal circles, unique projective, and non-constructible figures in geometry.

Momentum methods and nonlinear CG

Explores gradient descent with memory, momentum methods, conjugate gradients, and nonlinear CG on manifolds.

Optimization with Constraints: KKT Conditions

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Symmetry in Modern Geometry

Covers symmetry in modern geometry, reflections, translations, rotations, compositions of isometries, fundamental theorems, configurations of lines and planes, and surface analysis.