Geometry and Symmetry in Non-Convex Optimization

Related lectures (25)

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Introduces optimization on manifolds, covering classical and modern techniques in the field.

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Explores orthogonal projections, symmetry of matrices, and their applications.

Delves into modern geometry, covering transformations, isometries, and symmetries.

Explores symmetry and boundary conditions in finite element models, emphasizing the importance of maintaining symmetry for accurate modeling.

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.

Explores modern symmetry in geometry, covering transformations, isometries, orientations, and practical applications.

Introduces a new online format for the geometry course, emphasizing the study of isometries and the modern interpretation of symmetry.

Covers circle orthogonal and Poincaré disk concepts in geometry.