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Related lectures (30)
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Geodesic Convexity: Basic Definitions
Introduces geodesic convexity on Riemannian manifolds and explores its properties.
Ruelle resonances for geodesic flow on noncompact manifolds
Explores Ruelle resonances for geodesic flow on noncompact manifolds, delving into complex mathematical formulas.
Connections: Axiomatic Definition
Explores connections on manifolds, emphasizing the axiomatic definition and properties of derivatives in differentiating vector fields.
Group Theory in Physics
Covers the fundamentals of group theory in physics, focusing on symmetries and transformations leaving physical equations unchanged.
Differentiating vector fields: Why do it?
Explores the importance of differentiating vector fields and the correct methodology to achieve it, emphasizing the significance of going beyond the first order.
Riemann Surfaces: Complex Manifolds
Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.
Forcing of Topological Entropy
Delves into topological entropy in compact manifolds and Reeb flows, emphasizing the forcing of entropy via cylindrical contact homology.
Riemannian Gradient Descent: Convergence Theorem and Line Search Method
Covers the convergence theorem of Riemannian Gradient Descent and the line search method.
Momentum methods and nonlinear CG
Explores gradient descent with memory, momentum methods, conjugate gradients, and nonlinear CG on manifolds.
Smooth maps and differentials: Differentials
Explores smooth maps, differentials, composition properties, linearity, and extensions on manifolds.
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