Geodesics in Wasserstein Space

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Distance and geodesics: Distance, geodesics and complete manifolds

Covers the concept of distance induced by the Riemannian metric on manifolds.

Optimization on Manifolds: Context and Applications

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

Forcing of Topological Entropy

Delves into topological entropy in compact manifolds and Reeb flows, emphasizing the forcing of entropy via cylindrical contact homology.

Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Momentum methods and nonlinear CG

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

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.

Diophantine Approximation on Manifolds: Lower Bounds

Covers Diophantine approximation on manifolds with a focus on lower bounds.

Smooth maps and differentials: Differentials

Explores smooth maps, differentials, composition properties, linearity, and extensions on manifolds.

Connections: Axiomatic Definition

Explores connections on manifolds, emphasizing the axiomatic definition and properties of derivatives in differentiating vector fields.

Pseudorandomness: Theory and Applications

Explores pseudorandomness theory, AI challenges, pseudo-random graphs, random walks, and matrix properties.