Smoothness

Related lectures (29)

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Covers Eisenstein series properties and spectral decomposition of functions.

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

Explores differentiable functions in R², including vector fields and coordinate transformations.

Explores obtaining n-th derivatives through a recursive process and the regularity of functions defined by power series.

Explores the transition from embedded to general manifolds, upgrading foundational concepts and discussing mathematical reasons for both approaches.

Provides an overview of optimization techniques, focusing on gradient descent and properties of convex functions in machine learning.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers the concept of bounding the Poisson bracket invariant on surfaces, exploring joint work with A. Logunov and S. Tanny.

Explores differentiability, tangent planes, and algebraic derivatives in functions of two variables.