Lectures related to Untitled | EPFL Graph Search

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

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

Covers weak derivatives, their properties, and applications in functional analysis.

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Explores the dynamics of a block pulled by a spring under various conditions.

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Explores subsets and subgroups related to group actions on sets.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores group actions on sets, orbits, fixed points, and classic results.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

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

Explores quantum entanglement, Bell inequalities, and self-testing in quantum systems.

Covers the concept of graph sketching with a focus on connected components.

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Explores the conservation of linear momentum and stress in a continuum, focusing on governing equations and constitutive laws.