Simplices

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Related lectures (32)

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Simplicial and Singular Homology Equivalence

Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.

Simplicial Homology: Structure and Complexes

Covers the structure of topological spaces with A-complexes and chain complexes.

Singular Homology: First Properties

Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.

Convex Optimization: Elementary Results

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Convex Sets: MGT-418 Lecture

On Convex Optimization covers course organization, mathematical optimization problems, solution concepts, and optimization methods.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Hamiltonian dynamics on convex polytopes

Explores Hamiltonian dynamics on convex polytopes, covering symplectic capacities, EHZ capacity, and systolic ratio maximizers.

Homotopy Invariance: Homology Groups

Explores homotopy invariance and its application to homology groups of quotients, showcasing isomorphism and chain homotopy.

Convex Optimization

Covers an overview of convex optimization, affine sets, polyhedra, ellipsoids, and convex functions.

Convex Optimization: Convex Functions

Covers the concept of convex functions and their applications in optimization problems.