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Related lectures (41)

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.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Nerves and Geometric Realization

Covers the explicit computations of nerves of categories and geometric realisations of simplicial sets.

Introduction to simplicial sets: Simplicial sets

Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.

Natural Examples of Simplicial Sets

Introduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.

Convex Sets and Functions

Introduces convex sets and functions, discussing minimizers, optimality conditions, and characterizations, along with examples and key inequalities.

Higher-order Interactions in Brain Networks

Explores higher-order interactions in brain networks using simplicial complexes and information theory, analyzing data from fMRI, financial time-series, and infectious diseases.

Simplicial and Singular Homology Equivalence Log in to Mediaspace to watch this video

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

Simplicial Homology: Structure and Complexes Log in to Mediaspace to watch this video

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

Singular Homology: First Properties Log in to Mediaspace to watch this video

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

Convex Optimization: Elementary Results Log in to Mediaspace to watch this video

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

Convex Sets: MGT-418 Lecture Log in to Mediaspace to watch this video

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

Homotopy Invariance: Homology Groups Log in to Mediaspace to watch this video

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

Convex Optimization Log in to Mediaspace to watch this video

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

Convex Optimization: Convex Functions Log in to Mediaspace to watch this video

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

Convex Optimization: Introduction and Sets Log in to Mediaspace to watch this video

Covers the fundamentals of convex optimization, including mathematical problems, minimizers, and solution concepts, with an emphasis on efficient methods and practical applications.

Convex Sets: Mathematical Optimization Log in to Mediaspace to watch this video

Introduces convex optimization, covering convex sets, solution concepts, and efficient numerical methods in mathematical optimization.

Simplicial Homology Revisited Log in to Mediaspace to watch this video

Covers the concept of simplicial homology, focusing on finite complexes and induced maps.

Geodesic Convexity: Theory and Applications Log in to Mediaspace to watch this video

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

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