Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Home

Lecture

Shape of Data: Algebraic Topology and Shape Representation

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (39)

Chain Maps: Homotopy Invariance Log in to Mediaspace to watch this video

Covers chain maps, homotopy invariance, homology groups, and induced homomorphisms between cycles and boundaries.

Naturality: An Example Log in to Mediaspace to watch this video

Covers the concept of naturality in algebraic topology and the generation of homology groups through induction.

Naturality: Chain Complexes and Homology Groups Log in to Mediaspace to watch this video

Explores naturality in chain complexes, homology groups, and abelian groups, emphasizing the commutativity of squares and the Five-Lemma.

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

Explains relative homology, n-cycles, n-boundaries, and exact sequences of chain complexes.

Metric Spaces: Topology and Continuity Log in to Mediaspace to watch this video

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

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.

Cauchy Problem for EDPs Log in to Mediaspace to watch this video

Explores the Cauchy problem for EDPs, discussing local solutions and characteristic curves.

Invariance of Domain Log in to Mediaspace to watch this video

Delves into the invariance of domain theorem, proving that a subset homeomorphic to an open subset is open itself, with implications for embeddings and homeomorphisms.

Curl and Exact Sequences Log in to Mediaspace to watch this video

Covers the concept of curl in vector calculus and De Rham cohomology.

Universal Coefficient Theorems Log in to Mediaspace to watch this video

Delves into the universal coefficient theorems in homological algebra, showcasing their practical application in computing homology and cohomology groups.

Magnetic Materials: Exercise Course Overview Log in to Mediaspace to watch this video

Outlines the MSE 432 exercise course on magnetic materials, detailing course structure, activities, and grading criteria for student presentations and experiments.

Relative Homology: Exact Sequence Log in to Mediaspace to watch this video

Covers the long exact sequence of relative homology groups and chain complexes.

Free Abelian Groups and Homomorphisms Log in to Mediaspace to watch this video

Explores free abelian groups, homomorphisms, and exact sequences in the context of different categories.

Finite Abelian Groups: Classification Theorem Log in to Mediaspace to watch this video

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

A Lemma: Introduction to Homology Groups Log in to Mediaspace to watch this video

Introduces the concept of homology groups and focuses on a lemma about free abelian groups.

Induced Homomorphisms on Relative Homology Groups Log in to Mediaspace to watch this video

Covers induced homomorphisms on relative homology groups and their properties.

Cohomology: Abelian Cochains Log in to Mediaspace to watch this video

Introduces cohomology, focusing on abelian cochains and their correspondence with singular cochains.

Normed Spaces Log in to Mediaspace to watch this video

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

Distributed Intelligent Systems: Energy Efficiency in Wireless Sensor Networks Log in to Mediaspace to watch this video

Delves into energy-saving design principles in wireless sensor networks, exploring motivating applications and intelligent algorithms for energy efficiency.

Page 2 of 2