The Nerve and Geometric Realization

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Related lectures (30)

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Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Nerves and Geometric Realization

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

Clustering: k-means

Explains k-means clustering, assigning data points to clusters based on proximity and minimizing squared distances within clusters.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Functors and Adjunctions

Explores functors between categories and the conditions for left and right adjoints.

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Determinantal Point Processes and Extrapolation

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

The Simplex Category: Simplicial Sets

Covers the combinatorics of the simplex category and its equivalence to topological spaces, as well as the concept of functor categories for cosimplicial and simplicial objects.

The Role of Symmetries

Delves into symmetries in physics, covering group theory, perturbation, and quantification.