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Explore the concept of Urysohn width in this 54-minute lecture by Alexey Balitskiy from the Applied Algebraic Topology Network. Delve into the history and significance of this metric invariant, introduced by Soviet mathematician Pavel Urysohn in 1923. Understand how the d-width of a metric space quantifies its approximation by d-dimensional simplicial complexes. Discover the role of Urysohn width in dimension theory, approximation theory, and Gromov's work on systolic geometry. Examine the highlights of its 100-year history and learn why it often fails as a measure of dimensionality. Gain insights into this fundamental concept in topology and its applications in various mathematical fields.
