01:06:15
published on September 12, 2025
The Arithmetic of Power Series and Applications to Irrationality
By Yunqing Tang
Lecture 5 - Two-dimensional computational topology
Appears in collection : School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
This series of lectures will describe recent and not-so-recent works in computational topology of curves in the plane and on surfaces. Combinatorial and algorithmic aspects will be discussed.
Lecture 5. Curve simplification - homotopy moves - loops and bigons (Steinitz, Hass and Scott) - plane: $\Omega(n^{3/2})$ via defect - plane: $O(n^{3/2})$ via tangles and depth - surface: $\Omega(n^2)$ via winding distance - surface: $O(n^4)$ via singular bigons and graph moves
