02:09:09
published on May 21, 2025
Dimension Dependence of Critical Phenomena in Percolation
By Thomas Hutchcroft
Lecture 1 - 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 1. Historical roots of computational topology - topological invariants, combinatorial encodings, and algorithms - angle sums, rotation numbers, regular homotopy - winding numbers, signed area, point-in-polygon - graphs and Euler tours - Gauss/Dowker code planarity
