YoVDO

Degeneration of Singular Circle Patterns

Offered By: BIMSA via YouTube

Tags

Combinatorial Geometry Courses Topology Courses Euclidean Geometry Courses

Course Description

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Explore a comprehensive lecture on the degeneration of singular circle patterns presented by Xin Nie at ICBS2024. Delve into the intricacies of singular Euclidean circle patterns constructed from radius parameters assigned to triangulated surface vertices. Examine Thurston and Ge-Hua-Zhou's results demonstrating the cone-angle map's bijection from the parameter space to a convex polytope's interior. Discover the full description of the combinatorial structure of the "cone-angle polytope" and learn how to characterize degenerating sequences of circle patterns for every point on its boundary. Investigate the introduced concept of admissible partial edge orientation (APEO) and its one-to-one correspondence with polytope cells. Understand how each APEO defines a degeneration scheme for circle patterns and explore the generalization of Thurston's result, showing the bijection between the space of limiting objects from such degeneration and the cell corresponding to that APEO.

Syllabus

Xin Nie: Degeneration of singular circle patterns #ICBS2024


Taught by

BIMSA

Related Courses

An Introduction to Functional Analysis
École Centrale Paris via Coursera
Nonlinear Dynamics 1: Geometry of Chaos
Georgia Institute of Technology via Independent
Topology in Condensed Matter: Tying Quantum Knots
Delft University of Technology via edX
Математика для всех
Moscow Institute of Physics and Technology via Coursera
Геометрия и группы
Moscow Institute of Physics and Technology via Coursera