Seminar:
Group Actions, Geometry and Dynamics
Event time:
Monday, April 1, 2024 - 4:00pm
Location:
KT205
Speaker:
Yusheng Luo
Speaker affiliation:
Cornell University
Event description:
Circle packings have many applications in geometry, analysis and dynamics. The combinatorics of a circle packing is captured by the contact graph, called the nerve of the circle packing. It is natural and important to understand
- Given a graph G, when is it isomorphic to the nerve of a circle packing?
- Is the circle packing rigid? Or more generally, what is the moduli space of circle packings with nerve isomorphic to G?
- How are different circle packings with isomorphic nerves related?
For finite graphs, Kobe-Andreev-Thurston’s circle packing theorem give a complete answer to the above questions. The situation is more complicated for infinite graphs, and has been extensively studied for locally finite triangulations.
In this talk, I will describe how to use renormalization theory to study these questions for infinite graphs. In particular, I will explain how it gives complete answers to the above questions for graphs with subdivision rules.
I will also discuss some applications on quasiconformal geometries for dynamical gasket sets.
This is based on some joint works with Y. Zhang, D. Ntalampekos.