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Printer-friendly versionMonday, April 1, 2024
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| 4:00pm |
04/01/2024 - 4:00pm 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
1. Given a graph G, when is it isomorphic to the nerve of a circle packing?
2. Is the circle packing rigid? Or more generally, what is the moduli space of circle packings with nerve isomorphic to G?
3, 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.
Location:
KT205
04/01/2024 - 4:30pm I will discuss families of multilinear k-ary operations (“brackets”) that naturally arise in QFT. The brackets physically describe BRST anomalies generated by interactions/deformations of QFTs in perturbation theory, and are analogous to the beta-functions that describe quantum violations of scale symmetry due to interactions. Besides being formally interesting, I will show that the brackets are highly computable (requiring only a first course in QFT to compute), and contain familiar information like anomalies and OPEs. Time permitting, I will discuss how these brackets are very strongly constrained in Holomorphic-Topological scenarios, and a higher-dimensional analogue of Kontsevich’s formality theorem which implies the absence of perturbative corrections to HT theories with more than 1 topological direction. Based on arXiv:2403.13049 Location:
KT 217
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