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UID:bf1f3d094491d38784fb450c1979bc6f
CATEGORIES:Number Theory Seminar
CREATED:20230907T161027
SUMMARY:Renormalization on circle packings
LOCATION:Hill 525 (remote)
DESCRIPTION:<p>Abstract:<br>Circle packings have many applications in geometry, analysi
 s and dynamics. For a circle packing P, one can associate a plane graph cal
 led the nerve of P. It is natural and important to understand<br>1. Given a
  plane graph G, when is it isomorphic to the nerve of a circle packing?<br>
 2. Is the circle packing rigid? Or more generally, what is the moduli space
  of circle packings with nerve isomorphic to G?<br>3, How are different cir
 cle packings with isomorphic nerves related?<br>For finite graphs, Kobe-And
 reev-Thurston’s circle packing theorem give a complete answer to the above 
 questions. The situation is much more complicated for infinite graphs, and 
 has been extensively studied for locally finite triangulations.</p><p>In th
 is talk, I will describe a new perspective of using skinning map and renorm
 alization theory to study these questions for infinite graphs. In particula
 r, I will explain how it gives complete answers to the above questions for 
 graphs with subdivision rules.<br>I will discuss some similarities and diff
 erences between this and the renormalization theory for quadratic like maps
  and mapping class group action on quasi-Fuchsian groups. <br>If I have tim
 e, I will also discuss some applications on quasiconformal geometries for g
 asket Julia set and limit set.<br>This is based on some joint works with Y.
  Zhang, D. Ntalampekos.</p>
CONTACT:Yusheng Luo (Cornell)
DTSTAMP:20260827T171707
DTSTART;TZID=America/New_York:20231107T140000
DTEND;TZID=America/New_York:20231107T150000
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