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UID:bf1f3d094491d38784fb450c1979bc6f
CATEGORIES:Number Theory Seminar
CREATED:20230907T161027
SUMMARY:Renormalization on circle packings
LOCATION:Hill 525 (remote)
DESCRIPTION:Abstract:\nCircle packings have many applications in geometry, analysis and
  dynamics. For a circle packing P, one can associate a plane graph called t
 he nerve of P. It is natural and important to understand\n1. Given a plane 
 graph G, when is it isomorphic to the nerve of a circle packing?\n2. Is the
  circle packing rigid? Or more generally, what is the moduli space of circl
 e packings with nerve isomorphic to G?\n3, How are different circle packing
 s with isomorphic nerves related?\nFor finite graphs, Kobe-Andreev-Thurston
 ’s circle packing theorem give a complete answer to the above questions. Th
 e situation is much more complicated for infinite graphs, and has been exte
 nsively studied for locally finite triangulations.\nIn this talk, I will de
 scribe a new perspective of using skinning map and renormalization theory t
 o study these questions for infinite graphs. In particular, I will explain 
 how it gives complete answers to the above questions for graphs with subdiv
 ision rules.\nI will discuss some similarities and differences between this
  and the renormalization theory for quadratic like maps and mapping class g
 roup action on quasi-Fuchsian groups. \nIf I have time, I will also discuss
  some applications on quasiconformal geometries for gasket Julia set and li
 mit set.\nThis is based on some joint works with Y. Zhang, D. Ntalampekos.\
 n
X-ALT-DESC;FMTTYPE=text/html:<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:20260827T152221
DTSTART;TZID=America/New_York:20231107T140000
DTEND;TZID=America/New_York:20231107T150000
SEQUENCE:0
TRANSP:OPAQUE
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