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UID:34ea0fa224d53ca15ee62954fe7a4f81
CATEGORIES:Experimental Mathematics Seminar
CREATED:20240903T192654
SUMMARY:A two variable Vandermonde decomposition of q-binomials emerging from a complex dynamics problem
LOCATION:https://rutgers.zoom.us/j/91865817691  password: The 20th Catalan number\, 
 alias (40)!/(20!*21!)\, alias 6564120420 ] 
DESCRIPTION:When a holomorphic function $f:C to C$ has a fixed point f(0)=0 with deriva
 tive λ=f'(0) of unit size, the question arises of conjugating f to the rota
 tion z ->λ z. This is possible when the argument of λ has good approxima
 tion properties; eg, when it is Diophantine. The largest domain of conjugat
 ion is known as a Siegel disk.\n\n A famous open problem is to give bounds 
 on the size of Siegel disks. As a concrete case, if $Arg(lambda)$ is the Go
 lden Ratio, does the Siegel disk contain a disk of radius 1/4?\n\n In the t
 alk I will explore a circle of ideas emerging from our approach to this pro
 blem: The value 1/4 is connected to the growth of Catalan numbers enumerati
 ng binary trees. A consequence of this correspondence is a 2 variable versi
 on of the Vandermonde convolution for (deformed) q-binomials. The work is a
  joint collaboration with M. Aspenberg, Lund University\n
X-ALT-DESC;FMTTYPE=text/html:<p>When a holomorphic function $f:C to C$ has a fixed point f(0)=0 with der
 ivative λ=f'(0) of unit size, the question arises of conjugating f to the r
 otation z -&gt;λ z. This is possible when the argument of λ has good approx
 imation properties; eg, when it is Diophantine. The largest domain of conju
 gation is known as a Siegel disk.</p><p><br> A famous open problem is to gi
 ve bounds on the size of Siegel disks. As a concrete case, if $Arg(lambda)$
  is the Golden Ratio, does the Siegel disk contain a disk of radius 1/4?</p
 ><p><br> In the talk I will explore a circle of ideas emerging from our app
 roach to this problem: The value 1/4 is connected to the growth of Catalan 
 numbers enumerating binary trees. A consequence of this correspondence is a
  2 variable version of the Vandermonde convolution for (deformed) q-binomia
 ls. The work is a joint collaboration with M. Aspenberg, Lund University</p
 >
CONTACT: Rodrigo A. Perez, Indiana University, Indianapolis
DTSTAMP:20260827T115847
DTSTART;TZID=America/New_York:20240926T170000
DTEND;TZID=America/New_York:20240926T180000
SEQUENCE:0
TRANSP:OPAQUE
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