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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:<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:20260827T015800
DTSTART;TZID=America/New_York:20240926T170000
DTEND;TZID=America/New_York:20240926T180000
SEQUENCE:0
TRANSP:OPAQUE
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