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SUMMARY:Elias Wegert (Technische Universität Bergakademie Freiberg)
DTSTART:20220614T130000Z
DTEND:20220614T140000Z
DTSTAMP:20260422T201358Z
UID:CAvid/79
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/79/">N
 umerical range\, Blaschke products and Poncelet polygons</a>\nby Elias Weg
 ert (Technische Universität Bergakademie Freiberg) as part of CAvid: Comp
 lex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\n(Joint wor
 k with Ilya Spitkovsky\, New York University Abu Dhabi)\n\nIn 2016\, Gau\,
  Wang and Wu conjectured that a partial isometry\nA acting on a $n$-dimens
 ional complex Hilbert space cannot have \na circular numerical range with 
 a non-zero center.\nIn this talk we present a proof for operators with ran
 k $A=n-1$ \nand any n. It is based on the unitary similarity of A to a com
 pressed\nshift operator generated by a finite Blaschke product $B(z)$.\nWe
  then use the description of the numerical range by Poncelet\npolygons ass
 ociated with $zB(z)$\, a special representation of \nBlaschke products rel
 ated to boundary interpolation\, and an \nexplicit formula for the barycen
 ters of the vertices of Poncelet \npolygons involving elliptic functions.\
 n
LOCATION:https://researchseminars.org/talk/CAvid/79/
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