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UID:7246@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20180917T000000
DTEND;TZID=Europe/Paris:20180920T000000
DTSTAMP:20241120T203459Z
URL:https://www.i2m.univ-amu.fr/evenements/umi-simai-ptm-joint-meeting-wro
 claw-2018/
SUMMARY:Rencontre (...): UMI-SIMAI-PTM Joint Meeting - Wroclaw 2018
DESCRIPTION:Rencontre: http://umi-simai.ptm.org.pl/\nConsider a Gaussian An
 alytic Function on the disk\, that is\, a random series whose coefficients
  are independent complex Gaussians. In joint work with Yanqi Qiu and Alexa
 nder Shamov\, we show that the zero set iof a Gaussian Analyitc Function i
 s a uniqueness set for the Bergman space on the disk: in other words\, alm
 ost surely\, there does not exist a nonzero square-integrable holomorphic 
 function having these zeros. The key role in our argument is played by the
  determinantal structure of the zeros\, and we prove\, in general\, that t
 he family of reproducing kernels along a realization of a determinantal po
 int process generates the whole ambient Hilbert space\, thus settling a co
 njecture of Lyons and Peres.\nIn a sequel paper\, joint with Yanqi Qiu\, w
 e study how to recover a holomorphic function from its values on our set. 
 The talk is based on the preprints arXiv:1806.02306 and arXiv:1612.06751\n
 &nbsp\;
CATEGORIES:Event ERC IChaos
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