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UID:0-1152@lptms.universite-paris-saclay.fr
DTSTART;TZID=Europe/Paris:20261005T140000
DTEND;TZID=Europe/Paris:20261005T170000
DTSTAMP:20261002T151408Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/soutenance-de-the
 se-romain-usciati/
SUMMARY:Soutenance de thèse Romain Usciati - Petit amphi\, bâtiment Pasca
 l n° 530 - 5 Oct 26 14:00
DESCRIPTION:Probabilistic construction and conformal bootstrap of Imaginary
  Liouville theory \nRomain Usciati\n&nbsp\;\n\nConformal field theories de
 scribe systems that remain invariant under changes of scale. In two dimens
 ions\, they provide a common language for studying critical phenomena in s
 tatistical mechanics and quantum gravity. Among them\, Liouville theory oc
 cupies a distinguished place: it is the best-understood non-rational confo
 rmal field theory and has become an important meeting point between confor
 mal bootstrap\, probability and random geometry. Its conventional formulat
 ion\, however\, applies only to central charges greater than or equal to 2
 5. Extending Liouville theory to central charges below 1 is a long-standin
 g problem\, motivated in particular by its expected connection with non-lo
 cal observables in critical statistical models and applications to string 
 theory.\n\nIn this thesis\, we propose a constructive path-integral defini
 tion of Liouville theory at central charge below 1. Our approach combines 
 probabilistic tools with an original prescription to deal with the infrare
 d divergence of the theory\, inspired from methods for the analytic contin
 uation of functions of the complex variable. We provide both analytic and 
 numerical evidence that our construction reproduces the correlation functi
 ons expected in Imaginary Liouville theory.\n\nA second contribution is th
 e rigorous study of the theory’s local conformal structure. Our results 
 demonstrate that the proposed path integral possesses essential structural
  properties expected of a conformal field theory.\n\nFinally\, we take ini
 tial steps toward the quantization and conformal bootstrap description of 
 the theory. We present numerical investigations of four-point functions\, 
 together with a spectral analysis of a simplified Hamiltonian that reveals
  both discrete and continuous spectral components of the spectrum.\nJury :
  Denis Bernard\, Benoît Estienne (invité)\, Colin Guillarmou (co-directe
 ur de thèse)\, Alexey Litvinov (rapporteur)\, Titus Lupu (invité)\, Evel
 iina Peltola\, Raoul Santachiara (directeur de thèse)\, Christian Webb (r
 apporteur).
CATEGORIES:seminars
LOCATION:Petit amphi\, bâtiment Pascal n° 530\, rue André Rivière\, Ors
 ay\, 91405\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Rivière\, Orsay
 \, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Petit amphi\, bâtiment Pasca
 l n° 530:geo:0,0
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