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UID:6114@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220324T110000
DTEND;TZID=Europe/Paris:20220324T123000
DTSTAMP:20241120T200915Z
URL:https://www.i2m.univ-amu.fr/evenements/proof-nets-rings-and-ideals/
SUMMARY:William Troiani (LIPN\, Université Sorbonne Paris Nord): Proof net
 s\, rings\, and ideals
DESCRIPTION:William Troiani: What is cut elimination? When Gentzen wrote do
 wn the rewriting processes associated with his logical systems\, what seem
 ingly external mathematical structure was he also encapsulating? This ques
 tion is at the heart of Girard's Geometry of Interaction program. The rece
 nt work of Daniel Murfet and myself have laid down the foundations for a n
 ew approach to Girard's idea\, where proofs (here\, MLL proof structures) 
 are interpreted as suitable quotients of polynomial rings\, where the numb
 er of variables depends on the size of the formulas of the proof\, and the
  quotient ideal depends on the links of the proof. Cut elimination is then
  interpreted as suitable isomorphisms between these rings. Moreover\, elim
 ination theory can be used to give an interpretation of “plugging” of 
 formulas. This is the first work of a series of papers which will eventual
 ly give models of various fragments of linear logic inside a category of q
 uantum error correction codes\, and later\, more exotic algebraic-geometri
 c settings. Our current target is a model inside the bicategory of Landau-
 Ginzburg models.\nL’exposé sera retransmis ici :  https://greenlight.
 lal.cloud.math.cnrs.fr/b/lio-hdc-jef\n\n&nbsp\;
CATEGORIES:Séminaire,Logique et Interactions
LOCATION:I2M Luminy - Ancienne BU\, Salle Séminaire2 (RdC)\, 163 Avenue de
  Luminy\, 13009 Marseille\, France\, 
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 U\, Salle Séminaire2 (RdC):geo:0,0
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