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PRODID:-//Memento EPFL//
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SUMMARY:Information topology through topos cohomology
DTSTART:20260126T160000
DTEND:20260126T170000
DTSTAMP:20260416T135244Z
UID:92933841672fbb388d5acfce3d9d458b3acdd702a19c2a4a85f2e376
CATEGORIES:Conferences - Seminars
DESCRIPTION:Alexandre Bestandj\, EPFL \nAn observer describes a system by
  collecting data from many local points of observation whose domains can b
 e coherently glued together. A Grothendieck topos formalizes this process 
 through a site of observation points and their relations. In this view\, a
  topos is a space of phenomena where empirical data are relationally stru
 ctured. The cohomology of these sheaves measures obstructions to forming c
 oherent global descriptions or finer incompatibilities between different d
 escriptions.\n\nIn their 2015 article The Homological Nature of Entropy\,
  Pierre Baudot and Daniel Bennequin use cohomological tools from topos the
 ory to reinterpret Shannon entropy. A system is modeled as a ringed site o
 f experiments that partially or fully partition its space of possible stat
 es. On this site\, a sheaf of modules encodes all conceivable measures of 
 probabilistic information derived from these experiments\, with each exper
 iment acting on the sheaf to determine how information changes.\nThe cohom
 ology of this sheaf captures how well these information measures satisfy d
 esirable properties under observation\, interpreting entropy as a generato
 r of first-degree cohomology and extending information measures to higher 
 dimensions.\n\nIn this talk\, I will detail three cases of probabilistic i
 nformation cohomology : classical\, quantum and dynamical. You can find mo
 re materials here.\n 
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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