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SUMMARY:Linear representations of finite sets
DTSTART:20191120T151500
DTEND:20191120T163000
DTSTAMP:20260510T022720Z
UID:976fb4729fc2c9dd748f1779887b1ddb67c11ad350f683e80821d4e2
CATEGORIES:Conferences - Seminars
DESCRIPTION:Jacques Thévenaz\, EPFL\nGroups\, Arithmetic and Algebraic Ge
 ometry Seminar\nAbstract : A correspondence between two finite sets is a s
 ubset of their direct product. Correspondences can be composed and this gi
 ves rise to the category C of finite sets and correspondences. In a joint 
 work with Serge Bouc\, we study the linear representations of the category
  C\, which turn out to have many remarkable features. In particular\, we s
 hall explain how the simple representations are parametrized in terms of f
 inite posets. We shall sketch how to solve the difficult problem of findin
 g the dimension of every evaluation of such a simple representation. Final
 ly\, we shall describe precisely all the posets for which the associated s
 imple representations are projective. In the first part of the seminar\, s
 ome elementary results on the simple representations of a small category w
 ill be explained and the special case of the representations of C will be 
 considered. In the second part\, more details will be given about the conn
 ection with finite posets.
LOCATION:GC A3 30 https://plan.epfl.ch/?room==GC%20A3%2030
STATUS:CONFIRMED
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