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UID:8929@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260106T110000
DTEND;TZID=Europe/Paris:20260106T120000
DTSTAMP:20251217T150809Z
URL:https://www.i2m.univ-amu.fr/evenements/expose-2/
SUMMARY:Ugo Giocanti (Jagiellonian University\, Kraków): Coarse cops and r
 obber games
DESCRIPTION:Ugo Giocanti: Joint work with Louis Esperet and Harmender Gahla
 wat.\n\nLee\, Martínez-Pedroza\, and Rodríguez-Quinche recently introduc
 ed two coarse variants of the classical Cops and robber game in infinite 
 graphs. In these two variants\, finitely many cops want to prevent a robb
 er to enter inside a ball of finite radius infinitely often. Both the cop
 s and the robber have some speeds\, and the cops also have some radius of 
 capture. According to the order in which all these parameters are chosen\,
  we can define two different games\, a weak and a strong version. These 
 games allow define two parameters for infinite graphs\, respectively cal
 led weak and strong cop numbers.\n\nAn important property of these paramet
 ers proved by Lee\, Martínez-Pedroza and Rodríguez-Quinche\, is that the
 y are invariant under quasi-isometries. I will present a number of results
  and questions about these two parameters. In particular\, I will show how
  the weak cop number of a graph is related to the existence of some asympt
 otic minors of large treewidth\, establishing some connections with some r
 ecent question by Georgakopoulos and Papasoglou in coarse graph theory. I 
 will also show that graphs with strong cop number 1 are exactly the hyperb
 olic graphs (the converse direction was proved by Lee\, Martínez-Pedroza 
 and Rodríguez-Quinche)\, which complements in some way some previous resu
 lts of Chalopin\, Chepoi\, Nisse\, Papasoglou\, Pecatte and Vaxès in fin
 ite graphs. Eventually\, I will show some applications of these results wh
 en one works on finitely generated groups.
CATEGORIES:Séminaire,Ernest
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall
 e de Séminaire 304-306 (3ème étage):geo:0,0
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