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UID:20250706T111259EDT-2260peB405@132.216.98.100
DTSTAMP:20250706T151259Z
DESCRIPTION:Title: Non-orderability of random triangular groups by using ra
 ndom 3CNF formulas.\n\nAbstract: A random group in the triangular binomial
  model Gamma(n\,p) is given by the presentation <S|R>\, where S is a set o
 f n generators and R is a random set of cyclically reduced relators of len
 gth 3 over S\, with each relator included in R independently with probabil
 ity p. When n approaches infinity\, the asymptotic properties of groups in
  Gamma(n\,p) vary widely with the choice of p=p(n). By Antoniuk-Łuczak-Świ
 ątkowski and Żuk\, there exist constants C\, C' such that a random triangu
 lar group is asymptotically almost surely (a.a.s.) free\, if p < Cn^{-2}\,
  and a.a.s. infinite\, hyperbolic\, but not free\, if p \in (C'n^{-2}\, n^
 {-3/2 - epsilon}). We generalize the second statement by finding a constan
 t c such that\, if p \in (cn^{-2}\, n^{-3/2 - epsilon})\, then a random tr
 iangular group is a.a.s. not left-orderable. We prove this by linking left
 -orderability of Gamma \in Gamma(n\,p) to the satisfiability of a random p
 ropositional formula\, constructed from the presentation of Gamma. The lef
 t-orderability of quotients will also be discussed. \n\nLink: https://mcgi
 ll.zoom.us/j/98910726246?pwd=VHlzTzdTZGtqcHVuWGNKdys4d0FzQT09\n\nZoom ID: 
 989 1072 6246\n	Password: delta\n
DTSTART:20201202T200000Z
DTEND:20201202T210000Z
SUMMARY:Damian Orlef (IMPAN)
URL:/mathstat/channels/event/damian-orlef-impan-326542
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