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SUMMARY:Motiejus Valiunas (Wrocław)
DTSTART:20221213T140000Z
DTEND:20221213T160000Z
DTSTAMP:20260423T023014Z
UID:WienGAGT/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WienGAGT/28/
 ">Biautomatic and hierarchically hyperbolic groups</a>\nby Motiejus Valiun
 as (Wrocław) as part of Vienna Geometry and Analysis on Groups Seminar\n\
 n\nAbstract\nBiautomatic groups arose as groups explaining formal language
 -theoretic aspects of geodesics in word-hyperbolic groups.  Many classes o
 f non-positively curved finitely generated groups\, such as hyperbolic\, v
 irtually abelian\, cocompactly cubulated\, small cancellation and Coxeter 
 groups\, are known to be biautomatic.  On the other hand\, there are some 
 other classes\, such as CAT(0) or hierarchically hyperbolic groups\, for w
 hich the relationship to biautomaticity is more complicated.\n\nIn the fir
 st half of the talk\, I will outline the notions of non-positive curvature
  appearing in group theory and their connection to biautomaticity.  In par
 ticular\, I will overview recent results on the relationship between biaut
 omaticity\, hierarchical hyperbolicity and being CAT(0)\, as well as some 
 constructions of non-biautomatic non-positively curved groups.\n\nThe goal
  of the second half of the talk is to construct a non-biautomatic hierarch
 ically hyperbolic group\, giving the first known example of such a group. 
  Our group acts geometrically on the cartesian product of a tree and the h
 yperbolic plane\, and therefore satisfies many nice geometric properties. 
  The proof of non-biautomaticity will rely on the study of geodesic curren
 ts on a closed hyperbolic surface.  The talk is based on joint work with S
 am Hughes.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/28/
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