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UID:6rcknfuh2it1tl3n6rjb2bmjev@google.com
CATEGORIES:{lang hu}Algebra szeminárium{/lang}{lang en}Algebra seminar{/lang}
SUMMARY:Szakács Nóra (Bolyai Institute): Hyperbolic groups and generalizations I.
LOCATION: Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract. Given a finitely presented group, many algorithmic questions aris
e, most importantly the solvability and complexity of the word problem. In
the past few decades, geometric approaches have been developed and have pr
oven effective in studying these, resulting in the rich theory of geometric
group theory. A key factor in the development of the area was the notion
of hyperbolic groups, introduced by Gromov in 1987. The notion represented
a revolution in group theory due to a conjugation of factors: they can be
characterized using a geometric property of their Cayley graphs, called Rip
s condition; they have excellent algorithmic properties: they are biautomat
ic (in particular, they have an effectively solvable word problem), their g
eodesics constitute an automatic structure.\n\nIn this series of two talks,
we first introduce the basics of geometric group theory, mostly focusing o
n hyperbolic groups and their properties. In the second talk, we proceed to
describe how the notion of hyperbolicity can be generalized to inverse sem
igroups in a way that both the geometric interpretation and (some) algorith
mic properties are preserved. We will briefly describe possible application
s to the open problem of one-relator inverse monoids.
DTSTAMP:20200709T141446Z
DTSTART;TZID=Europe/Budapest:20180314T100000
DTEND;TZID=Europe/Budapest:20180314T120000
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