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TZID:Europe/Budapest
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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.

In this series of two
talks, we first introduce the basics of geometric group theory, mostly focu
sing on hyperbolic groups and their properties. In the second talk, we proc
eed to describe how the notion of hyperbolicity can be generalized to inver
se semigroups in a way that both the geometric interpretation and (some) al
gorithmic properties are preserved. We will briefly describe possible appli
cations to the open problem of one-relator inverse monoids.
DTSTAMP:20191115T233322Z
DTSTART;TZID=Europe/Budapest:20180314T100000
DTEND;TZID=Europe/Budapest:20180314T120000
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