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BEGIN:VEVENT
DTSTART:20240227T093000Z
DTEND:20240227T093000Z
DTSTAMP:20240224T192654Z
UID:38834@calendar.unige.ch
CREATED:20240207T103907Z
LAST-MODIFIED:20240207T142521Z
SUMMARY:Dyer groups (Luis Paris, Université de Bourgogne)
DESCRIPTION:Coxeter groups and right-angled Artin groups share the same solution to the word problem: that given by Tits for Coxeter groups and that given by Green for right-angled Artin groups. This algorithm goes beyond the simple solution to the word problem, since it allows to determine whether an expression is reduced or not, and it is an essential tool for defining normal forms in both families. Hence the question: what do these two families of groups have in common that makes them have the same solution to the word problem? The answer sits inside Dyer's thesis published in 1990 where a family of groups is described which contains both, Coxeter groups and right-angled Artin groups. We prove that all Dyer groups have this solution to the word problem and that any group which admits such a solution is a Dyer group up to a small modification of the definition. The coincidence does not stop there because these two families of groups share many other properties. This talk will be a propaganda for Dyer's groups.\n
LOCATION:Room 1-05, Tuesday 27.02.2024, Séminaire "Groupes et Géométrie"\n
TRANSP:TRANSPARENT
CATEGORIES:Séminaire
CONTACT:
URL:http://agenda.unige.ch/events/view/38834
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DTSTART:20240305T093000Z
DTEND:20240305T093000Z
DTSTAMP:20240224T192654Z
UID:38974@calendar.unige.ch
CREATED:20240216T100505Z
LAST-MODIFIED:20240216T102431Z
SUMMARY:Hyperbolic Coxeter polyhedra with mutually intersecting facets (Naomi Bredon, Université de Fribourg)
DESCRIPTION:The classification of hyperbolic Coxeter polyhedra in dimensions beyond 3 is far from being complete. In this talk, we discuss the known classification results and present a method to construct hyperbolic Coxeter polyhedra with mutually intersecting facets. We establish a lower bound for their dihedral angles, and we provide the complete classification of hyperbolic Coxeter polyhedra with mutually intersecting facets and dihedral angles \pi/2, \pi\3 and \pi/6.
LOCATION:Room 1-05, Tuesday 05.03.2024, Séminaire "Groupes et Géométrie"\n
TRANSP:TRANSPARENT
CATEGORIES:Séminaire
CONTACT:
URL:http://agenda.unige.ch/events/view/38974
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BEGIN:VEVENT
DTSTART:20240312T093000Z
DTEND:20240312T093000Z
DTSTAMP:20240224T192654Z
UID:39028@calendar.unige.ch
CREATED:20240222T132837Z
LAST-MODIFIED:20240222T133613Z
SUMMARY:The Identity Problem in subsemigroups of metabelian groups (Ruiwen Dong, Saarbrucken)
DESCRIPTION:Algorithmic problems in metabelian groups have been studied as early as the 1950s since the work of Hall. In the 1970s Romanovskii proved decidability of the Group Membership problem (given the generators of a subgroup and a target element, decide whether the target element is in the subgroup) in metabelian groups. However, Semigroup Membership (same as Group Membership, but with sub-semigroups) has been shown to be undecidable in several instances of metabelian groups. In this talk we consider two "intermediate" decision problems: the Identity Problem (deciding if a sub-semigroup contains the neutral element) and the Group Problem (deciding if a sub-semigroup is a group). We reduce them to solving linear equations over the polynomial semiring N[X] and show decidability using a Positivstellensatz-type local-global principle.
LOCATION:Room 1-05, Tuesday 12.03.2024, Séminaire "Groupes et Géométrie"\n
TRANSP:TRANSPARENT
CATEGORIES:Séminaire
CONTACT:
URL:http://agenda.unige.ch/events/view/39028
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