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BEGIN:VEVENT
SUMMARY:Vandit Trivedi (ANU)
DTSTART:20261022T230000Z
DTEND:20261022T233000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/1
DESCRIPTION:Title: Commensurability of Droms right-angled Artin groups\nby Vandit Tri
vedi (ANU) as part of World of GroupCraft VI\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luka Carrol (UTS)
DTSTART:20261022T223000Z
DTEND:20261022T230000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/2
DESCRIPTION:Title: The complexity of the epimorphism problem for the bicyclic monoid\
nby Luka Carrol (UTS) as part of World of GroupCraft VI\n\n\nAbstract\nThe
bicyclic monoid (or bicyclic semigroup) $\\mathcal{B}$
is the infinite monoid on two generators $a\,b$ subject only to the relati
on $ab=1$. The monoid $\\mathcal{B}$ is a fundamental algebraic structure
that has found numerous applications in algebra\, combinatorics\, and theo
retical computer science. The monoid $\\mathcal{B}$ is an inverse mono
id\; that is\, $\\mathcal{B}$ is a monoid in which every $x\\in\\math
cal{B}$ has a unique generalised inverse $x^{-1}\\in\\mathcal{B}$
\, meaning $x^{-1}$ satisfies only the identities $xx^{-1}x=x$ and $x^{-1}
xx^{-1}=x^{-1}$ rather than the stronger identity $xx^{-1}=x^{-1}x=1$ sati
sfied by group inverses. In this talk we consider the computational comple
xity of the epimorphism problem for the bicyclic monoid. This is
the problem of deciding if there exists a surjective homomorphism from an
arbitrary\, finitely presented inverse monoid $\\mathcal{M}$ onto the bicy
clic monoid (or\, equivalently\, if $\\mathcal{M}$ has a quotient that is
isomorphic to $\\mathcal{B}$). We analyse this problem via a reduction to
Presburger arithmetic\, the first-order theory of linear arithmet
ic over the integers. Through this analysis we gain new insights into the
complexity of an extension of Presburger arithmetic. This is joint work wi
th Murray Elder.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Siddiq Wira Awaldy (Institut Teknologi Bandung)
DTSTART:20261023T000000Z
DTEND:20261023T003000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/3
DESCRIPTION:Title: The Congruence Subgroup Property for Finitely Generated Branch Groups<
/a>\nby Muhammad Siddiq Wira Awaldy (Institut Teknologi Bandung) as part o
f World of GroupCraft VI\n\n\nAbstract\nBranch group is a class of groups
that act faithfully on a rooted tree which transitive at each level of the
tree and satisfying certain conditions.\n\nWe study the congruence subgro
up property for finitely generated branch group where we compare the profi
nite completion of the group with the group's closure as the subgroup of t
he automorphism group of the rooted tree. We prove that a finitely generat
ed branch group satisfies congruence subgroup problem (CSP) if and only if
it has a just infinite profinite completion. And furthermore\, we give an
algebraic characterization on such class of finitely generated branch gro
ups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kane Townsend (UTS)
DTSTART:20261022T220000Z
DTEND:20261022T223000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/4
DESCRIPTION:Title: The isomorphism problem for virtually cyclic groups\nby Kane Towns
end (UTS) as part of World of GroupCraft VI\n\n\nAbstract\nIn 2018\, Seniz
ergues and Weiss established complexity bounds for the isomorphism problem
for virtually free groups\, where each group is given as a context-free g
rammar generating its word problem. In this talk\, we consider the more re
strictive class of virtually cyclic groups\, with the aim of obtaining a s
harper complexity bound. In 1991\, Herbst proved that a group is virtually
cyclic if and only if its word problem is accepted by a one-counter autom
aton. We therefore take as input one-counter automata accepting the word p
roblems of the groups in question.\n\nThis is joint work with Murray Elder
and Adam Piggott.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Xu (KIAS)
DTSTART:20261023T020000Z
DTEND:20261023T023000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/7
DESCRIPTION:Title: An exotic embedding of the hyperbolic plane into the infinite-dimensio
nal hyperbolic space via convex bodies\nby David Xu (KIAS) as part of
World of GroupCraft VI\n\n\nAbstract\nA classical theorem by Karpelevich a
nd Mostow states that every continuous and isometric action of PSL(2\,R) o
n a finite-dimensional hyperbolic space must preserve a totally geodesic c
opy of the hyperbolic plane. It is known that this fact no longer holds wh
en we consider actions of PSL(2\,R) on an infinite-dimensional hyperbolic
space\, thanks to the works of Delzant\, Monod and Py. In this talk\, I wi
ll discuss a way to embed the hyperbolic plane into that infinite-dimensio
nal space which is equivariant with respect to the action of PSL(2\,R)\, b
ut not totally geodesic. This construction is based on the hyperbolic mode
l of convex bodies of Debin and Fillastre\, and is a joint work with Fran
çois Fillastre and Yusen Long.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khánh Lê (KAIST)
DTSTART:20261023T023000Z
DTEND:20261023T030000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/8
DESCRIPTION:Title: The space of left-orderings of group and fractal dimensions\nby Kh
ánh Lê (KAIST) as part of World of GroupCraft VI\n\n\nAbstract\nIn this
talk\, I will give an introduction to left-orderable groups and an overvie
w of the study of the space of left-orderings of these groups. In this dir
ection\, I will speak about previous results as well as my new contributio
n to this line of inquiry. In particular\, I will discuss different notion
s of fractal dimensions of the space of left orderings\, their properties
and compute these fractal dimensions in some examples: including abelian g
roup\, BS(1\,n)\, free group\, surface group and more generally a class of
torsion free one-relator groups. This work answers some questions posed b
y Andre Navas. This is joint work in progress with Leonardo Dinamarca\, Da
vid Xu.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miri Son (National University of Singapore)
DTSTART:20261023T030000Z
DTEND:20261023T033000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/9
DESCRIPTION:Title: Smooth local linearization of SL(n\,R)-actions near fixed points\n
by Miri Son (National University of Singapore) as part of World of GroupCr
aft VI\n\n\nAbstract\nHow does the algebraic structure of a group constrai
n the local geometry of its actions? We study this question for smooth Lie
group action near fixed points. The local linearization problem asks whet
her the action near a fixed points are locally conjugate to its derivative
representation. We prove that a smooth SL(n\,R)-action is smoothly linear
izable near fixed points if its derivative representation is the direct su
m of the standard representation and m copies of the trivial representatio
n. This is joint work with Insung Park.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonardo Dinamarca (KIAS)
DTSTART:20261023T040000Z
DTEND:20261023T043000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/10
DESCRIPTION:Title: Characterizing the exact embeddability for RAAGs into piecewise linea
r homeomorphisms of the circle\nby Leonardo Dinamarca (KIAS) as part o
f World of GroupCraft VI\n\n\nAbstract\nIt is a well-known result of Bleak
and Salazar-Diaz that the group Z^2∗Z cannot embed in Thompson’s grou
p V \, and so in particular cannot embed in Thompson’s group T\, the lat
ter of which is identified with a group of piecewise linear homeomorphisms
of the circle. We generalize this results by giving a classification on t
he RAAG's that can be embbeds into the piecewise linear homeomorphisms of
the circle.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takeru Asaka (Tohoku University)
DTSTART:20261023T043000Z
DTEND:20261023T050000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/11
DESCRIPTION:Title: Earthquake theorem for cluster algebras of finite type\nby Takeru
Asaka (Tohoku University) as part of World of GroupCraft VI\n\n\nAbstract
\nThurston’s earthquake theorem states that there is a unique earthquake
which deforms one into another in Teichmüller space. It is important fo
r mapping class groups. We extend the earthquake theorem to the case of cl
uster algebras of finite type.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongtaek Jung (KIAS)
DTSTART:20261023T050000Z
DTEND:20261023T053000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/12
DESCRIPTION:Title: Cataclysm deformations for Anosov representations and applications\nby Hongtaek Jung (KIAS) as part of World of GroupCraft VI\n\n\nAbstract
\nA cataclysm\, originally defined on Teichmuller space\, is a deformation
that transforms a given Anosov representation into another with respect t
o a prescribed measured lamination. We show that if a sequence of measured
laminations converges\, then the sequence of corresponding cataclysm defo
rmations converges uniformly on compact sets. As one of the applications\,
we show that the set of strongly dense G-Hitchin representations is not o
pen when the Weyl group of G contains -1.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bratati Som (TIFR Bombay)
DTSTART:20261023T060000Z
DTEND:20261023T063000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/13
DESCRIPTION:Title: Conjugacy problem for Dehn twists of free products of free abelian gr
oups\nby Bratati Som (TIFR Bombay) as part of World of GroupCraft VI\n
\n\nAbstract\nDehn twist automorphisms of groups are defined in terms of g
raph-of-groups decompositions and provide algebraic analogues of Dehn twis
t homeomorphisms of surfaces. In this talk\, we will discuss the key steps
in an algorithm for solving the conjugacy problem for Dehn twists of free
products of free abelian groups\, mainly using a ''canonical'' splitting
of the mapping torus associated to a Dehn twist. This is based on joint wo
rk with Amir Weiss Behar and Chris Karpinski.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Athira E V (Kerala School of Mathematics)
DTSTART:20261023T063000Z
DTEND:20261023T070000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/14
DESCRIPTION:Title: Geometric Monodromy of Mixed Braid Groups and the Multivariate Burau
Representation\nby Athira E V (Kerala School of Mathematics) as part o
f World of GroupCraft VI\n\n\nAbstract\nWe study the geometric monodromy a
ction of mixed braid groups on the first cohomology of cyclic branched cov
ers of the Riemann sphere\, for arbitrary irreducible covers. Using lifts
of Pochhammer contours and figure-eight curves\, we construct explicit spa
nning classes and compute their Hermitian intersection form. We show that
the monodromy representation factors through a reduced mixed braid group\,
with generators acting as complex reflections or unitary transvections. W
hen the local monodromy at infinity is non-trivial\, we identify the resul
ting representation with the reduced multivariate Burau representation. Th
is is joint work with Pranav Haridas.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sagar Saha (IISER Mohali)
DTSTART:20261023T070000Z
DTEND:20261023T073000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/15
DESCRIPTION:Title: A Family of Branch Groups with Non-Torsion Rigid Kernels\nby Saga
r Saha (IISER Mohali) as part of World of GroupCraft VI\n\n\nAbstract\nWe
present an infinite family of branch groups in the class of non-contractin
g self-similar groups. We show that these groups are super strongly fracta
l\, are not regular branch\, and have exponential growth. We further prove
that they do not have the congruence subgroup property by explicitly dete
rmining the structure of their rigid kernels. This family provides the fir
st examples of branch groups with non-torsion rigid kernels. Moreover\, we
compute the Hausdorff dimensions of the closures of these groups in the f
ull automorphism groups of the corresponding regular rooted trees. This is
a joint work with K. V. Krishna.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deblina Das (IIT Palakkad)
DTSTART:20261023T080000Z
DTEND:20261023T083000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/16
DESCRIPTION:Title: On Orderability and Asymptotic Structure of the Quasi-Isometry Group
of Euclidean Spaces\nby Deblina Das (IIT Palakkad) as part of World of
GroupCraft VI\n\n\nAbstract\nIn this talk\, we discuss some of the algebr
aic and dynamical structure of certain normal subgroups of the quasi-isome
try group of Euclidean spaces. We first consider the normal subgroup consi
sting of quasi-isometries that are asymptotically equal to the identity\,
and introduce a nested family of normal subgroups that distinguish differe
nt orders of sublinear deviation from the identity. We show that the cente
rs of the resulting quotient groups are trivial. We further prove that the
se quotient groups are neither left-orderable nor locally indicable. This
is a joint work with Dr. Swarup Bhowmik and Prof. Kashyap Rajeevsarathy.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debamita Chatterjee (ISI Bangalore)
DTSTART:20261023T083000Z
DTEND:20261023T090000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/17
DESCRIPTION:Title: Characterisation of distal actions of automorphisms on the space of o
ne-parameter subgroups of Lie groups\nby Debamita Chatterjee (ISI Bang
alore) as part of World of GroupCraft VI\n\n\nAbstract\nLet $G$ be a conne
cted Lie group and let $\\mathrm{Sub}_G$ be the space of all closed subgro
ups of $G$\, endowed with the Chabauty topology. We consider $\\mathrm{Sub
}^p_G$ the closure (in $\\mathrm{Sub}_G$) of the set of closed one-paramet
er subgroups of $G$. There is a natural action of $\\mathrm{Aut}(G)$\, the
group of automorphisms of $G$\, on $\\mathrm{Sub}_G$ which keeps $\\mathr
m{Sub}^p_G$ invariant. We study the dynamics of $\\mathrm{Aut}(G)$-action
on $\\mathrm{Sub}^p_G$ in terms of distality and characterise the class of
automorphisms which act distally on $\\mathrm{Sub}^p_G$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rana Sardar (IISER Mohali)
DTSTART:20261023T090000Z
DTEND:20261023T093000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/18
DESCRIPTION:Title: On 2-sphere Bowditch boundaries attaining conformal dimension\nby
Rana Sardar (IISER Mohali) as part of World of GroupCraft VI\n\n\nAbstrac
t\nThe relative Cannon conjecture predicts that a relatively hyperbolic gr
oup whose Bowditch boundary is homeomorphic to the standard 2-sphere is Kl
einian\, with virtually $\\mathbb{Z}^2$ peripheral subgroups. In this talk
\, I will establish this conjecture under an additional analytic assumptio
n on the boundary.\n\nI will begin by recalling the basic notions of a rel
atively hyperbolic group $(G\,\\mathcal{P})$ and its Bowditch boundary\, f
ollowed by the relevant metric notions: Ahlfors $Q$-regularity and the Ahl
fors regular conformal dimension. I will then discuss the background to th
e problem\, including the classical Cannon conjecture for hyperbolic group
s and its analytic formulation due to Bonk and Kleiner. Finally\, I will p
resent the main result: if $(G\,\\mathcal{P})$ is relatively hyperbolic\,
its Bowditch boundary is homeomorphic to the standard 2-sphere\, and the b
oundary admits an Ahlfors $Q$-regular metric attaining the Ahlfors regular
conformal dimension\, then $G$ acts discretely and isometrically on hyper
bolic 3-space $\\mathbb{H}^3$\, and every peripheral subgroup $P \\in \\ma
thcal{P}$ is virtually $\\mathbb{Z}^2$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Cavalieri (University of Padua)
DTSTART:20261023T100000Z
DTEND:20261023T103000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/19
DESCRIPTION:Title: Proportion of commutators in some weakly regular branch groups\nb
y Francesca Cavalieri (University of Padua) as part of World of GroupCraft
VI\n\nAbstract: TBA\n\nWe study the proportion of commutators in the clos
ure of (weakly) regular branch groups $G$ contained in the standard Sylow
pro-$p$ subgroup of $\\Aut(T)$. In some branch groups\, such as certain GG
S groups and the Grigorchuk group\, not every element of the derived subgr
oup is a single commutator\, yet many are. We prove that the lower box dim
ension of the set of commutators with a fixed element\, with respect to th
e level stabilizer filtration\, equals 1 in the closure of $G$. Under addi
tional hypothesis\, this extends to other filtrations\, such as the lower
$p$ central series. In contrast\, this fails for some pro-$p$ groups\; for
instance\, in the $d$-generated free pro-$p$ group.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Unai Marin (University of the Basque Country)
DTSTART:20261023T103000Z
DTEND:20261023T110000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/20
DESCRIPTION:Title: Is every sofic tree shift group of finite type?\nby Unai Marin (U
niversity of the Basque Country) as part of World of GroupCraft VI\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikel E. Garciarena (University of Düsseldorf)
DTSTART:20261023T110000Z
DTEND:20261023T113000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/21
DESCRIPTION:Title: Generalized torsion in amenable groups\nby Mikel E. Garciarena (U
niversity of Düsseldorf) as part of World of GroupCraft VI\n\n\nAbstract\
nGeneralized torsion extends the notion of finite order by allowing produc
ts of conjugates of an element in place of its powers. We study how amenab
ility and the structure of normal subgroups can be used to detect such rel
ations.\n\nIn this talk\, we present an amenability-based method for detec
ting generalized torsion. If the normal closure $N$ of an element is finit
ely generated and amenable\, then the element is generalized torsion preci
sely when its image in the quotient by $N'=[N\,N]$ is generalized torsion.
The proof uses invariant means to construct homomorphisms to the additive
group of real numbers that detect the absence of positive conjugacy relat
ions.\n\nWe apply this criterion to finitely generated amenable branch gro
ups\, proving that an element is generalized torsion exactly when its imag
e in the abelianization has finite order. In particular\, the generalized
torsion elements\, together with the identity\, form a characteristic subg
roup. We also show that every finite-index subgroup of a finitely generate
d amenable just-infinite branch group consists entirely of generalized tor
sion elements\, with the conjugators chosen inside that subgroup.\n\nThis
is joint work with Marialaura Noce.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Merladet (University of Southampton)
DTSTART:20261023T120000Z
DTEND:20261023T123000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/22
DESCRIPTION:Title: Virtual retracts in free constructions\nby Jon Merladet (Universi
ty of Southampton) as part of World of GroupCraft VI\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Pineda (University of the Basque Country)
DTSTART:20261023T123000Z
DTEND:20261023T130000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/23
DESCRIPTION:Title: Automorphisms of graphs of groups\nby Jon Pineda (University of t
he Basque Country) as part of World of GroupCraft VI\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clara Skowronek (Complutense University of Madrid)
DTSTART:20261023T130000Z
DTEND:20261023T133000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/24
DESCRIPTION:Title: Generalizing structures of branch groups to nearly branch groups\
nby Clara Skowronek (Complutense University of Madrid) as part of World of
GroupCraft VI\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Talia Shlomovich (Heriot-Watt University)
DTSTART:20261023T140000Z
DTEND:20261023T143000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/25
DESCRIPTION:Title: Non-planarity of Morse boundaries\nby Talia Shlomovich (Heriot-Wa
tt University) as part of World of GroupCraft VI\n\n\nAbstract\nAlthough n
on-planar boundaries are common among hyperbolic groups\, it is surprising
ly difficult to construct them. In this talk\, we discuss an approach to d
oing so for the Morse boundary. Introduced by Cordes (2017)\, this roughly
describes the boundary as a set of Morse geodesics\, which can be thought
of as “hyperbolic directions” in non-hyperbolic spaces.\n\nWe then di
scuss right-angled Coxeter groups as a useful class of candidate groups\,
where useful properties such as hyperbolicity and Morse subgroups can be c
haracterised in terms of the defining graph. I will give examples of non-M
orse subgroups known as burst cycles\, and explain how this relates to the
problem of constructing non-planar Morse boundaries. I will then share my
progress towards a right-angled Coxeter group with non-planar Morse bound
ary.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean O'Brien (University of Glasgow)
DTSTART:20261023T143000Z
DTEND:20261023T150000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/26
DESCRIPTION:Title: The dual Artin group and isomorphism problem\nby Sean O'Brien (Un
iversity of Glasgow) as part of World of GroupCraft VI\n\n\nAbstract\nThe
dual Artin group is a group construction coming from an interval of reflec
tion factorisations in Coxeter groups\, and is conjectured to be isomorphi
c to the corresponding (standard) Artin group. It has played a key role in
the last decade in advancing some problems related to Artin groups\, espe
cially those of affine type\, where it was vital in providing a solution t
o the word problem and proving the K($\\pi$\,1) conjecture.\n\nWe explore
the construction and the isomorphism conjectured above. We give necessary
and sufficient conditions for the isomorphism\, and argue why these hold w
hen all defining relations in the Coxeter group are sufficiently long e.g.
abab = baba (length 4)\, or longer. Our methods use simple arguments abou
t embedded paths in the plane\, and exploit how these interact and constra
in the solution to the word problem in Coxeter groups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Poppy Azmi (University of Warwick)
DTSTART:20261023T150000Z
DTEND:20261023T153000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/27
DESCRIPTION:Title: Walls in Coxeter groups\nby Poppy Azmi (University of Warwick) as
part of World of GroupCraft VI\n\n\nAbstract\nCoxeter groups have strong
underlying geometry\, being generated by reflections. In this talk\, I wil
l introduce Coxeter groups and discuss their action on the Davis complex.
I will talk about how we can construct a set of walls on the complex to sh
ow that Coxeter groups are cubulated\, which gives many interesting conseq
uences such as solvability of the word problem and the homology being fini
tely generated in every dimension.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katie Reilly (University of East Anglia)
DTSTART:20261023T160000Z
DTEND:20261023T163000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/28
DESCRIPTION:Title: Rational subsets of one-relator free-by-cyclic groups\nby Katie R
eilly (University of East Anglia) as part of World of GroupCraft VI\n\n\nA
bstract\nMembership problems in groups have been widely studied throughout
the past century. Typically\, membership problems ask\, for a given group
G and substructure H of G\, whether there exists an algorithm which\, giv
en g ∈ G\, decides whether g ∈ H. Well-known membership problems inclu
de the subgroup membership problem and the submonoid membership problem.\n
\nRational subsets are more general substructures of a group. A subset R o
f G is rational if it is the image of a regular language over the set of g
enerators and their inverses\, under the canonical morphism. Every subgrou
p and submonoid is a rational subset\, but there are many rational subsets
which are neither. The rational subset membership problem asks\, given a
rational subset R of a group G\, whether there exists an algorithm which\,
given g ∈ G\, decides whether g ∈ R.\n\nIn 2019\, Gray proved that th
e group Gp has undecidable r
ational subset membership problem. This was the first example of a one-rel
ator group with undecidable rational subset membership problem. This group
is also a one-relator group which is free-by-cyclic\, meaning it can be e
xpressed in the form F⋊Z\, where F is a free group.\n\nIn this talk\, I
will present two main results. The first concerns free-by-cyclic groups wh
ere F is a free group of finite rank and gives conditions under which the
rational subset membership problem is (un)decidable. I will explain how th
is relates to the rational subset membership problem for certain one-relat
or groups\, and also to the word problem for one-relator inverse monoids.
The second result concerns certain one-relator free-by-cyclic groups where
F is not necessarily of finite rank and proves that membership in certain
rational subsets is decidable. I will discuss some consequences of this r
esult for families of one-relator groups\, including surface groups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paula Heim (University of Oxford and MPIM Leipzig)
DTSTART:20261023T163000Z
DTEND:20261023T170000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/29
DESCRIPTION:Title: Realising all countable groups as quasiisometry groups\nby Paula
Heim (University of Oxford and MPIM Leipzig) as part of World of GroupCraf
t VI\n\n\nAbstract\nWhen studying a metric space\, it can be interesting t
o consider the group of maps preserving its large scale geometry. These ma
ps are called quasiisometries and the associated group is called the QI gr
oup. Determining the QI group of a metric space is\, in general\, a hard p
roblem. Few QI groups are known explicitly\, and most of these results ari
se from a phenomenon called QI rigidity\, which essentially says that QI(X
)=Isom(X). In this talk we will explore these concepts and give a partial
answer to the question which groups can arise as QI groups of metric space
s. This talk is based on joint work with Joe MacManus and Lawk Mineh.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harry Iveson (University of Southampton)
DTSTART:20261023T170000Z
DTEND:20261023T173000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/30
DESCRIPTION:Title: Decidability of the R-Infinity Property for Hyperbolic Groups and The
ir Automorphisms\nby Harry Iveson (University of Southampton) as part
of World of GroupCraft VI\n\n\nAbstract\nThis talk will introduce the "aut
omorphism-twisted conjugacy" relation for groups\, on which the R-infinity
property is based. We will quickly see that\, in general\, this property
is undecidable — that is\, there is no algorithm which can tell us wheth
er a given (finitely presented) group has Property R-infinity or not. Howe
ver\, this need not be the case if we restrict ourselves to a smaller clas
s of groups.\n\nI will demonstrate an algorithm which\, given a finite pre
sentation of a hyperbolic group\, decides whether or not that group satisf
ies the R-infinity property.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Madeline Horton (George Mason University)
DTSTART:20261023T193000Z
DTEND:20261023T200000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/31
DESCRIPTION:Title: Divergence on average in hyperbolic metric spaces\nby Madeline Ho
rton (George Mason University) as part of World of GroupCraft VI\n\n\nAbst
ract\nIn 1984\, Sullivan proved that the Hausdorff dimension of the limit
set of a geometrically finite Kleinian group acting on real hyperbolic 3-s
pace can be completely determined by the growth rate of the group. Bishop
and Jones later generalized this result to further show that the Hausdorff
dimension of the conical limit set of any nonelementary Kleinian group ag
rees with its critical exponent\, which has since paved the way for a myri
ad of analogous results in a variety of settings. In recent work\, Riquelm
e and Velozo show that the Hausdorff dimension of geodesic directions that
are both recurrent and diverge on average agrees with the critical expone
nt at infinity for any complete\, pinched negative curvature Riemannian ma
nifold. In this talk\, I discuss work that extends Riquelme and Velozo's r
esult to Gromov hyperbolic spaces. This result further serves to provide a
bridge between the theory in Kleinian groups\, higher rank representation
s\, and certain subgroups of mapping class groups. This is joint with Harr
ison Bray\, Anton Lukyanenko\, and Gabriel Lumpkin.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colby Kelln (University of Minnesota)
DTSTART:20261023T200000Z
DTEND:20261023T203000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/32
DESCRIPTION:Title: Filling flatly fibered cusps of Hyperbolic $n$-manifolds\nby Colb
y Kelln (University of Minnesota) as part of World of GroupCraft VI\n\n\nA
bstract\nDehn filling is a classical tool for producing negatively curved
manifolds from cusped hyperbolic 3-manifolds\, and results of Mosher-Sagee
v and Fujiwara-Manning extend this idea to higher dimensions when cusp cro
ss sections are tori. In this talk\, I will discuss a generalization to hy
perbolic manifolds whose cusps can have more complicated cross sections---
ones that admit a Riemannian submersion onto a flat base with totally geod
esic fiber. Filling along the fibers of such a cusp can still produce a no
npositively (and in some cases negatively) curved space\, provided that th
e fibers have large enough systole. Group theoretically\, this filling tak
es a relatively hyperbolic fundamental group and creates a related hyperbo
lic one. I'll introduce the Ratcliffe-Tschantz hyperbolic 5-manifold\, who
se cusps are bundles with Hantzsche-Wendt fiber over the circle\, and show
how the filling result\, coupled with some group theory\, gives informati
on about the geometry of its cusps.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Megha Bhat (CUNY)
DTSTART:20261023T203000Z
DTEND:20261023T210000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/33
DESCRIPTION:Title: Boundedness of certain homeomorphism groups\nby Megha Bhat (CUNY)
as part of World of GroupCraft VI\n\n\nAbstract\nA group is said to be bo
unded if it has finite diameter under any bi-invariant metric. Bi-invarian
t metrics can be used to encode various algebraic properties of the group\
, such as perfectness and normal generation\; and boundedness of a metric
corresponds to a uniform bound on the associated algebraic property. In th
is talk\, we will define portable manifolds and show that the homeomorphis
m group of a portable manifold is bounded. We will give two proofs of this
fact\, one using an algebraic construction and the other using the geomet
ry of the group.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Shaji (University of Utah)
DTSTART:20261023T213000Z
DTEND:20261023T220000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/34
DESCRIPTION:Title: Švarc-Milnor actions and asymptotic dimension for big mapping class
groups\nby George Shaji (University of Utah) as part of World of Group
Craft VI\n\n\nAbstract\nIn their paper\, Branman\, Domat\, Hoganson and Ly
mann proved that if a topological group acts in a "nice" way on a simplici
al graph\, then the group has a well defined geometry that makes it quasi-
isometric to the graph. These actions generalize a Svârc-Milnor action to
the context of coarsely boundedly (CB) generated Polish groups.\n\nWe ada
pt these ideas to the context of locally bounded Polish groups and then co
nstruct an arc and curve model coarsely equivalent to Map(S) when Map(S) i
s locally bounded and S has a non-displaceable subsurface. We then use thi
s model to show that the asymptotic dimension of Map(S) is infinite.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Karpinski (McGill University)
DTSTART:20261023T220000Z
DTEND:20261023T223000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/35
DESCRIPTION:Title: Decent actions of groups on restricted products\nby Christopher K
arpinski (McGill University) as part of World of GroupCraft VI\n\n\nAbstra
ct\nAn action of a group G on a set X is decent if: \n\nEvery subgroup of
G with a finite orbit in X must fix a point in X\, and \nEvery finitely ge
nerated subgroup of G having the property that all of its elements fix a p
oint of X must fix a point in X. \nA motivating example of a decent action
is any isometric action on a tree. We discuss actions of groups on so-cal
led "restricted products" of sets\, giving sufficient conditions for when
such actions are decent. We conclude with applications to subgroups of the
Cremona group Cr_n(k) over a field k\, the group of all birational automo
rphisms of the projective space P^n(k).\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fotis Ioannidis (University of Tennessee\, Knoxville)
DTSTART:20261023T223000Z
DTEND:20261023T230000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/36
DESCRIPTION:Title: Quasiconformal uniformization and extension for planar trees\nby
Fotis Ioannidis (University of Tennessee\, Knoxville) as part of World of
GroupCraft VI\n\n\nAbstract\nA classical uniformization theorem of Rickman
from 1966 asserts that every bounded turning planar arc is the image of t
he unit segment under a quasiconformal self-map of the plane. We prove an
analogous uniformization theorem for planar trees by showing that every pl
anar quasiconformal tree with uniform branch separation is quasiconformall
y equivalent to a quasiconvex planar tree with uniform branch separation a
nd Hausdorff dimension arbitrarily close to 1. Along the way\, we show tha
t every quasisymmetric (resp. bi-Lipschitz) homeomorphism between planar q
uasiconformal trees that respects the counterclockwise orientation of the
branches at every branch point can be extended quasisymmetrically (resp. b
i-Lipschitz) to the whole plane. As a corollary of the extension theorem w
e construct a large class of quadrivalent quasiconformal trees\, which inc
ludes the Vicsek fractal\, so that each tree in this class is the Julia se
t of a uniformly quasiregular map of $\\mathbb{R}^2$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Spessato (University Cusano)
DTSTART:20261023T113000Z
DTEND:20261023T120000Z
DTSTAMP:20261107T204344Z
UID:GroupCraft6/37
DESCRIPTION:Title: Graph bundles and Cayley graphs\nby Stefano Spessato (University
Cusano) as part of World of GroupCraft VI\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GroupCraft6/37/
END:VEVENT
END:VCALENDAR