BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Yuya Kodama (Kagoshima University)
DTSTART:20250831T230000Z
DTEND:20250831T233000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/37
DESCRIPTION:Title: Divergence properties of Thompson-like groups\nby Yuya Kodama (Ka
goshima University) as part of World of GroupCraft V\n\n\nAbstract\nThe di
vergence function of a finitely generated group is the function that is th
e length of the path connecting two points at the same distance from the o
rigin while avoiding a small ball with the center at the origin in its Cay
ley graph. This function represents a "degree of connectedness at the infi
nity" of a Cayley graph and provides a quasi-isometry invariant of finitel
y generated groups. In this talk\, we will discuss the results of the func
tions for Thompson’s groups and their generalizations.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aoi Wakuda (University of Tokyo)
DTSTART:20250831T233000Z
DTEND:20250901T000000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/38
DESCRIPTION:Title: Separability Criteria for Two Loops on an Orientable Surface and the
Goldman Bracket\nby Aoi Wakuda (University of Tokyo) as part of World
of GroupCraft V\n\n\nAbstract\nIn this talk\, we present algebraic criteri
a—via the Goldman bracket—for determining when two (not necessarily si
mple) free homotopy classes of loops on an oriented surface admit disjoint
representatives. As an application\, we compute the center of the Goldman
Lie algebra of a pair of pants. We extend a method of Kabiraj\, which was
originally restricted to oriented surfaces filled by simple closed geodes
ics\, and show that in our case\, the center is generated by the class of
contractible loops and the classes of loops that wind multiple times aroun
d a single puncture or boundary component.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryoya Arimoto (RIMS\, Kyoto)
DTSTART:20250901T000000Z
DTEND:20250901T003000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/39
DESCRIPTION:Title: Topological full group arising from Cuntz--Toeplitz algebras\nby
Ryoya Arimoto (RIMS\, Kyoto) as part of World of GroupCraft V\n\n\nAbstrac
t\nIt is well known that the Higman--Thompson groups\, which are one of th
e generalizations of the celebrated Thompson group\, arise from Cuntz alge
bras.\nIn this talk\, I will discuss a new generalization of the Thompson
group arising from Cuntz--Toeplitz algebras\, focusing particularly on the
ir normal subgroups and abelianizations.\nThis is part of joint work with
T. Sogabe.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takatoshi Hama (Nihon University)
DTSTART:20250901T010000Z
DTEND:20250901T013000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/40
DESCRIPTION:Title: Hyperbolicity and the exponential growth rate of the affine cactus gr
oup of degree three\nby Takatoshi Hama (Nihon University) as part of W
orld of GroupCraft V\n\n\nAbstract\nThe affine cactus group was introduced
by Ilin\, Kamnitzer\, Li\, Przytycki\, and Rybnikov. In this talk\, we wi
ll show that the affine cactus group $AJ_3$ of degree three is hyperbolic\
, which implies that its growth rate is exponential. We will also provide
an explicit growth function with respect to the standard generating set fo
r $AJ_3$ and calculate its precise exponential growth rate.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreani Petrou (Okinawa Institute of Science & Technology)
DTSTART:20250901T013000Z
DTEND:20250901T020000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/41
DESCRIPTION:Title: Knots\, links and Harer-Zagier factorisability\nby Andreani Petro
u (Okinawa Institute of Science & Technology) as part of World of GroupCra
ft V\n\n\nAbstract\nThe topological information contained in the HOMFLY-PT
polynomial becomes more transparent after taking its discrete Laplace tra
nsform\, called the Harer-Zagier (HZ) transform. In some special cases of
knots and links\, which are related by full twists and Jucys-Murphy braids
\, the latter admits a simple factorised form and hence it is fully encode
d in a set of integer exponents. By considering the character expansion of
the HOMFLY-PT polynomial\, further insight into the structure of HZ can b
e obtained. The relation of HZ factorisability with other knot invariants
will be discussed.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bingxue Tao (Kyoto University)
DTSTART:20250901T020000Z
DTEND:20250901T023000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/42
DESCRIPTION:Title: The extension problem of quasimorphisms\nby Bingxue Tao (Kyoto Un
iversity) as part of World of GroupCraft V\n\n\nAbstract\nIn recent years\
, one active area of research on quasimorphisms has been the extension pro
blem—that is\, whether a quasimorphism defined on a subgroup can be exte
nded to a quasimorphism on the whole group. \nThis problem has been proved
important\, e.g.\, in the study of commuting symplectomorphisms by Kawasa
ki\, Kimura\, Matsushita and Mimura\, and in the study of hierarchical hyp
erbolicity of quotients of mapping class groups by Fournier-Facio\, Mangio
ni and Sisto. \nAs a notable answer to this problem\, Hull and Osin showed
the extendability of any antisymmetric quasimorphism on a hyperbolically
embedded subgroup in 2013.\nIn this talk\, I will explain how Hull-Osin's
result can be generalized in the context of weak relative hyperbolicity to
include examples of normal subgroups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugen Rogozinnikov (Korea Institute for Advanced Study (KIAS))
DTSTART:20250901T030000Z
DTEND:20250901T033000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/43
DESCRIPTION:Title: Positive representations\nby Eugen Rogozinnikov (Korea Institute
for Advanced Study (KIAS)) as part of World of GroupCraft V\n\n\nAbstract\
nHigher rank Techmüller theory deals with spaces of representations of th
e fundamental group of a surface into a reductive Lie group $G$\, modulo t
he conjugation\, especially with the connected components (called higher r
ank Teichmüller spaces) that consist entirely of injective representation
s with discrete image.\n\nIn the last two decades in works of Fock\, Gonch
arov\, Burger\, Iozzi\, Guichard\, Wienhard\, and others researchers\, it
was discovered that the most interesting higher Teichmüller spaces are em
erging from the groups $G$ having a positive structure\, i.e. certain subm
onoid $G_+$ with no invertible non-unit elements. Some of these submonoids
have been known since 1930’s as totally positive matrices and then gene
ralized by Lustzig for split real Lie groups. However it lefts out a large
class of non-split reductive Lie groups such as $SO(p\,q)$. O. Guichard a
nd A. Wienhard filled this gap in 2018 by introducing the Theta-positivity
\, which also includes submonoids $SO(p\,q)_+$ sitting in unipotent group
of $SO(p\,q)$ and $Sp(2n\,R)_+$ which is the set of upper uni-triangular b
lock 2x2-matrices with a symmetric positive definite matrix in the upper r
ight corner.\n\nIn my talk\, I introduce the Theta-positivity for Lie grou
ps and explain how the spaces of positive representations of the fundament
al group of a punctured surface into a Lie group with a positive structure
can be parametrized\, and how we can describe the topology of these space
s using this parametrization. This is a joint work with O. Guichard and A.
Wienhard.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seungyeol Park (KAIST)
DTSTART:20250901T033000Z
DTEND:20250901T040000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/44
DESCRIPTION:Title: Deformations of Coxeter 3-orbifolds\nby Seungyeol Park (KAIST) as
part of World of GroupCraft V\n\n\nAbstract\nCoxeter orbifolds arise from
convex polytopes by silvering their codimension-one faces and removing ce
rtain higher-codimension faces. Like other manifolds and orbifolds\, they
admit real projective structures\, whose deformation spaces are natural ob
jects of study. For Coxeter polytopes\, these deformation spaces admit a c
anonical map into the so-called realization spaces of polytopes. This pers
pective allows us to investigate both local and global properties of the d
eformation spaces. In particular\, it provides a method to establish the s
moothness of the deformation spaces of orderable Coxeter 3-orbifolds.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seunghoon Hwang (Seoul National University)
DTSTART:20250901T040000Z
DTEND:20250901T043000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/45
DESCRIPTION:Title: Convex projective deformations of cusped hyperbolic 3-manifolds\n
by Seunghoon Hwang (Seoul National University) as part of World of GroupCr
aft V\n\n\nAbstract\nLet M be a non-compact\, complete hyperbolic 3-manifo
ld with finite volume. By Mostow-Prasad rigidity\, such a structure on M i
s unique up to isometry. However\, this unique structure gives a distingui
shed point in the deformation space of properly convex projective structur
es on M\, in which the hyperbolic structure can be deformed without losing
completeness. The goal of this talk is to tell you the story of convex pr
ojective deformations\, the ends of M that arise from the structures defor
med in such a way\, and some of the strategies people have chosen to under
stand this world.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Homin Lee (Korea Institute for Advanced Study (KIAS))
DTSTART:20250901T050000Z
DTEND:20250901T053000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/46
DESCRIPTION:Title: Introduction to Zimmer program\nby Homin Lee (Korea Institute for
Advanced Study (KIAS)) as part of World of GroupCraft V\n\n\nAbstract\nIn
this talk\, we survey higher rank lattice actions on manifolds\, so calle
d Zimmer program. The aim of the program is to classify (or reveal rigidit
y of) smooth higher rank lattice actions on manifolds. We will discuss mot
ivations\, known results\, and some of open questions in this direction.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kee Taek Kim (KAIST)
DTSTART:20250901T053000Z
DTEND:20250901T060000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/47
DESCRIPTION:Title: Equivariant Unknotting Number and Involutive Khovanov Homology\nb
y Kee Taek Kim (KAIST) as part of World of GroupCraft V\n\n\nAbstract\nA k
not $K$ is said to be \\emph{strongly invertible} if there exists an orien
tation-preserving involution of $S^3$ that preserves $K$ while reversing i
ts orientation. Many knot invariants can be extended to an equivariant set
ting. For example\, the \\emph{equivariant unknotting number} is defined a
s the minimal number of crossing changes required to transform a given str
ongly invertible knot $K$ into the unknot $U$\, under the constraint that
the knot must remain symmetric with respect to the original involution. In
this talk\, I will introduce Taketo Sano’s involutive version of Khovan
ov homology for strongly invertible knots\, and demonstrate how it can be
applied to provide a lower bound for the equivariant unknotting number.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swarup Bhowmik (IISER Bhopal)
DTSTART:20250901T070000Z
DTEND:20250901T073000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/49
DESCRIPTION:Title: Quasi-isometry group of the Euclidean spaces\nby Swarup Bhowmik (
IISER Bhopal) as part of World of GroupCraft V\n\n\nAbstract\nThe notion o
f quasi-isometry is one of the fundamental concepts in geometric group the
ory. For a given metric space $X$\, the group of quasi-isometries from $X$
to itself is denoted as $QI(X)$ and serves as a quasi-isometric invariant
of $X$. It is well-knowm that when $\\Gamma$ is a finitely generated grou
p\, a choice of finite generating set $S$ gives the word metric $d_S$ on $
\\Gamma$\, making it a metric space. Then one can talk about the quasi-iso
metry group $QI(\\Gamma)$ and it can be shown that $QI(\\Gamma)$ does not
depend on the choice of $S$. However\, the determination of $QI(\\Gamma)$
for arbitrary groups remains a challenging task\, and very limited knowle
dge is available concerning these groups in general.\n\n\nEven for $\\Gamm
a=\\mathbb{Z}^n$\, $QI(\\mathbb{Z}^n)(\\cong QI(\\mathbb{R}^n))$ remain la
rgely unexplored\, especially for $n>1$ [3]. In [1]\, the authors provide
a combinatorial criterion reliant on the vertices and edges of simplicial
structures\, to determine whether a piecewise-linear homeomorphism to be a
quasi-isometry. By employing this criterion\, it can be shown that the ce
nter of the group $QI(\\mathbb{R}^n)$ is trivial [1].\n\n\nIn particular w
hen $n=1$\, Gromov and Pansu observed that $Bilip(\\mathbb{R})\\rightarrow
QI(\\mathbb{R})$ is surjective. Furthermore\, Sankaran [4] proved that th
ere is a surjection from $PL_\\delta(\\mathbb{R})$ to $QI(\\mathbb{R})$. I
n [2]\, the authors introduce an invariant for the elements of $QI(\\mathb
b{R_{+}})$ and split it into smaller units.\n\n\nIn recent times left-orde
rability and locally indicability of a group are drawing the attention of
many researchers since the left-orderable groups\, left-invariant orders o
n groups and locally indicable groups have strong connections with algebra
\, dynamics and topology. It is known that every locally indicable group i
s left orderable\; it is an interesting question whether the converse is t
rue. In [2]\, the author came up with a counterexample.\n\n[1] S. Bhowmik\
, P. Chakraborty\, : A combinatorial criterion and center for the quasi-is
ometry groups of Euclidean spaces. Topol. Appl.\,342 (2024)\, 108795.\n\n[
2] S. Bhowmik\, P. Chakraborty\, : A structure theorem and left-orderabili
ty of a quotient of quasi-isometry group of the real line. Geom. Dedicata\
, 218\, 12 (2024).\n\n[3] O. Mitra\, P. Sankaran\, : Embedding certain di
ffeomorphism groups in the quasi-isometry groups of Euclidean spaces\, Top
ology Appl.\, 265 (2019)\, 11pp.\n\n[4] P. Sankaran\, : On homeomorphisms
and quasi-isometries of the real line. Proc. of the Amer. Math. Soc.\, 134
(2005) 1875-1880.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sagar Kalane (IMSc\, Chennai)
DTSTART:20250901T073000Z
DTEND:20250901T080000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/50
DESCRIPTION:Title: Discrete subgroups generated by two parabolic maps from rank-one isom
etry groups\nby Sagar Kalane (IMSc\, Chennai) as part of World of Grou
pCraft V\n\n\nAbstract\nLet $A$ and $B$ be two Heisenberg translations in
$\\mathrm{Sp}(2\,1)$\nor $\\mathrm{SU}(2\,1)$ with distinct fixed points.
Here\,\n$\\mathrm{Sp}(2\,1)$ and $\\mathrm{SU}(2\,1)$ act isometrically on
the\nquaternionic and complex hyperbolic spaces\, respectively. We provid
e\nsufficient conditions that guarantee that the subgroup $\\langle A\, B\
n\\rangle$ is discrete and free\, using Klein’s combination theorem.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pabitra Barman (IISER Mohali)
DTSTART:20250901T080000Z
DTEND:20250901T083000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/51
DESCRIPTION:Title: Dominating surface-group representations in $\\mathrm{PSL}_n(\\mathbb
{C})$ and $\\mathrm{PU}(2\,1)$\nby Pabitra Barman (IISER Mohali) as pa
rt of World of GroupCraft V\n\n\nAbstract\nLet $S$ be a connected\, orient
ed\, punctured surface of negative Euler characteristic. In this talk\, we
present two comparison results for representations of $\\pi_1(S)$ into hi
gher-rank Lie groups. First\, we show that a generic representation $\\rho
:\\pi_1(S)\\rightarrow \\mathrm{PSL}_n(\\mathbb{C})$ is dominated by a `po
sitive' representation $\\rho_0:\\pi_1(S)\\rightarrow \\mathrm{PSL}_n(\\ma
thbb{R})$ in both the Hilbert length spectrum and the translation length s
pectrum in the symmetric space $\\mathbb{X}_n= \\mathrm{PSL}_n(\\mathbb{C}
)/ \\mathrm{PSU}(n)$\, while preserving the lengths of the peripheral curv
es. This is a joint work with Subhojoy Gupta.\n\n Second\, we extend th
is perspective to complex hyperbolic geometry: we show that a $T$-bent rep
resentation $\\rho:\\pi_1(S)\\rightarrow \\mathrm{PU}(2\,1)$ is dominated
by a discrete and faithful representation $\\rho_0:\\pi_1(S)\\rightarrow \
\mathrm{PO}(2\,1)$ in the Bergman translation length spectrum\, again pre
serving the lengths of peripheral curves. This is a joint work with Krishn
endu Gongopadhyay.\n \n These results offer new insights into the rol
e of positivity in higher-rank Teichm\\"{u}ller theory and complex hyperbo
lic geometry.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debattam Das (IISER Mohali)
DTSTART:20250901T090000Z
DTEND:20250901T093000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/52
DESCRIPTION:Title: Combinatorial growth of the reciprocal classes in the Hecke groups\nby Debattam Das (IISER Mohali) as part of World of GroupCraft V\n\n\nAb
stract\nAn element in a group is said to be reciprocal if it is conjugate
to its own inverse. In this talk\, we will discuss about the classificatio
n of the reciprocal elements of the Hecke group. Subsequently\, we discuss
about the counting problem for reciprocal classes with respect to the wor
d length in the context of Hecke groups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neha Malik (Chennai Mathematical Institute)
DTSTART:20250901T093000Z
DTEND:20250901T100000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/53
DESCRIPTION:Title: The Subalgebra of Stiefel-Whitney Classes for Finite Symplectic Group
s\nby Neha Malik (Chennai Mathematical Institute) as part of World of
GroupCraft V\n\n\nAbstract\nTitle: The Subalgebra of Stiefel-Whitney Class
es for Finite Symplectic Groups\n\nAbstract: Let $G$ be a finite group. As
sociated to a complex orthogonal representation $\\pi$ of $G$ is a sequenc
e of cohomological invariants $w_i(\\pi)$\, called the Stiefel-Whitney Cla
sses (SWCs) of $\\pi$\, which live in the group cohomology $H^*(G\, Z/2Z)$
.\n There are not many explicit calculations in the literature on t
hese characteristic classes for non-abelian groups $G$. In a series of joi
nt works with Prof. Steven Spallone\, we have computed SWCs for several fi
nite groups of Lie type in terms of character values at diagonal involutio
ns. These calculations can answer some interesting questions\, such as: Wh
at is the subalgebra of $H^*(G\, Z/2Z)$ generated by SWCs of all orthogona
l $\\pi$? Is it the whole group cohomology ring? This talk will give an ov
erview of some of our results for $G=Sp(2n\,q)$ when $q$ is odd.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shrinit Singh (ICTS-TIFR\, Bengaluru)
DTSTART:20250901T100000Z
DTEND:20250901T103000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/54
DESCRIPTION:Title: On the almost palindromic width of certain free constructions of grou
ps\nby Shrinit Singh (ICTS-TIFR\, Bengaluru) as part of World of Group
Craft V\n\n\nAbstract\nWe show that the $m$-almost palindromic width of an
HNN extension or an amalgamated free product is infinite\, except in the
special case where the amalgamated subgroup has index two in each factor.
This is a joint work with Prof. Krishnendu Gongopadhyay.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bianca Marchionna (Heidelberg)
DTSTART:20250901T110000Z
DTEND:20250901T113000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/55
DESCRIPTION:Title: A Stallings-Swan-Dunwoody theorem for totally disconnected locally co
mpact groups\nby Bianca Marchionna (Heidelberg) as part of World of Gr
oupCraft V\n\n\nAbstract\nThe Stallings-Swan-Dunwoody theorem characterise
s finitely generated\nvirtually free groups as the finitely generated grou
ps of rational\ncohomological dimension at most 1 or\, equivalently\, as t
hose groups\nacting properly and coboundedly on a tree. We extend this the
orem within\nthe class of unimodular totally disconnected locally compact
(=t.d.l.c.)\ngroups.\nThe "locally profinite" structure of t.d.l.c. groups
facilitates the\ngeneralisation of results from cohomology or geometric g
roup theory\,\nalthough the arguments might not smoothly follow from the a
bstract case\n(as in the result we present). A key step towards our result
involves\ninformation about the sign of the Euler characteristic of the r
elevant\ngroups. Joint work with I. Castellano and T. Weigel.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Silva (University of Münster)
DTSTART:20250901T113000Z
DTEND:20250901T120000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/56
DESCRIPTION:Title: Continuity of asymptotic entropy and Poisson boundaries of random wal
ks on groups\nby Eduardo Silva (University of Münster) as part of Wor
ld of GroupCraft V\n\n\nAbstract\nThe asymptotic entropy of a random walk
on a countable group is a non-negative number that determines the existenc
e of non-constant bounded harmonic functions on the group. A natural quest
ion to ask is whether the asymptotic entropy\, seen as a function of the s
tep distribution of the random walk\, is continuous. In this talk\, I will
explain two recent results on the continuity of asymptotic entropy: one f
or groups whose Poisson boundaries can be identified with a compact metric
space carrying a unique stationary measure\, and another for wreath produ
cts $A \\wr Z^d$\, where $A$ is a countable group and $d \\geq 3$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andoni Zozaya (Public University of Navarre)
DTSTART:20250901T120000Z
DTEND:20250901T123000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/57
DESCRIPTION:Title: New families of strongly verbally concise groups\nby Andoni Zozay
a (Public University of Navarre) as part of World of GroupCraft V\n\n\nAbs
tract\nA word $w$ is said to be strongly concise in a profinite group $G$
if the corresponding verbal subgroup $w(G)$ is finite whenever the set of
w-values in G is of smaller cardinality than the continuum. In this talk\,
we will survey what is known about conciseness\; and\, drawing on the con
cept of equationally Noetherian groups\, present new families of groups wh
ere every word is strongly concise\, namely\, profinite linear groups and
profinite completions of abelian-by-polycyclic groups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Sabatino (University of the Basque Country)
DTSTART:20250901T133000Z
DTEND:20250901T140000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/59
DESCRIPTION:Title: Profinite groups with permutably complemented closed subgroups\nb
y Giulia Sabatino (University of the Basque Country) as part of World of G
roupCraft V\n\n\nAbstract\nIf $G$ is a group\, $G$ is said to be a $C$-gro
up if any subgroup $H$ of $G$ admits a permutable complement\, that is\, a
subgroup $K$ such that $G = H K$ and $H \\cap K = \\{1\\}$. The structure
of $C$-groups is well known\; a group $G$ is a $C$-group if and only if i
t can be expressed as a semidirect product $A = \\underset{i\\in I}{\\math
rm{Dr}} A_i$ by $A = \\underset{j \\in I}{\\mathrm{Dr}} A_j$\, where all f
actors $A_i$ and $B_j$ are finite of prime order and\, for each $i\\in I$\
, the subgroup $A_i$ is $G$-invariant.\n\nLet $G$ be a profinite group. We
say that $G$ is a profinite-$C$ group if every closed subgroup of $G$ adm
its a closed permutable complement. The purpose of this talk is to show th
e main properties of profinite-$C$ groups and to describe their structure.
Moreover\, we will provide a necessary and sufficient condition for the p
rofinite-$C$ group to be a $C$-group. This is joint work with G. A. Ferná
ndez Alcober.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leon Pernak (Saarland University)
DTSTART:20250901T140000Z
DTEND:20250901T143000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/60
DESCRIPTION:Title: Quadratic equations in wreath products of Abelian groups\nby Leon
Pernak (Saarland University) as part of World of GroupCraft V\n\n\nAbstra
ct\nQuadratic equations in wreath products of abelian groups\n\nOne of the
strongest results that one can hope for when studying decidability questi
ons in groups is the decidability of equations - is there an algorithm tha
t\, if we feed it a group equation\, tells us if the equation has or does
not have a solution in a given group? I will discuss this problem in the s
etting of wreath products of abelian groups. In particular\, I will explai
n how to prove that the problem is decidable for quadratic equations\, usi
ng techniques and intuitions inspired by commutative algebra. This is join
t work with Ruiwen Dong and Jan-Philipp Wächter.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harsh Patil
DTSTART:20250901T150000Z
DTEND:20250901T153000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/61
DESCRIPTION:Title: Coarse separation of metric spaces\nby Harsh Patil as part of Wor
ld of GroupCraft V\n\n\nAbstract\nA subset $A$ of a topological space $X$
is said to separate $X$ if $X-A$ has more than one connected component. Th
e large-scale geometric analogue is that of 'Coarse separation': \n A s
ubset $A$ of a metric space $X$ is said to coarsely separate $X$ if there
exists a set $C$ such that: i) neither $C$ nor $X-C$ are not in a finite n
eighbourhood $N_R(A)$\, and ii) for any positive real number $R$\, there e
xists $R'>0$\, such that for any $x \\in C$\, $y \\in X-C$ with $d(x\,y)<
R$\, there exists $z$ in $A$ such that $d(x\,z)< R' $ and $d(y\,z)< R'$. \
n Coarse separation arises naturally in geometric group theory\, suppo
se a finitely generated group $G$ splits over a subgroup $C$ then $C$ coar
sely separates $G$. I will go through the definition in detail and discuss
some results about coarsely separating subsets in of the n-dimensional Eu
clidean space.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oli Jones
DTSTART:20250901T153000Z
DTEND:20250901T160000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/62
DESCRIPTION:Title: Cyclic splittings of Artin groups\nby Oli Jones as part of World
of GroupCraft V\n\n\nAbstract\nArtin groups are a class of groups generali
sing right-angled\nArtin groups and braid groups\, with close connections
to Coxeter groups.\nIn this talk I will present a complete characterisatio
n of when Artin\ngroups split over $\\mathbb{Z}$\, generalising a result o
f Clay for RAAGs. I will\nthen discuss an application to the isomorphism p
roblem for Artin groups.\n\nThe talk is based on joint work with Giorgio M
angioni and Giovanni Sartori.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucia Asencio Martin
DTSTART:20250901T160000Z
DTEND:20250901T163000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/63
DESCRIPTION:Title: Stallings foldings for submonoids in automatic groups\nby Lucia A
sencio Martin as part of World of GroupCraft V\n\n\nAbstract\nThis talk wi
ll introduce work in progress on the submonoid and rational subset members
hip problem in automatic groups\, following an algorithmic\, Stallings fol
dings-like approach to the problem. \n\nThis project comes as a generalisa
tion of work by Kharlampovich\, Miasnikov and Weil from 2017\, where they
introduced Stallings foldings techniques for subgroups of automatic groups
providing a solution to the membership problem for subgroups that are qua
siconvex with respect to the automatic structure of the group. \n\nWe prop
ose an approach to work with subsets more general than subgroups\, where t
he folding technique and the notion of quasiconvexity is adapted to the fa
ct that our subsets are no longer closed under inversion. \n\nThe presente
d work is finished in the case of submonoids of automatic groups\, and sti
ll a work in progress for their rational subsets. Joint work with J. Britn
ell\, A. Duncan\, D. Francoeur and S. Rees.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Corrigan
DTSTART:20250901T170000Z
DTEND:20250901T173000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/64
DESCRIPTION:Title: Finiteness properties of some automorphism groups of right-angled Art
in groups\nby Gabriel Corrigan as part of World of GroupCraft V\n\n\nA
bstract\nRight-angled Artin groups (RAAGs) can be viewed as a generalisati
on of free groups. One prominent tool for studying automorphism groups of
free groups is Culler-Vogtmann's Outer space\; in recent years this has be
en generalised to 'untwisted Outer space' for RAAGs. A consequence of this
construction is an upper bound on the virtual cohomological dimension of
the 'untwisted subgroup' of outer automorphisms of a RAAG. However\, thi
s bound is sometimes larger than one expects\; I present work showing that
in fact it can be arbitrarily so\, by forming a new complex as a deformat
ion retraction of the untwisted Outer space. In a different direction\,
generalising work in the free groups setting from 1989\, I present an Out
er space for the symmetric automorphism group of a RAAG. A consequence o
f the proof is a strong finiteness property for many other subgroups of th
e outer automorphism group.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaked Bader
DTSTART:20250901T173000Z
DTEND:20250901T180000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/65
DESCRIPTION:Title: Group cohomology with Banach space coefficients\nby Shaked Bader
as part of World of GroupCraft V\n\n\nAbstract\nGromov conjectured that th
e $L^p$-cohomology of simple groups vanishes below the rank.\nFarb conject
ured a fixed point property for actions of lattices in such groups on CAT(
0) cell complexes of dimension lower than the rank.\nIn this talk I will g
ive a short introduction to group cohomology and prove that vanishing of
$\\ell^1$-cohomology up to degree $n$ implies a finite orbit for every act
ion on an $n$-dim contactible complex\, thus in particular establishing th
at Gromov's conjecture implies Farb's conjecture. I will then give some in
sight to the proof of Gromov's conjecture. \nThis talk is based on joint w
ork with Saar Bader\, Uri Bader and Roman Sauer\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abigail Hollingsworth
DTSTART:20250901T180000Z
DTEND:20250901T183000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/66
DESCRIPTION:Title: From the Boundary of Dehn Surgery Space to the Real Locus of the Shap
e Variety.\nby Abigail Hollingsworth as part of World of GroupCraft V\
n\n\nAbstract\nPoints on the shape variety of an ideal triangulation of a
hyperbolic three-manifold correspond to points in Dehn surgery space. We w
ill explore the points on the shape variety that correspond to the boundar
y of Dehn surgery space\, with a focus on the real locus of the shape vari
ety and examples like the figure-eight knot complement and $L^{2R}$ torus
bundle.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaitlin Ragosta (Brandeis University)
DTSTART:20250901T190000Z
DTEND:20250901T193000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/67
DESCRIPTION:Title: A marking graph for finite-type Artin groups.\nby Kaitlin Ragosta
(Brandeis University) as part of World of GroupCraft V\n\n\nAbstract\nBra
id groups are examples of both finite-type Artin groups and mapping class
groups. One important tool in the study of mapping class groups is the mar
king graph\, a graph whose vertex set consists of certain collections of c
urves on a surface S and which is quasi-isometric to the mapping class gro
up of S. In this talk\, I will recall Masur and Minsky’s definition of t
he marking graph for surfaces\, and I will define an analogue of the marki
ng graph whose vertex set consists of certain collections of irreducible p
arabolic subgroups of a finite-type Artin group A and which is quasi-isome
tric to A modulo its center.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Udall (Rice University)
DTSTART:20250901T193000Z
DTEND:20250901T200000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/68
DESCRIPTION:Title: Combinations of parabolically geometrically finite subgroups of mappi
ng class groups\nby Brian Udall (Rice University) as part of World of
GroupCraft V\n\n\nAbstract\nParabolically geometrically finite (PGF) group
s are a particular class of relatively hyperbolic subgroups of mapping cla
ss groups of surfaces whose coned-off Cayley graph quasi-isometrically emb
eds into the curve graph. Examples of such groups include convex cocompact
groups\, Veech groups\, and free products of free abelian groups of Dehn
twists on sufficiently far apart curves. The main result we'll discuss is
a combination theorem for PGF groups\, allowing for the construction of ma
ny more examples of PGF groups\, a notable one being the Leininger-Reid su
rface groups. Some intuition on the proof will be provided\, and with any
time remaining more recent work on a more general class of groups\, as wel
l as a variety of open problems\, will be introduced.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Hill (University of Utah)
DTSTART:20250901T200000Z
DTEND:20250901T203000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/69
DESCRIPTION:Title: Asymptotically rigid mapping class groups of infinite graphs.\nby
Thomas Hill (University of Utah) as part of World of GroupCraft V\n\n\nAb
stract\nWe introduce and study asymptotically rigid mapping class groups o
f certain infinite graphs. We determine their finiteness properties and sh
ow that these depend on the number of ends of the underlying graph. In a s
pecial case where the graph has finitely many ends\, we construct an expli
cit presentation for the so-called pure graph Houghton group and investiga
te several of its algebraic and geometric properties. Additionally\, we sh
ow that the graph Houghton groups are not commensurable with other known H
oughton-like groups\, namely the classical\, surface\, braided\, and doubl
ed handlebody Houghton groups\, demonstrating that this graph-based constr
uction defines a genuinely new class of groups. This is joint work with S
anghoon Kwak\, Brian Udall\, and Jeremy West.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Ng (Brandeis University)
DTSTART:20250901T210000Z
DTEND:20250901T213000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/70
DESCRIPTION:Title: Random walk quotients preserve negative curvature.\nby Thomas Ng
(Brandeis University) as part of World of GroupCraft V\n\n\nAbstract\nSinc
e the introduction of hyperbolic groups in the 1980s\, generalizations suc
h as relative\, hierarchical\, and acylindrical hyperbolicity continue to
demonstrate strong algebraic implications of metric negative curvature whi
le allowing increasingly flexible subgroup structures.. Quotients are a r
ich source of such negatively curved groups. I will describe one model fo
r constructing generic quotients from finitely many independent random wal
ks. I will explain why such random quotients generically preserve aspects
of negative curvature. This is joint work with C. Abbott\, D. Berlyne\,
G. Mangioni\, and A. Rasmussen.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vicky Wen (University of Wisconsin–Madison)
DTSTART:20250901T213000Z
DTEND:20250901T220000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/71
DESCRIPTION:Title: Sublinear Morseness in Higher Rank Symmetric Spaces\nby Vicky Wen
(University of Wisconsin–Madison) as part of World of GroupCraft V\n\n\
nAbstract\nThe Morse property of geodesics in hyperbolic spaces has always
been a useful tool in proving many rigidity results. People in the past d
ecade have tried to generalize this property in many different ways. I wil
l present to you some of those generalizations and explain why they are st
ill somewhat restrictive in the setting of higher rank symmetric spaces\,
which in turn motivates my definition of “sublinear Morseness”.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ping Wan (University of Illinois at Chicago)
DTSTART:20250901T220000Z
DTEND:20250901T223000Z
DTSTAMP:20260405T183323Z
UID:GroupCraft5/72
DESCRIPTION:Title: Quasiconvex subgroups of Acylindrically Hyperbolic Groups\nby Pin
g Wan (University of Illinois at Chicago) as part of World of GroupCraft V
\n\n\nAbstract\nIn this talk I will introduce acylindrically hyperbolic gr
oups and present a new notion of quasiconvex subgroups of acylindrically h
yperbolic groups. I will also talk about some applications of this notion
of quasiconvex subgroups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft5/72/
END:VEVENT
END:VCALENDAR