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BEGIN:VEVENT
SUMMARY:Jerry Shen (University of Technology Sydney)
DTSTART:20240908T230000Z
DTEND:20240908T233000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/1
DESCRIPTION:Title: The complexity of the epimorphism problem with Dihedral Targets
.\nby Jerry Shen (University of Technology Sydney) as part of World of
GroupCraft IV\n\n\nAbstract\nKuperberg and Samperton showed that the epim
orphism problem from certain 3-manifold groups to finite non-abelian simpl
e groups is \\textsf{NP}-hard. It follows that epimorphism problem from fi
nitely presented groups to finite non-abelian groups is \\textsf{NP}-compl
ete. In this talk I will show the epimorphism problem from finitely presen
ted groups to finite dihedral groups is \\textsf{NP}-hard using different
methods by using system of equations. I will then discuss how the use of s
ystem of equations generalises to other groups\, and that it is closely re
lated to the epimorphism problem.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Vitor Pinto e Silva
DTSTART:20240908T233000Z
DTEND:20240909T000000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/2
DESCRIPTION:Title: Iterated wreath products on t.d.l.c. groups\nby João Vitor
Pinto e Silva as part of World of GroupCraft IV\n\n\nAbstract\nWreath pro
ducts is an useful concept when constructing groups with some interesting
properties. In this talk I will show how I am adapting the definition of p
re-wreath structures from "Elementary amenable subgroups of R. Thompson's
group F" to the context of t.d.l.c. by defining a group action on an infin
ite ordered set. In the talk I will initially give an idea on how to defin
e such groups and then discuss how I want to apply such definition in my r
esearch.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Fresacher (Western Sydney University)
DTSTART:20240909T000000Z
DTEND:20240909T003000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/3
DESCRIPTION:Title: Congruence Lattices of Finite Twisted Brauer and Temperley-Lieb
Monoids\nby Matthias Fresacher (Western Sydney University) as part of
World of GroupCraft IV\n\n\nAbstract\nIn 2022\, East and Ruškuc publishe
d the congruence lattice of the infinite twisted partition monoid. As a by
product\, they established the congruence lattices of the finite $d$-twis
ted partition monoids. This talk is a first step in adapting the work of E
ast and Ruškuc to the setting of the Brauer and Temperley-Lieb monoid. Sp
ecifically\, it presents the newly established congruence lattice of the $
0$-twisted Brauer and Temperley-Lieb monoids. With simple to grasp visual
multiplication and applications in theoretical physics and representation
theory\, the family of diagram monoids are of particular interest to a num
ber of fields as well are of stand alone interest.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Gorazd (The University of Newcastle)
DTSTART:20240909T010000Z
DTEND:20240909T013000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/4
DESCRIPTION:Title: What trees are almost Isomorphic to Cocompact trees?\nby Ro
man Gorazd (The University of Newcastle) as part of World of GroupCraft IV
\n\n\nAbstract\nCocompact trees are trees that have finitely many orbits o
f their automorphism group. This allows us to easier describe actions of g
roups on these trees (for example via local action diagrams). Relatively l
ittle is known about their almost structure. In this talk\, I will describ
e these trees as unfolding trees of finite directed rooted graphs and intr
oduce a labelling on graphs that determines when their unfolding trees are
cocompact. This\, together with previous work on almost isomorphic unfold
ing trees shows what trees are almost isomorphic to cocompact trees.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kane Townsend (The Australian National University)
DTSTART:20240909T013000Z
DTEND:20240909T020000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/5
DESCRIPTION:Title: Geodetic groups are virtually free\nby Kane Townsend (The A
ustralian National University) as part of World of GroupCraft IV\n\n\nAbst
ract\nA graph is called geodetic if it has a unique geodesic between each
pair of distinct vertices. A group is called geodetic if it has an associa
ted finite generating set such that its undirected Cayley graph is geodeti
c. In this talk I will review a recent proof that geodetic groups are virt
ually free. The proof is motivated by a topological characterisation of hy
perbolic groups via the Gromov boundary.\n\nThis is joint work with Murray
Elder\, Giles Graham\, Adam Piggott and Davide Spriano.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua J Abraham (IISER Mohali)
DTSTART:20240909T020000Z
DTEND:20240909T023000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/6
DESCRIPTION:Title: Geodetic groups and length functions\nby Joshua J Abraham (
IISER Mohali) as part of World of GroupCraft IV\n\n\nAbstract\nA connected
graph is called geodetic when there is a unique geodesic between any pair
of vertices. Groups that admit at least one geodetic Cayley graph are cal
led geodetic. It was conjectured by Shapiro in 1997 that geodetic groups a
re precisely the plain groups. The problem of classifying geodetic groups
remains open. In this talk\, I will summarize recent progress on the probl
em\, introduce the concept of length functions (in the sense of Lyndon)\,
and describe how the existence of length functions satisfying certain prop
erties is related to the geodetic problem.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhun Baik (KAIST)
DTSTART:20240909T030000Z
DTEND:20240909T033000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/7
DESCRIPTION:Title: Topological normal generation of big mapping class groups\n
by Juhun Baik (KAIST) as part of World of GroupCraft IV\n\n\nAbstract\nBy
Lanier and Margalit\, any pseudo-Anosov map with stretch factor is less th
an $\\sqrt{2}$ normally generates the mapping class group. Also\, for clos
ed surfaces of genus more than 2\, any torsion element except hyperellipti
c involution is a normal generator. We ask for the case of a big mapping c
lass group\, namely the mapping class group of infinite type surfaces. In
this talk\, I will first introduce the the topology of big mapping class g
roups. After that I will answer when the big mapping class group is topolo
gically normally generated by one element\, and give an upper bound of how
many generators are needed to topologically normally generate the group.\
n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sanghoon Kwak (KIAS)
DTSTART:20240909T033000Z
DTEND:20240909T040000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/8
DESCRIPTION:Title: Nonunique Ergodicity on the Boundary of Outer Space\nby San
ghoon Kwak (KIAS) as part of World of GroupCraft IV\n\n\nAbstract\nThe Cul
ler--Vogtmann's Outer space $CV_n$ is a space of marked metric graphs\, an
d it \ncompactifies to a set of $F_n$-trees. Each $F_n$-tree on the bounda
ry of Outer space is equipped with a length measure\, and varying length m
easures on a topological $F_n$-tree gives a simplex in the boundary. The e
xtremal points of the simplex correspond to ergodic length measures. By th
e results of Gabai and Lenzhen-Masur\, the maximal simplex of transverse m
easures on a fixed filling geodesic lamination on a complete hyperbolic su
rface of genus $g$ has dimension $3g-4$. In this talk\, we give the maxima
l simplex of length measures on an arational $F_n$-tree has dimension in t
he interval $[2n-7\, 2n-2]$. This is a joint work with Mladen Bestvina\, a
nd Elizabeth Field.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donsung Lee (Seoul National University)
DTSTART:20240909T040000Z
DTEND:20240909T043000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/9
DESCRIPTION:Title: On the Faithfulness of the Burau Representation of $B_3$ Modulo
$p$\nby Donsung Lee (Seoul National University) as part of World of G
roupCraft IV\n\n\nAbstract\nThe Burau representation is one of the most ex
tensively studied representations of the braid group. While the question o
f its faithfulness has a long history\, the case of $B_3$ was relatively e
asily solved in the mid-20th century by using the fact that the quotient o
f $B_3$ by its center is isomorphic to the modular group. In this talk\, I
try to extend this result to the Burau representation of $B_3$ modulo $p$
\, where $p$ is any prime\, and I present an algorithm for determining whe
ther the representation is faithful\, given a prime $p$.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kangrae Park (Seoul National University)
DTSTART:20240909T050000Z
DTEND:20240909T053000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/10
DESCRIPTION:Title: Fellow Traveling of Geodesics on the Modular Surface\nby K
angrae Park (Seoul National University) as part of World of GroupCraft IV\
n\n\nAbstract\nThe modular surface \\( M = \\mathrm{SL}_2(\\mathbb{R}) \\b
ackslash \\mathbb{H}^2 \\) has a well-known connection between its geodesi
c flow \\( g_t \\) and continued fraction expansions. We aim to study the
Hausdorff dimension of the set\n\\[\n\\mathscr{B}_v^M(R) = \\{ w \\in T^1M
\\\,:\\\, d(g_t v\, g_t w) < R \\\; \\forall t \\in \\mathbb{R} \\}.\n\\]
\nThis problem generalizes the question of the Hausdorff dimension of badl
y approximable numbers. Using the relationship between continued fractions
and the coding of geodesic flows\, we translate the criteria for elements
of \\(\\mathscr{B}_v^M(R)\\) into conditions on continued fraction digits
. These findings provide insights into \\(\\mathscr{B}_v^M(R)\\)\, even th
ough a complete proof is still pending.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Wu (University of Sydney)
DTSTART:20240909T053000Z
DTEND:20240909T060000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/11
DESCRIPTION:Title: Bass--Serre theory in a C*-algebraic context\nby Victor Wu
(University of Sydney) as part of World of GroupCraft IV\n\n\nAbstract\nT
he fundamental theorem of Bass–Serre theory tells us that there is a one
-to-one correspondence between group actions on trees and graphs of groups
. One can associate a C*-algebra to each of these objects\, and the corres
pondence from Bass–Serre theory has a natural analogue in the C*-algebra
ic context. In this talk\, I will discuss this C*-algebraic version of Bas
s–Serre theory and what we (C*-algebraists) can do with it.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takao Yuyama (RIMS Kyoto)
DTSTART:20240909T060000Z
DTEND:20240909T063000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/12
DESCRIPTION:Title: Groups Whose Word Problems Are Accepted by Abelian $G$-Automat
a\nby Takao Yuyama (RIMS Kyoto) as part of World of GroupCraft IV\n\n\
nAbstract\nIn 2008\, Elder\, Kambites\, and Ostheimer showed that if a fin
itely generated group $H$ has a word problem accepted by a $G$-automaton f
or an abelian group $G$\, then $H$ has an abelian subgroup of finite index
. However\, their proof relies on Gromov's theorem on groups of polynomial
growth\, despite the combinatorial setting. We give an elementary and com
binatorial proof of the theorem\, which does not involve any geometric arg
uments.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pravin Kumar (IISER Mohali)
DTSTART:20240909T070000Z
DTEND:20240909T073000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/13
DESCRIPTION:Title: Brunnian planar braid groups and Brunnian doodles\nby Prav
in Kumar (IISER Mohali) as part of World of GroupCraft IV\n\n\nAbstract\nT
win groups are planar analogues of Artin braid groups and play a crucial r
ole in the Alexander-Markov correspondence for the theory of doodles\, whi
ch is the isotopy classes of immersed circles on the 2-sphere without trip
le and higher intersections. These groups can be represented diagrammatica
lly\, with maps obtained by adding and removing strands. In this talk\, we
will explore Brunnian twin groups\, which are subgroups of twin groups co
nsisting of twins that become trivial when any of their strands are delete
d\, and a Brunnian doodle on the 2-sphere. We will also discuss some gener
alizations of Brunnian twins\, namely\, k-decomposable twins and Cohen twi
ns.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajesh Dey (IISER Bhopal)
DTSTART:20240909T073000Z
DTEND:20240909T080000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/14
DESCRIPTION:Title: Liftability of periodic mapping classes under alternating cove
rs\nby Rajesh Dey (IISER Bhopal) as part of World of GroupCraft IV\n\n
\nAbstract\nDue to the Nielsen realization theorem\, any finite subgroup o
f the mapping class group Mod$(S_g)$ of closed\, orientable surface $S_g$
acts on $S_g$ via orientation-preserving isometries\, and induces a finite
-sheeted\, regular\, branched (Riemannian) covering on $S_g$. For such a c
over\, the Birman-Hilden theorem asserts that the liftable mapping class g
roup is isomorphic to the quotient of the symmetric mapping class group by
the group of deck transformations. In this talk\, I will try to motivate
the liftability problem in mapping class groups for covers induced by fini
te subgroups of Mod$(S_g)$. I will conclude by presenting some of our resu
lts on the liftability of periodic mapping classes under alternating cover
s and illustrating these results with examples.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pankaj Kapari (IISER Bhopal)
DTSTART:20240909T080000Z
DTEND:20240909T083000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/15
DESCRIPTION:Title: Primitivity of pseudo-periodic mapping classes\nby Pankaj
Kapari (IISER Bhopal) as part of World of GroupCraft IV\n\n\nAbstract\nFor
$g \\ge 2$\, let Mod$(S_g)$ be the mapping class group of the closed\nori
ented surface $S_g$ of genus $g$. A nontrivial $G \\in$ Mod$(S_g)$ is said
to\nbe a root of $F \\in$ Mod$(S_g)$ of degree $n$ if there exists an int
eger $n > 1$\nsuch that $G^n = F$ and $|G| = n|F|$. If $F$ does not have a
ny roots\,\nthen it is said to be primitive. A natural question is whether
one can\ndetermine if an arbitrary $F \\in$ Mod$(S_g)$ is primitive and c
ompute the\nroots of $F$ (up to conjugacy) when it is not primitive. We ca
ll this the\ngeneral primitivity problem in Mod$(S_g)$. To begin with\, we
provide a solution to this problem for reducible mapping classes of infin
ite order. Using this solution\, the canonical decomposition of (non-perio
dic) mapping classes\, and some known algorithms\, we formulate a theoreti
cal algorithm for solving the general primitivity problem in Mod$(S_g)$.Th
en we discuss realizable bounds on the degree of roots of reducible mappin
g classes in Mod$(S_g)$\, the Torelli group $I(S_g)$\, and the level $m$ c
ongruence subgroup Mod$(S_g)[m]$ of Mod$(S_g)$. We conclude the talk with
a result on normal closure of pseudo-periodic mapping classes in Mod$(S_g)
$.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ajay Nair (IISc\, Bengaluru)
DTSTART:20240909T090000Z
DTEND:20240909T093000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/16
DESCRIPTION:Title: The Goldman bracket characterises the homeomorphisms between n
on-compact surfaces\nby Ajay Nair (IISc\, Bengaluru) as part of World
of GroupCraft IV\n\n\nAbstract\nThe automorphisms of the fundamental group
s of surfaces are always induced by homotopy equivalences. For non-compact
surfaces\, we prove that these homotopy equivalences are homotopic to a h
omeomorphism if and only if they preserve the Goldman bracket. This result
is based on joint work with Siddhartha Gadgil and Sumanta Das.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bhola Nath Saha (IIT Kanpur)
DTSTART:20240909T093000Z
DTEND:20240909T100000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/17
DESCRIPTION:Title: Filling with separating curves\nby Bhola Nath Saha (IIT Ka
npur) as part of World of GroupCraft IV\n\n\nAbstract\nA pair $(\\alpha\,
\\beta)$ of simple closed curves on a closed and orientable surface $S_g$
of\ngenus $g$ is called a filling pair if the complement is a disjoint uni
on of topological discs. If\n$\\alpha$ is separating\, then we call it as
separating filling pair. We find a necessary and sufficient condition for
existence of a separating filling pair on $S_g$ with exactly two complemen
tary discs. We study the combinatorics of the action of the mapping class
group Mod$(S_g)$ on the set of such filling pairs. Furthermore\, we constr
uct a Morse function $\\mathscr{F}_g$ on the moduli space $\\mathscr{M}_g$
which\, for a given hyperbolic space $X$\, outputs the length of shortest
such filling pair with respect to the metric in $X$. We show that the car
dinality of the set of global minima of the function $\\mathscr{F}_g$ is s
ame as the number of Mod$(S_g)$-orbits of such filling pair.\nThis is a jo
int work with Dr. Bidyut Sanki.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nishant Rathee (IISER Mohali)
DTSTART:20240909T100000Z
DTEND:20240909T103000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/18
DESCRIPTION:Title: Rota–Baxter operators and skew brace structures over Heisenb
erg Group\nby Nishant Rathee (IISER Mohali) as part of World of GroupC
raft IV\n\n\nAbstract\nIn this talk\, we will discuss the relationship bet
ween skew left braces and Rota–Baxter operators. Skew left braces are we
ll-known for inducing non-degenerate solutions to the Yang-Baxter equation
. As an application\, we classify certain skew left brace structures over
the three-dimensional Heisenberg Lie group. This classification involves f
irst identifying all Rota–Baxter operators of weight 1 on the Heisenberg
Lie algebra by solving the defining equations. We then transfer these ope
rators to the Heisenberg Lie group\, utilizing the fact that the exponenti
al map from the Heisenberg Lie algebra to the Heisenberg group is bijectiv
e.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Tarocchi (University of Milano-Bicocca)
DTSTART:20240909T110000Z
DTEND:20240909T113000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/19
DESCRIPTION:Title: Rearrangement Groups of Fractals and their Conjugacy Problem\nby Matteo Tarocchi (University of Milano-Bicocca) as part of World of
GroupCraft IV\n\n\nAbstract\nIn 2019 J. Belk and B. Forrest introduced the
family of Rearrangement Groups. These are groups of certain "piecewise-ca
nonical" homeomorphisms of many fractals that act by "canonically" permuti
ng the self-similar pieces that make up the fractal. In particular\, this
family includes the famous trio Richard Thompson groups\, which are groups
of piecewise-linear homeomorphisms of the unit interval\, the unit circle
and the Cantor space\, respectively. Despite being countable\, rearrangem
ent groups seem to often be dense in the group of all homeomorphisms of th
e fractal on which they act.\nKnown results about rearrangement groups inc
lude the simplicity of commutator subgroups in many examples\, a general r
esult about invariable generation\, rationality of the fractal spaces on w
hich they act and a method to tackle their conjugacy problem. This talk wi
ll introduce this family of groups and highlight some facts about them\, f
ocusing on the solution to the conjugacy problem.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dario Ascari (University of the Basque Country)
DTSTART:20240909T113000Z
DTEND:20240909T120000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/20
DESCRIPTION:Title: Isoperimetric inequalities for subgroups of products of free g
roups\nby Dario Ascari (University of the Basque Country) as part of W
orld of GroupCraft IV\n\n\nAbstract\nSubgroups of direct products of free
groups can be very wild in general\; however\, they become much more contr
olled once they are required to satisfy some finiteness condition. We inve
stigate the Dehn functions of such groups\, i.e. an isoperimetric inequali
ty which encodes the complexity of solving the word problem. We show that\
, for subgroups of type $F_{n-1}$ in a product of $n$ factors\, there is a
uniform polynomial bound of $N^9$ on all the Dehn functions. We also show
an example of a subgroup whose Dehn function is exactly $N^4$.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inga Valentiner-Branth (University of Ghent)
DTSTART:20240909T120000Z
DTEND:20240909T123000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/21
DESCRIPTION:Title: Constructing high-dimensional expanders\nby Inga Valentine
r-Branth (University of Ghent) as part of World of GroupCraft IV\n\n\nAbst
ract\nHigh-dimensional expanders are a generalization of the notion of exp
ander graphs to simplicial complexes and give rise to a variety of applica
tions in computer science and other fields. We construct new high-dimensio
nal expanders from quotients of certain Kac-Moody-Steinberg groups\, using
their rich structure. These groups are developments of complexes of group
s related to groups of Lie type and their generalizations. In this talk\,
I will introduce the concepts of spectral and topological high-dimensional
expansion and I will present our construction of spectral expanders. The
talk is based on a joint work with L. Grave de Peralta.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Bogliolo (Università di Pisa)
DTSTART:20240909T130000Z
DTEND:20240909T133000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/22
DESCRIPTION:Title: Stable commutator length of verbal wreath products\nby Ele
na Bogliolo (Università di Pisa) as part of World of GroupCraft IV\n\n\nA
bstract\nStable commutator length (scl) is a group invariant that appears
in different areas of mathematics such as low-dimensional topology and dyn
amics.\nWe provide a vanishing condition for the scl of verbal wreath prod
ucts\, which are groups obtained by generalizing the construction of lampl
ighter groups with the use of verbal products. Our approach is based on th
e strong relation between scl and bounded cohomology expressed by Bavard
’s duality theorem.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio López Neumann (IMPAN (Warsaw))
DTSTART:20240909T133000Z
DTEND:20240909T140000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/23
DESCRIPTION:Title: On $L^p$-cohomology of semisimple groups\nby Antonio Lópe
z Neumann (IMPAN (Warsaw)) as part of World of GroupCraft IV\n\n\nAbstract
\n$L^p$-cohomology ($1\\lt p\\lt \\infty$) is a quasi-isometry invariant p
opularized by Gromov. He conjectured that for semisimple groups\, $L^p$-co
homology vanishes in degrees below the rank for all $1\\lt p\\lt \\infty$
and that it is sometimes nonzero in degree equal to the rank. These conjec
tures are known to be true when the degree is 1\, but for higher degrees o
nly partial results have been obtained. This talk will present general asp
ects of $L^p$-cohomology\, as well as some new results around these questi
ons\, such as vanishing in degree 2 and non-vanishing in degree equal to t
he rank.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raad Al Kohli (University of St Andrews)
DTSTART:20240909T140000Z
DTEND:20240909T143000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/24
DESCRIPTION:Title: A new connection between formal languages and groups\nby R
aad Al Kohli (University of St Andrews) as part of World of GroupCraft IV\
n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sofiya Yatsyna (Royal Holloway)
DTSTART:20240909T150000Z
DTEND:20240909T153000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/25
DESCRIPTION:Title: Homological finiteness conditions for totally disconnected loc
ally compact groups\nby Sofiya Yatsyna (Royal Holloway) as part of Wor
ld of GroupCraft IV\n\n\nAbstract\nGedrich and Gruenberg introduced two ho
mological invariants for a ring $R$\, the supremum of the injective length
s of the projectives\, $\\textit{silp}~R$\, and the supremum of the projec
tive lengths of the injectives\, $\\textit{spli}~R$. For a suitable commut
ative ring $R$ and group $G$\, they showed if $\\textit{spli}~RG$ is finit
e\, then $\\textit{silp}~RG$ is also finite. I will discuss ongoing resear
ch that aims to extend these and related results for totally disconnected
locally compact groups through rational discrete cohomology.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph MacManus (University of Oxford)
DTSTART:20240909T153000Z
DTEND:20240909T160000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/26
DESCRIPTION:Title: Coarsely characterising planarity in Cayley graphs\nby Jos
eph MacManus (University of Oxford) as part of World of GroupCraft IV\n\n\
nAbstract\nRecall a graph is said to be planar if it can be drawn in the p
lane without edges crossing. Classically\, it is known that a group which
(virtually) admits a planar Cayley graph is virtually a free product of su
rface and cyclic groups. \n\nIn this talk I will present results character
ising these groups in terms of their coarse geometry\, illustrating the ph
ilosophy that this class of groups is “very rigid”. I will also advert
ise some fun open problems which aim to push this philosophy even further.
\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Penelope Azuelos (University of Bristol)
DTSTART:20240909T160000Z
DTEND:20240909T163000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/27
DESCRIPTION:Title: A geometric criterion for detecting virtual fiber subgroups\nby Penelope Azuelos (University of Bristol) as part of World of GroupCr
aft IV\n\n\nAbstract\nA finitely generated subgroup H of a finitely genera
ted group G is a virtual fiber subgroup if G admits a finite index subgrou
p which surjects onto the integers and the kernel has finite index in H. I
f the Schreier graph of G/H is in some way geometrically similar to the in
tegers (e.g. it has two ends\, it's a quasi-line...) then when is H a virt
ual fiber subgroup? Answers to this question naturally depend on the geome
tric property imposed on the Schreier graph and answers in the case where
H has two relative ends and two filtered ends were provided by Houghton an
d Kropholler-Roller respectively. We will consider this question under a d
ifferent condition\, requiring instead that the Schreier graph is "narrow"
(e.g. has linear growth\, is a finitely ended quasi-tree) and has at leas
t two ends and\, under this hypothesis\, give a characterisation of virtua
l fiber subgroups. Time permitting\, we will also discuss examples of fini
tely generated subgroups whose Schreier graphs are quasi-lines but which f
ail to be virtual fibers.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawk Mineh (University of Southampton)
DTSTART:20240909T170000Z
DTEND:20240909T173000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/28
DESCRIPTION:Title: Separability of products of subgroups\nby Lawk Mineh (Univ
ersity of Southampton) as part of World of GroupCraft IV\n\n\nAbstract\nA
subset U of a group G is called separable if elements outside of U can be
distinguished from it in finite quotients of G. Separability of subgroups
has long been an important tool in both group theory and topology\, and in
recent years the separability of more general subsets has shown itself to
be increasingly useful. We will explore the extent of what is known befor
e discussing some recent work on the topic.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefanie Zbinden (Heriot-Watt University)
DTSTART:20240909T173000Z
DTEND:20240909T180000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/29
DESCRIPTION:Title: Using strong contraction to obtain hyperbolicity\nby Stefa
nie Zbinden (Heriot-Watt University) as part of World of GroupCraft IV\n\n
\nAbstract\nFor almost 10 years\, it has been known that if a group contai
ns a strongly contracting element\, then it is acylindrically hyperbolic.
Moreover\, one can use the Projection Complex of Bestvina\, Bromberg and F
ujiwara to construct a hyperbolic space where said element acts WPD. For a
long time\, the following question remained unanswered: if Morse is equiv
alent to strongly contracting\, does there exist a space where all general
ized loxodromics act WPD? In this talk\, I will introduce the contraction
space\, a space which answers this question positively.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Layne Hall (Warwick University)
DTSTART:20240909T180000Z
DTEND:20240909T183000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/30
DESCRIPTION:Title: Recognising pseudo-Anosov flows without homotopic orbits\n
by Layne Hall (Warwick University) as part of World of GroupCraft IV\n\n\n
Abstract\nOn a three-manifold\, there are rich interactions between the ge
ometry and topology with the dynamics of a flow on the manifold. A prototy
pical example is the mapping torus of a pseudo-Anosov homeomorphism\, wher
e the flow `walks upwards'. Such a flow lies in an abundant class of so-ca
lled pseudo-Anosov flows. The periodic orbits of a flow are loops\, and th
eir homotopy properties play a crucial role in understanding these flows.
In particular\, when a pseudo-Anosov flow has no freely homotopic orbits\,
we know (through the work of many) a lot about the structure of the manif
old and the flow. For example\, the fundamental group of the manifold must
be hyperbolic. The flow is also uniquely encoded by a triangulation. A na
tural decision problem is then: given a finite description of a pseudo-Ano
sov flow\, determine if there are any homotopic orbits. We will motivate t
his problem and briefly discuss a solution.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katherine Goldman (McGill University)
DTSTART:20240909T190000Z
DTEND:20240909T193000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/31
DESCRIPTION:Title: Curvature of Shephard Groups\nby Katherine Goldman (McGill
University) as part of World of GroupCraft IV\n\n\nAbstract\nShephard gro
ups are closely related to complex reflection groups and generalize Coxete
r groups and Artin groups. It is well known that Coxeter groups are CAT(0)
\, and it is conjectured that Artin groups are CAT(0). But because their d
efinition is quite general\, there are Shephard groups which exhibit seemi
ngly pathological behavior\, at least in regards to curvature. We will foc
us on two such classes. The first is a class of CAT(0) Shephard groups whi
ch exhibit “Coxeter-like” behavior\, and strictly contains the Coxeter
groups. The second class lies more squarely between the Artin and Coxeter
groups\, and consists of groups which cannot be CAT(0). However\, they ar
e relatively and acylindrically hyperbolic. We will give some motivation a
s to why this behavior occurs and why it doesn’t contradict the conjectu
ral non-positive curvature of Artin groups.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Rasmussen (Stanford University)
DTSTART:20240909T193000Z
DTEND:20240909T200000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/32
DESCRIPTION:Title: Disintegrating curve graphs\nby Alex Rasmussen (Stanford U
niversity) as part of World of GroupCraft IV\n\n\nAbstract\nUnderstanding
the geometry of curve graphs is important for proving results on mapping c
lass groups of surfaces. In this talk\, we will shed light on the geometry
of curve graphs by describing “filtrations” of them by hyperbolic gra
phs. These graphs are arranged in a sequence via distance non-increasing m
aps\, and the fibers are quasi-trees. This yields a new proof of finite as
ymptotic dimension of curve graphs. We also describe some useful aspects o
f the dynamics of the mapping class group actions on the graphs in the fil
trations.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maya Verma (The University of Oklahoma)
DTSTART:20240909T200000Z
DTEND:20240909T203000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/33
DESCRIPTION:Title: Leighton’s Property of $X_{m\,n}$\nby Maya Verma (The Un
iversity of Oklahoma) as part of World of GroupCraft IV\n\n\nAbstract\nIn
1982\, Leighton proved that any two finite graphs with a common cover admi
ts a finite sheeted common cover. In this talk\, I will introduce the comb
inatorial model $X_{m\,n}$ for Baumslag-Solitar group BS(m\,n)\, and clas
sify for which pairs of integers $(m\,n)$ the Leighton’s theorem can be
extended to the orbit space of covering actions on $X_{m\,n}$.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Reyes (Yale University)
DTSTART:20240909T210000Z
DTEND:20240909T213000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/34
DESCRIPTION:Title: Approximating hyperbolic lattices by cubulations\nby Eduar
do Reyes (Yale University) as part of World of GroupCraft IV\n\n\nAbstract
\nThe fundamental group of an $n$-dimensional closed hyperbolic manifold a
dmits a natural isometric action on the hyperbolic space $\\mathbb{H}^n$.
If $n$ is at most 3 or the manifold is arithmetic of simplest type\, then
the group also admits many geometric actions on CAT(0) cube complexes. I w
ill talk about a joint work with Nic Brody in which we approximate the asy
mptotic geometry of the action on $\\mathbb{H}^n$ by actions on these comp
lexes\, solving a conjecture of Futer and Wise. The main tool is a codimen
sion-1 generalization of the space of geodesic currents introduced by Bona
hon.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberta Shapiro (University of Michigan)
DTSTART:20240909T213000Z
DTEND:20240909T220000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/35
DESCRIPTION:Title: Non-hyperbolicity of large subgraphs of the fine curve graph\nby Roberta Shapiro (University of Michigan) as part of World of GroupC
raft IV\n\n\nAbstract\nThe fine curve graph of a surface is a graph whose
vertices are essential simple closed curves in the surface and whose edges
connect disjoint curves. Following a rich history of hyperbolicity in var
ious graphs based on surfaces\, the fine curve was shown to be hyperbolic
by Bowden–Hensel–Webb\, while the curve graph\, which collapses subgra
phs corresponding to isotopy classes\, was proven to be hyperbolic by Masu
r–Minsky. In this talk\, we prove that subgraphs of the fine curve graph
corresponding to curves that essentially intersect a common curve contain
a quasi-isometrically embedded flat of every dimension and therefore are
not hyperbolic. In particular\, the subgraph of the fine curve graph induc
ed by any single isotopy class—a graph whose properties are captured by
neither the curve graph nor fine curve graph—is not hyperbolic. This is
joint work with Ryan Dickmann.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tam Cheetham-West (Yale University)
DTSTART:20240909T220000Z
DTEND:20240909T223000Z
DTSTAMP:20260921T093240Z
UID:GroupCraft4/36
DESCRIPTION:Title: Finite quotients and Property FA\nby Tam Cheetham-West (Ya
le University) as part of World of GroupCraft IV\n\n\nAbstract\nSome group
s have actions on trees that have no global fixed point while other groups
always have a global fixed point whenever they act on a tree. The latter
are said to have Property FA. I will discuss examples of group pairs where
both groups in each pair have all the same finite quotients\, but one gro
up has Property FA and the other group doesn't. This is joint work with Al
ex Lubotzky\, Alan Reid\, and Ryan Spitler.\n
LOCATION:
END:VEVENT
END:VCALENDAR