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BEGIN:VEVENT
SUMMARY:Jerry Shen (University of Technology Sydney)
DTSTART;VALUE=DATE-TIME:20240908T230000Z
DTEND;VALUE=DATE-TIME:20240908T233000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/1
DESCRIPTION:Title: The complexity of the epimorphism problem with Dihedral Targets.\n
by Jerry Shen (University of Technology Sydney) as part of World of GroupC
raft IV\n\n\nAbstract\nKuperberg and Samperton showed that the epimorphism
problem from certain 3-manifold groups to finite non-abelian simple group
s is \\textsf{NP}-hard. It follows that epimorphism problem from finitely
presented groups to finite non-abelian groups is \\textsf{NP}-complete. In
this talk I will show the epimorphism problem from finitely presented gro
ups to finite dihedral groups is \\textsf{NP}-hard using different methods
by using system of equations. I will then discuss how the use of system o
f equations generalises to other groups\, and that it is closely related t
o the epimorphism problem.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Vitor Pinto e Silva
DTSTART;VALUE=DATE-TIME:20240908T233000Z
DTEND;VALUE=DATE-TIME:20240909T000000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
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 products i
s an useful concept when constructing groups with some interesting propert
ies. In this talk I will show how I am adapting the definition of pre-wrea
th 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 infinite ord
ered set. In the talk I will initially give an idea on how to define such
groups and then discuss how I want to apply such definition in my research
.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Fresacher (Western Sydney University)
DTSTART;VALUE=DATE-TIME:20240909T000000Z
DTEND;VALUE=DATE-TIME:20240909T003000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/3
DESCRIPTION:Title: Congruence Lattices of Finite Twisted Brauer and Temperley-Lieb Monoid
s\nby Matthias Fresacher (Western Sydney University) as part of World
of GroupCraft IV\n\n\nAbstract\nIn 2022\, East and Ruškuc published the c
ongruence lattice of the infinite twisted partition monoid. As a by produc
t\, they established the congruence lattices of the finite $d$-twisted par
tition monoids. This talk is a first step in adapting the work of East and
Ruškuc to the setting of the Brauer and Temperley-Lieb monoid. Specifica
lly\, it presents the newly established congruence lattice of the $0$-twis
ted Brauer and Temperley-Lieb monoids. With simple to grasp visual multipl
ication and applications in theoretical physics and representation theory\
, the family of diagram monoids are of particular interest to a number of
fields as well are of stand alone interest.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Gorazd (The University of Newcastle)
DTSTART;VALUE=DATE-TIME:20240909T010000Z
DTEND;VALUE=DATE-TIME:20240909T013000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/4
DESCRIPTION:Title: What trees are almost Isomorphic to Cocompact trees?\nby Roman Gor
azd (The University of Newcastle) as part of World of GroupCraft IV\n\n\nA
bstract\nCocompact trees are trees that have finitely many orbits of their
automorphism group. This allows us to easier describe actions of groups o
n these trees (for example via local action diagrams). Relatively little i
s known about their almost structure. In this talk\, I will describe these
trees as unfolding trees of finite directed rooted graphs and introduce a
labelling on graphs that determines when their unfolding trees are cocomp
act. This\, together with previous work on almost isomorphic unfolding tre
es shows what trees are almost isomorphic to cocompact trees.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kane Townsend (The Australian National University)
DTSTART;VALUE=DATE-TIME:20240909T013000Z
DTEND;VALUE=DATE-TIME:20240909T020000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/5
DESCRIPTION:Title: Geodetic groups are virtually free\nby Kane Townsend (The Australi
an National University) as part of World of GroupCraft IV\n\n\nAbstract\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 associated fin
ite generating set such that its undirected Cayley graph is geodetic. In t
his talk I will review a recent proof that geodetic groups are virtually f
ree. The proof is motivated by a topological characterisation of hyperboli
c groups via the Gromov boundary.\n\nThis is joint work with Murray Elder\
, Giles Graham\, Adam Piggott and Davide Spriano.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua J Abraham (IISER Mohali)
DTSTART;VALUE=DATE-TIME:20240909T020000Z
DTEND;VALUE=DATE-TIME:20240909T023000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/6
DESCRIPTION:Title: Geodetic groups and length functions\nby Joshua J Abraham (IISER M
ohali) 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 ver
tices. Groups that admit at least one geodetic Cayley graph are called geo
detic. It was conjectured by Shapiro in 1997 that geodetic groups are prec
isely the plain groups. The problem of classifying geodetic groups remains
open. In this talk\, I will summarize recent progress on the problem\, in
troduce the concept of length functions (in the sense of Lyndon)\, and des
cribe how the existence of length functions satisfying certain properties
is related to the geodetic problem.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhun Baik (KAIST)
DTSTART;VALUE=DATE-TIME:20240909T030000Z
DTEND;VALUE=DATE-TIME:20240909T033000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/7
DESCRIPTION:Title: Topological normal generation of big mapping class groups\nby Juhu
n 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 than $\\s
qrt{2}$ normally generates the mapping class group. Also\, for closed surf
aces of genus more than 2\, any torsion element except hyperelliptic invol
ution is a normal generator. We ask for the case of a big mapping class gr
oup\, namely the mapping class group of infinite type surfaces. In this ta
lk\, I will first introduce the the topology of big mapping class groups.
After that I will answer when the big mapping class group is topologically
normally generated by one element\, and give an upper bound of how many g
enerators are needed to topologically normally generate the group.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sanghoon Kwak (KIAS)
DTSTART;VALUE=DATE-TIME:20240909T033000Z
DTEND;VALUE=DATE-TIME:20240909T040000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/8
DESCRIPTION:Title: Nonunique Ergodicity on the Boundary of Outer Space\nby Sanghoon K
wak (KIAS) as part of World of GroupCraft IV\n\n\nAbstract\nThe Culler--Vo
gtmann's Outer space $CV_n$ is a space of marked metric graphs\, and it \n
compactifies to a set of $F_n$-trees. Each $F_n$-tree on the boundary of O
uter space is equipped with a length measure\, and varying length measures
on a topological $F_n$-tree gives a simplex in the boundary. The extremal
points of the simplex correspond to ergodic length measures. By the resul
ts of Gabai and Lenzhen-Masur\, the maximal simplex of transverse measures
on a fixed filling geodesic lamination on a complete hyperbolic surface o
f genus $g$ has dimension $3g-4$. In this talk\, we give the maximal simpl
ex of length measures on an arational $F_n$-tree has dimension in the inte
rval $[2n-7\, 2n-2]$. This is a joint work with Mladen Bestvina\, and Eliz
abeth Field.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donsung Lee (Seoul National University)
DTSTART;VALUE=DATE-TIME:20240909T040000Z
DTEND;VALUE=DATE-TIME:20240909T043000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
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 GroupCra
ft IV\n\n\nAbstract\nThe Burau representation is one of the most extensive
ly studied representations of the braid group. While the question of its f
aithfulness has a long history\, the case of $B_3$ was relatively easily s
olved in the mid-20th century by using the fact that the quotient of $B_3$
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 $p$\, wher
e $p$ is any prime\, and I present an algorithm for determining whether th
e representation is faithful\, given a prime $p$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kangrae Park (Seoul National University)
DTSTART;VALUE=DATE-TIME:20240909T050000Z
DTEND;VALUE=DATE-TIME:20240909T053000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/10
DESCRIPTION:Title: Fellow Traveling of Geodesics on the Modular Surface\nby Kangrae
Park (Seoul National University) as part of World of GroupCraft IV\n\n\nAb
stract\nThe modular surface \\( M = \\mathrm{SL}_2(\\mathbb{R}) \\backslas
h \\mathbb{H}^2 \\) has a well-known connection between its geodesic flow
\\( g_t \\) and continued fraction expansions. We aim to study the Hausdor
ff 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 badly appro
ximable numbers. Using the relationship between continued fractions and th
e 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 though a
complete proof is still pending.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Wu (University of Sydney)
DTSTART;VALUE=DATE-TIME:20240909T053000Z
DTEND;VALUE=DATE-TIME:20240909T060000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/11
DESCRIPTION:Title: Bass--Serre theory in a C*-algebraic context\nby Victor Wu (Unive
rsity of Sydney) as part of World of GroupCraft IV\n\n\nAbstract\nThe fund
amental 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 c
an associate a C*-algebra to each of these objects\, and the correspondenc
e from Bass–Serre theory has a natural analogue in the C*-algebraic cont
ext. In this talk\, I will discuss this C*-algebraic version of Bass–Ser
re theory and what we (C*-algebraists) can do with it.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takao Yuyama (RIMS Kyoto)
DTSTART;VALUE=DATE-TIME:20240909T060000Z
DTEND;VALUE=DATE-TIME:20240909T063000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/12
DESCRIPTION:Title: Groups Whose Word Problems Are Accepted by Abelian $G$-Automata\n
by Takao Yuyama (RIMS Kyoto) as part of World of GroupCraft IV\n\n\nAbstra
ct\nIn 2008\, Elder\, Kambites\, and Ostheimer showed that if a finitely g
enerated group $H$ has a word problem accepted by a $G$-automaton for an a
belian group $G$\, then $H$ has an abelian subgroup of finite index. Howev
er\, their proof relies on Gromov's theorem on groups of polynomial growth
\, despite the combinatorial setting. We give an elementary and combinator
ial proof of the theorem\, which does not involve any geometric arguments.
\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pravin Kumar (IISER Mohali)
DTSTART;VALUE=DATE-TIME:20240909T070000Z
DTEND;VALUE=DATE-TIME:20240909T073000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/13
DESCRIPTION:Title: Brunnian planar braid groups and Brunnian doodles\nby Pravin Kuma
r (IISER Mohali) as part of World of GroupCraft IV\n\n\nAbstract\nTwin gro
ups are planar analogues of Artin braid groups and play a crucial role in
the Alexander-Markov correspondence for the theory of doodles\, which is t
he isotopy classes of immersed circles on the 2-sphere without triple and
higher intersections. These groups can be represented diagrammatically\, w
ith maps obtained by adding and removing strands. In this talk\, we will e
xplore Brunnian twin groups\, which are subgroups of twin groups consistin
g of twins that become trivial when any of their strands are deleted\, and
a Brunnian doodle on the 2-sphere. We will also discuss some generalizati
ons of Brunnian twins\, namely\, k-decomposable twins and Cohen twins.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajesh Dey (IISER Bhopal)
DTSTART;VALUE=DATE-TIME:20240909T073000Z
DTEND;VALUE=DATE-TIME:20240909T080000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/14
DESCRIPTION:Title: Liftability of periodic mapping classes under alternating covers\
nby Rajesh Dey (IISER Bhopal) as part of World of GroupCraft IV\n\n\nAbstr
act\nDue to the Nielsen realization theorem\, any finite subgroup of the m
apping class group Mod$(S_g)$ of closed\, orientable surface $S_g$ acts on
$S_g$ via orientation-preserving isometries\, and induces a finite-sheete
d\, regular\, branched (Riemannian) covering on $S_g$. For such a cover\,
the Birman-Hilden theorem asserts that the liftable mapping class group is
isomorphic to the quotient of the symmetric mapping class group by the gr
oup of deck transformations. In this talk\, I will try to motivate the lif
tability problem in mapping class groups for covers induced by finite subg
roups of Mod$(S_g)$. I will conclude by presenting some of our results on
the liftability of periodic mapping classes under alternating covers and i
llustrating these results with examples.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pankaj Kapari (IISER Bhopal)
DTSTART;VALUE=DATE-TIME:20240909T080000Z
DTEND;VALUE=DATE-TIME:20240909T083000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
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 $g \\g
e 2$\, let Mod$(S_g)$ be the mapping class group of the closed\noriented s
urface $S_g$ 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 integer $n
> 1$\nsuch that $G^n = F$ and $|G| = n|F|$. If $F$ does not have any root
s\,\nthen it is said to be primitive. A natural question is whether one ca
n\ndetermine if an arbitrary $F \\in$ Mod$(S_g)$ is primitive and compute
the\nroots of $F$ (up to conjugacy) when it is not primitive. We call this
the\ngeneral primitivity problem in Mod$(S_g)$. To begin with\, we provid
e a solution to this problem for reducible mapping classes of infinite ord
er. Using this solution\, the canonical decomposition of (non-periodic) ma
pping classes\, and some known algorithms\, we formulate a theoretical alg
orithm for solving the general primitivity problem in Mod$(S_g)$.Then we d
iscuss realizable bounds on the degree of roots of reducible mapping class
es in Mod$(S_g)$\, the Torelli group $I(S_g)$\, and the level $m$ congruen
ce subgroup Mod$(S_g)[m]$ of Mod$(S_g)$. We conclude the talk with a resul
t on normal closure of pseudo-periodic mapping classes in Mod$(S_g)$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ajay Nair (IISc\, Bengaluru)
DTSTART;VALUE=DATE-TIME:20240909T090000Z
DTEND;VALUE=DATE-TIME:20240909T093000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/16
DESCRIPTION:Title: The Goldman bracket characterises the homeomorphisms between non-comp
act surfaces\nby Ajay Nair (IISc\, Bengaluru) as part of World of Grou
pCraft IV\n\n\nAbstract\nThe automorphisms of the fundamental groups of su
rfaces are always induced by homotopy equivalences. For non-compact surfac
es\, we prove that these homotopy equivalences are homotopic to a homeomor
phism if and only if they preserve the Goldman bracket. This result is bas
ed on joint work with Siddhartha Gadgil and Sumanta Das.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bhola Nath Saha (IIT Kanpur)
DTSTART;VALUE=DATE-TIME:20240909T093000Z
DTEND;VALUE=DATE-TIME:20240909T100000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/17
DESCRIPTION:Title: Filling with separating curves\nby Bhola Nath Saha (IIT Kanpur) a
s 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\ngen
us $g$ is called a filling pair if the complement is a disjoint union of t
opological discs. If\n$\\alpha$ is separating\, then we call it as separat
ing filling pair. We find a necessary and sufficient condition for existen
ce of a separating filling pair on $S_g$ with exactly two complementary di
scs. We study the combinatorics of the action of the mapping class group M
od$(S_g)$ on the set of such filling pairs. Furthermore\, we construct a M
orse function $\\mathscr{F}_g$ on the moduli space $\\mathscr{M}_g$ which\
, for a given hyperbolic space $X$\, outputs the length of shortest such f
illing pair with respect to the metric in $X$. We show that the cardinalit
y of the set of global minima of the function $\\mathscr{F}_g$ is same as
the number of Mod$(S_g)$-orbits of such filling pair.\nThis is a joint wor
k with Dr. Bidyut Sanki.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nishant Rathee (IISER Mohali)
DTSTART;VALUE=DATE-TIME:20240909T100000Z
DTEND;VALUE=DATE-TIME:20240909T103000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/18
DESCRIPTION:Title: Rota–Baxter operators and skew brace structures over Heisenberg Gro
up\nby Nishant Rathee (IISER Mohali) as part of World of GroupCraft IV
\n\n\nAbstract\nIn this talk\, we will discuss the relationship between sk
ew left braces and Rota–Baxter operators. Skew left braces are well-know
n for inducing non-degenerate solutions to the Yang-Baxter equation. As an
application\, we classify certain skew left brace structures over the thr
ee-dimensional Heisenberg Lie group. This classification involves first id
entifying all Rota–Baxter operators of weight 1 on the Heisenberg Lie al
gebra by solving the defining equations. We then transfer these operators
to the Heisenberg Lie group\, utilizing the fact that the exponential map
from the Heisenberg Lie algebra to the Heisenberg group is bijective.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Tarocchi (University of Milano-Bicocca)
DTSTART;VALUE=DATE-TIME:20240909T110000Z
DTEND;VALUE=DATE-TIME:20240909T113000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
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 GroupCr
aft IV\n\n\nAbstract\nIn 2019 J. Belk and B. Forrest introduced the family
of Rearrangement Groups. These are groups of certain "piecewise-canonical
" homeomorphisms of many fractals that act by "canonically" permuting the
self-similar pieces that make up the fractal. In particular\, this family
includes the famous trio Richard Thompson groups\, which are groups of pie
cewise-linear homeomorphisms of the unit interval\, the unit circle and th
e Cantor space\, respectively. Despite being countable\, rearrangement gro
ups seem to often be dense in the group of all homeomorphisms of the fract
al on which they act.\nKnown results about rearrangement groups include th
e simplicity of commutator subgroups in many examples\, a general result a
bout invariable generation\, rationality of the fractal spaces on which th
ey act and a method to tackle their conjugacy problem. This talk will intr
oduce this family of groups and highlight some facts about them\, focusing
on the solution to the conjugacy problem.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dario Ascari (University of the Basque Country)
DTSTART;VALUE=DATE-TIME:20240909T113000Z
DTEND;VALUE=DATE-TIME:20240909T120000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/20
DESCRIPTION:Title: Isoperimetric inequalities for subgroups of products of free groups\nby Dario Ascari (University of the Basque Country) as part of World of
GroupCraft IV\n\n\nAbstract\nSubgroups of direct products of free groups
can be very wild in general\; however\, they become much more controlled o
nce they are required to satisfy some finiteness condition. We investigate
the Dehn functions of such groups\, i.e. an isoperimetric inequality whic
h encodes the complexity of solving the word problem. We show that\, for s
ubgroups of type $F_{n-1}$ in a product of $n$ factors\, there is a unifor
m polynomial bound of $N^9$ on all the Dehn functions. We also show an exa
mple of a subgroup whose Dehn function is exactly $N^4$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inga Valentiner-Branth (University of Ghent)
DTSTART;VALUE=DATE-TIME:20240909T120000Z
DTEND;VALUE=DATE-TIME:20240909T123000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/21
DESCRIPTION:Title: Constructing high-dimensional expanders\nby Inga Valentiner-Brant
h (University of Ghent) as part of World of GroupCraft IV\n\n\nAbstract\nH
igh-dimensional expanders are a generalization of the notion of expander g
raphs to simplicial complexes and give rise to a variety of applications i
n computer science and other fields. We construct new high-dimensional exp
anders from quotients of certain Kac-Moody-Steinberg groups\, using their
rich structure. These groups are developments of complexes of groups relat
ed to groups of Lie type and their generalizations. In this talk\, I will
introduce the concepts of spectral and topological high-dimensional expans
ion and I will present our construction of spectral expanders. The talk is
based on a joint work with L. Grave de Peralta.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Bogliolo (Università di Pisa)
DTSTART;VALUE=DATE-TIME:20240909T130000Z
DTEND;VALUE=DATE-TIME:20240909T133000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/22
DESCRIPTION:Title: Stable commutator length of verbal wreath products\nby Elena Bogl
iolo (Università di Pisa) as part of World of GroupCraft IV\n\n\nAbstract
\nStable commutator length (scl) is a group invariant that appears in diff
erent areas of mathematics such as low-dimensional topology and dynamics.\
nWe provide a vanishing condition for the scl of verbal wreath products\,
which are groups obtained by generalizing the construction of lamplighter
groups with the use of verbal products. Our approach is based on the stron
g relation between scl and bounded cohomology expressed by Bavard’s dual
ity theorem.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio López Neumann (IMPAN (Warsaw))
DTSTART;VALUE=DATE-TIME:20240909T133000Z
DTEND;VALUE=DATE-TIME:20240909T140000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/23
DESCRIPTION:Title: On $L^p$-cohomology of semisimple groups\nby Antonio López Neuma
nn (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 populari
zed by Gromov. He conjectured that for semisimple groups\, $L^p$-cohomolog
y vanishes in degrees below the rank for all $1\\lt p\\lt \\infty$ and tha
t it is sometimes nonzero in degree equal to the rank. These conjectures a
re known to be true when the degree is 1\, but for higher degrees only par
tial results have been obtained. This talk will present general aspects of
$L^p$-cohomology\, as well as some new results around these questions\, s
uch as vanishing in degree 2 and non-vanishing in degree equal to the rank
.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raad Al Kohli (University of St Andrews)
DTSTART;VALUE=DATE-TIME:20240909T140000Z
DTEND;VALUE=DATE-TIME:20240909T143000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/24
DESCRIPTION:Title: A new connection between formal languages and groups\nby Raad Al
Kohli (University of St Andrews) as part of World of GroupCraft IV\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sofiya Yatsyna (Royal Holloway)
DTSTART;VALUE=DATE-TIME:20240909T150000Z
DTEND;VALUE=DATE-TIME:20240909T153000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/25
DESCRIPTION:Title: Homological finiteness conditions for totally disconnected locally co
mpact groups\nby Sofiya Yatsyna (Royal Holloway) as part of World of G
roupCraft IV\n\n\nAbstract\nGedrich and Gruenberg introduced two homologic
al invariants for a ring $R$\, the supremum of the injective lengths of th
e projectives\, $\\textit{silp}~R$\, and the supremum of the projective le
ngths of the injectives\, $\\textit{spli}~R$. For a suitable commutative r
ing $R$ and group $G$\, they showed if $\\textit{spli}~RG$ is finite\, the
n $\\textit{silp}~RG$ is also finite. I will discuss ongoing research that
aims to extend these and related results for totally disconnected locally
compact groups through rational discrete cohomology.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph MacManus (University of Oxford)
DTSTART;VALUE=DATE-TIME:20240909T153000Z
DTEND;VALUE=DATE-TIME:20240909T160000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/26
DESCRIPTION:Title: Coarsely characterising planarity in Cayley graphs\nby Joseph Mac
Manus (University of Oxford) as part of World of GroupCraft IV\n\n\nAbstra
ct\nRecall a graph is said to be planar if it can be drawn in the plane wi
thout edges crossing. Classically\, it is known that a group which (virtua
lly) admits a planar Cayley graph is virtually a free product of surface a
nd cyclic groups. \n\nIn this talk I will present results characterising t
hese groups in terms of their coarse geometry\, illustrating the philosoph
y that this class of groups is “very rigid”. I will also advertise som
e fun open problems which aim to push this philosophy even further.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Penelope Azuelos (University of Bristol)
DTSTART;VALUE=DATE-TIME:20240909T160000Z
DTEND;VALUE=DATE-TIME:20240909T163000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/27
DESCRIPTION:Title: A geometric criterion for detecting virtual fiber subgroups\nby P
enelope Azuelos (University of Bristol) as part of World of GroupCraft IV\
n\n\nAbstract\nA finitely generated subgroup H of a finitely generated gro
up G is a virtual fiber subgroup if G admits a finite index subgroup which
surjects onto the integers and the kernel has finite index in H. If the S
chreier graph of G/H is in some way geometrically similar to the integers
(e.g. it has two ends\, it's a quasi-line...) then when is H a virtual fib
er subgroup? Answers to this question naturally depend on the geometric pr
operty imposed on the Schreier graph and answers in the case where H has t
wo relative ends and two filtered ends were provided by Houghton and Kroph
oller-Roller respectively. We will consider this question under a differen
t condition\, requiring instead that the Schreier graph is "narrow" (e.g.
has linear growth\, is a finitely ended quasi-tree) and has at least two e
nds and\, under this hypothesis\, give a characterisation of virtual fiber
subgroups. Time permitting\, we will also discuss examples of finitely ge
nerated subgroups whose Schreier graphs are quasi-lines but which fail to
be virtual fibers.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawk Mineh (University of Southampton)
DTSTART;VALUE=DATE-TIME:20240909T170000Z
DTEND;VALUE=DATE-TIME:20240909T173000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/28
DESCRIPTION:Title: Separability of products of subgroups\nby Lawk Mineh (University
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 disting
uished from it in finite quotients of G. Separability of subgroups has lon
g 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 inc
reasingly useful. We will explore the extent of what is known before discu
ssing some recent work on the topic.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefanie Zbinden (Heriot-Watt University)
DTSTART;VALUE=DATE-TIME:20240909T173000Z
DTEND;VALUE=DATE-TIME:20240909T180000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/29
DESCRIPTION:Title: Using strong contraction to obtain hyperbolicity\nby Stefanie Zbi
nden (Heriot-Watt University) as part of World of GroupCraft IV\n\n\nAbstr
act\nFor almost 10 years\, it has been known that if a group contains a st
rongly contracting element\, then it is acylindrically hyperbolic. Moreove
r\, one can use the Projection Complex of Bestvina\, Bromberg and Fujiwara
to construct a hyperbolic space where said element acts WPD. For a long t
ime\, the following question remained unanswered: if Morse is equivalent t
o strongly contracting\, does there exist a space where all generalized lo
xodromics act WPD? In this talk\, I will introduce the contraction space\,
a space which answers this question positively.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Layne Hall (Warwick University)
DTSTART;VALUE=DATE-TIME:20240909T180000Z
DTEND;VALUE=DATE-TIME:20240909T183000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/30
DESCRIPTION:Title: Recognising pseudo-Anosov flows without homotopic orbits\nby Layn
e Hall (Warwick University) as part of World of GroupCraft IV\n\n\nAbstrac
t\nOn a three-manifold\, there are rich interactions between the geometry
and topology with the dynamics of a flow on the manifold. A prototypical e
xample is the mapping torus of a pseudo-Anosov homeomorphism\, where the f
low `walks upwards'. Such a flow lies in an abundant class of so-called ps
eudo-Anosov flows. The periodic orbits of a flow are loops\, and their hom
otopy properties play a crucial role in understanding these flows. In part
icular\, when a pseudo-Anosov flow has no freely homotopic orbits\, we kno
w (through the work of many) a lot about the structure of the manifold and
the flow. For example\, the fundamental group of the manifold must be hyp
erbolic. The flow is also uniquely encoded by a triangulation. A natural d
ecision problem is then: given a finite description of a pseudo-Anosov flo
w\, determine if there are any homotopic orbits. We will motivate this pro
blem and briefly discuss a solution.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katherine Goldman (McGill University)
DTSTART;VALUE=DATE-TIME:20240909T190000Z
DTEND;VALUE=DATE-TIME:20240909T193000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/31
DESCRIPTION:Title: Curvature of Shephard Groups\nby Katherine Goldman (McGill Univer
sity) as part of World of GroupCraft IV\n\n\nAbstract\nShephard groups are
closely related to complex reflection groups and generalize Coxeter group
s 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 definiti
on is quite general\, there are Shephard groups which exhibit seemingly pa
thological behavior\, at least in regards to curvature. We will focus on t
wo such classes. The first is a class of CAT(0) Shephard groups which exhi
bit “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 are relat
ively and acylindrically hyperbolic. We will give some motivation as to wh
y this behavior occurs and why it doesn’t contradict the conjectural non
-positive curvature of Artin groups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Rasmussen (Stanford University)
DTSTART;VALUE=DATE-TIME:20240909T193000Z
DTEND;VALUE=DATE-TIME:20240909T200000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/32
DESCRIPTION:Title: Disintegrating curve graphs\nby Alex Rasmussen (Stanford Universi
ty) as part of World of GroupCraft IV\n\n\nAbstract\nUnderstanding the geo
metry of curve graphs is important for proving results on mapping class gr
oups of surfaces. In this talk\, we will shed light on the geometry of cur
ve graphs by describing “filtrations” of them by hyperbolic graphs. Th
ese graphs are arranged in a sequence via distance non-increasing maps\, a
nd the fibers are quasi-trees. This yields a new proof of finite asymptoti
c dimension of curve graphs. We also describe some useful aspects of the d
ynamics of the mapping class group actions on the graphs in the filtration
s.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maya Verma (The University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20240909T200000Z
DTEND;VALUE=DATE-TIME:20240909T203000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/33
DESCRIPTION:Title: Leighton’s Property of $X_{m\,n}$\nby Maya Verma (The Universit
y 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 admits a fi
nite sheeted common cover. In this talk\, I will introduce the combinatori
al model $X_{m\,n}$ for Baumslag-Solitar group BS(m\,n)\, and classify fo
r which pairs of integers $(m\,n)$ the Leighton’s theorem can be extende
d to the orbit space of covering actions on $X_{m\,n}$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Reyes (Yale University)
DTSTART;VALUE=DATE-TIME:20240909T210000Z
DTEND;VALUE=DATE-TIME:20240909T213000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/34
DESCRIPTION:Title: Approximating hyperbolic lattices by cubulations\nby Eduardo Reye
s (Yale University) as part of World of GroupCraft IV\n\n\nAbstract\nThe f
undamental group of an $n$-dimensional closed hyperbolic manifold admits 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 gro
up also admits many geometric actions on CAT(0) cube complexes. I will tal
k about a joint work with Nic Brody in which we approximate the asymptotic
geometry of the action on $\\mathbb{H}^n$ by actions on these complexes\,
solving a conjecture of Futer and Wise. The main tool is a codimension-1
generalization of the space of geodesic currents introduced by Bonahon.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberta Shapiro (University of Michigan)
DTSTART;VALUE=DATE-TIME:20240909T213000Z
DTEND;VALUE=DATE-TIME:20240909T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
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 GroupCraft IV
\n\n\nAbstract\nThe fine curve graph of a surface is a graph whose vertice
s are essential simple closed curves in the surface and whose edges connec
t disjoint curves. Following a rich history of hyperbolicity in various gr
aphs based on surfaces\, the fine curve was shown to be hyperbolic by Bowd
en–Hensel–Webb\, while the curve graph\, which collapses subgraphs cor
responding to isotopy classes\, was proven to be hyperbolic by Masur–Min
sky. In this talk\, we prove that subgraphs of the fine curve graph corres
ponding to curves that essentially intersect a common curve contain a quas
i-isometrically embedded flat of every dimension and therefore are not hyp
erbolic. In particular\, the subgraph of the fine curve graph induced by a
ny single isotopy class—a graph whose properties are captured by neither
the curve graph nor fine curve graph—is not hyperbolic. This is joint w
ork with Ryan Dickmann.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tam Cheetham-West (Yale University)
DTSTART;VALUE=DATE-TIME:20240909T220000Z
DTEND;VALUE=DATE-TIME:20240909T223000Z
DTSTAMP;VALUE=DATE-TIME:20241112T114536Z
UID:GroupCraft4/36
DESCRIPTION:Title: Finite quotients and Property FA\nby Tam Cheetham-West (Yale Univ
ersity) as part of World of GroupCraft IV\n\n\nAbstract\nSome groups 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 sai
d to have Property FA. I will discuss examples of group pairs where both g
roups in each pair have all the same finite quotients\, but one group has
Property FA and the other group doesn't. This is joint work with Alex Lubo
tzky\, Alan Reid\, and Ryan Spitler.\n
LOCATION:https://researchseminars.org/talk/GroupCraft4/36/
END:VEVENT
END:VCALENDAR