BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Vandit Trivedi (Australian National University)
DTSTART:20230904T003000Z
DTEND:20230904T010000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/1
DESCRIPTION:Title: The isomorphism $ \\text{Aut}(B_{4}) \\cong \\text{Aut}(F_{2}) \\cong
\\text{Aut}(W_{3}) $ and its implications\nby Vandit Trivedi (Australi
an National University) as part of World of GroupCraft III\n\n\nAbstract\n
In this talk\, we discuss the known result that the automorphism group of
the free group of rank 2\, the automorphism group of the universal Coxeter
group of rank 3 and the automorphism group of the braid group on 4 strand
s are isomorphic. We give an outline of existing proofs of these isomorphi
sms and provide explicit maps between these groups. We then discuss the si
gnificance of this result and some implications for the study of automorph
isms of free groups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Fresacher (Western Sydney University)
DTSTART:20230903T233000Z
DTEND:20230904T000000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/2
DESCRIPTION:Title: Congruence Lattice of the Finite Twisted Brauer Monoid\nby Matthia
s Fresacher (Western Sydney University) as part of World of GroupCraft III
\n\n\nAbstract\nIn 2022\, East and Ruškuc published the congruence lattic
e of the infinite twisted partition monoid. As a by product\, they establi
shed the congruence lattices of the finite $d$-twisted partition monoids.
This talk is a first step in adapting the work of East and Ruškuc to the
setting of the Brauer monoid. Specifically\, it presents the newly establi
shed congruence lattice of the $0$-twisted Brauer monoid. With simple to g
rasp visual multiplication and applications in theoretical physics and rep
resentation theory\, the family of partition monoids are of particular int
erest to a number of fields as well are of stand alone interest.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgina Liversidge (The University of Auckland)
DTSTART:20230904T000000Z
DTEND:20230904T003000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/3
DESCRIPTION:Title: Labelled Coset Graphs\nby Georgina Liversidge (The University of A
uckland) as part of World of GroupCraft III\n\n\nAbstract\nWe introduce a
procedure to create a labelled coset graph for a subgroup $H$ of finite in
dex in a finitely-presented group $G$. This labelled coset graph can be us
ed for finding a presentation for the subgroup $H$\, and also for finding
expressions for subgroup elements in terms of a given set of generators fo
r $H$. We demonstrate the use of this procedure in finding `nice' generati
ng sets for torsion-free normal subgroups of ordinary triangle groups\, an
d expressions for the conjugates of those generators by the generators of
the parent group. This has implications for the study of regular maps and
large automorphism groups of compact Riemann surfaces.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Seelig (University of New South Wales)
DTSTART:20230904T010000Z
DTEND:20230904T013000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/4
DESCRIPTION:Title: Simplicity of forest-skein groups\nby Ryan Seelig (University of N
ew South Wales) as part of World of GroupCraft III\n\n\nAbstract\nIn 1965
Richard Thompson discovered three fascinating groups: $F$\, $T$\, and $V$\
, which are groups of homeomorphisms of the Cantor space. Thompson's group
s exhibit many rare properties\, notably\, $T$ and $V$ were the first exam
ples of finitely presented infinite simple groups. Since then\, Thompson-l
ike groups have been a fruitful source of groups with these properties.\n
\nIn 2022 Arnaud Brothier introduced \\textit{forest-skein} (FS) groups. T
hese are similar to Thompson's original groups\, though they are augmented
with \\textit{skein}-relations\, reminiscent of Vaughan Jones' subfactor
theory. FS groups come in three flavours: $G^F$\, $G^T$\, and $G^V$\, whic
h share many of the same properties as $F$\, $T$\, and $V$.\n \nSurprising
ly however\, not all FS groups enjoy analogous simplicity properties to $F
$\, $T$\, and $V$. In this talk we will discuss necessary and sufficient c
onditions under which a triple $G^F$\, $G^T$\, $G^V$ of FS groups admits n
ice simplicity properties\, give an infinite class of concrete examples\,
and mention some open questions.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dilshan Wijesena (University of New South Wales)
DTSTART:20230904T013000Z
DTEND:20230904T020000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/5
DESCRIPTION:Title: Irreducible Pythagorean representations of Thompson’s groups\nby
Dilshan Wijesena (University of New South Wales) as part of World of Grou
pCraft III\n\n\nAbstract\nRichard Thompson’s groups $F$\, $T$ and $V$ ar
e one of the most fascinating discrete infinite groups for their several u
nusual properties and their analytical properties have been challenging ex
perts for many decades. One reason for this is because very little is know
n about its representation theory. Luckily\, thanks to the novel technolog
y of Jones\, a rich family of so-called Pythagorean unitary representation
of Thompson’s groups can be constructed by simply specifying a pair of
finite-dimensional operators satisfying a certain equality. These represen
tations can even be extended to the celebrated Cuntz algebra and carry a p
owerful diagrammatic calculus which we use to develop techniques to study
their properties. This permits to reduce very difficult questions concerni
ng irreducibility and equivalence of infinite-dimensional representations
into problems in finite-dimensional linear algebra. This provides a new ri
ch class of irreducible representations of $F$. Moreover\, we introduce th
e Pythagorean dimension which is a new invariant for all representations o
f the Cuntz algebra and Pythagorean representations of $F\,T\,V$. For each
dimension $d$\, we show the irreducible classes form a moduli space of a
real manifold of dimension $2d^2+1$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerry Shen (University of Technology Sydney)
DTSTART:20230904T020000Z
DTEND:20230904T023000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/6
DESCRIPTION:Title: Linear Algebra Approach for Deciding Isomorphism of Virtually Abelian
Groups\nby Jerry Shen (University of Technology Sydney) as part of Wor
ld of GroupCraft III\n\n\nAbstract\nThe isomorphism problem for two groups
has long known to be undecidable for arbitrary groups (Dehn 1911)\, as su
ch we focus on the class of virtually abelian groups which is known to be
decidable as a subclass of polycylic-by-finite groups (Segal 1990) however
no complexity bound has yet to be given. We provide a new approach for th
is problem by constructing equivalent extensions for both groups and consi
dering the automorphisms induced on these extension components. With this
method we investigate the relationship between the isomorphism problem and
an equivalent or reduction of an linear algebra problem.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yo Hasegawa (Osaka University)
DTSTART:20230904T030000Z
DTEND:20230904T033000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/7
DESCRIPTION:Title: Gromov boundaries of non-proper hyperbolic geodesic spaces\nby Yo
Hasegawa (Osaka University) as part of World of GroupCraft III\n\n\nAbstra
ct\nIn a proper hyperbolic geodesic space\, it is well known that the sequ
ential boundary can be identified as topological spaces with the geodesic
boundary. We show that in a (not necessarily proper) hyperbolic geodesic s
pace\, the sequential boundary can be identified as topological spaces wit
h the quasi-geodesic boundary.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wonyong Jang (Korea Advanced Institute of Science and Technology)
DTSTART:20230904T033000Z
DTEND:20230904T040000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/8
DESCRIPTION:Title: On the freeness of the groups generated by two parabolic matrices\
nby Wonyong Jang (Korea Advanced Institute of Science and Technology) as p
art of World of GroupCraft III\n\n\nAbstract\nFor a given complex number a
\, consider the following two parabolic matrices\; A=((1\,1)\,(0\,1)) and
B(a)=((1\,0)\,(a\,1)) and let G(a) be the subgroup in SL(2\,C)\, generated
by A and B(a).\nDetermining whether G(a) is the free group rank 2\, is on
e of the long-standing open problems.\nIn this talk\, first I introduce a
geometric aspect of these groups and give previous results of the problem.
\nNext\, I will introduce my work joint with KyeongRo Kim\, including new
criteria for non-freeness.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renxing Wan (Beijing International Center for Mathematical Researc
h (BICMR) Peking University)
DTSTART:20230904T040000Z
DTEND:20230904T043000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/9
DESCRIPTION:Title: Uniform exponential growth for groups with proper product actions on h
yperbolic spaces\nby Renxing Wan (Beijing International Center for Mat
hematical Research (BICMR) Peking University) as part of World of GroupCra
ft III\n\n\nAbstract\nWe study the locally uniform exponential growth of a
finitely generated group acting properly on a finite product of hyperboli
c spaces. Under the assumption of coarsely dense orbits or shadowing prope
rty on factors\, we prove that any finitely generated non-virtually abelia
n subgroup has uniform exponential growth. These assumptions are full-fill
ed in many hierarchically hyperbolic groups\, including mapping class grou
ps\, specially cubulated groups and BMW groups. This is joint work with We
nyuan Yang.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josiah Oh (Fudan University)
DTSTART:20230904T050000Z
DTEND:20230904T053000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/10
DESCRIPTION:Title: Quasi-isometric rigidity of high-dimensional graph manifolds\nby
Josiah Oh (Fudan University) as part of World of GroupCraft III\n\n\nAbstr
act\nFrigerio-Lafont-Sisto define a high-dimensional graph manifold to be
a manifold that is built from pieces\, where each piece is the product of
a torus and a finite-volume non-compact hyperbolic manifold of dimension a
t least 3. They prove that any group quasi-isometric to the fundamental gr
oup of a high-dimensional graph manifold must split as the fundamental gro
up of a graph of groups\, where the algebraic structure of the vertex and
edge groups is determined. In this talk we discuss this theorem\, the main
ideas in the proof\, and work in progress towards a generalization.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inhyeok Choi (Korea Institute For Advanced Study)
DTSTART:20230904T053000Z
DTEND:20230904T060000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/11
DESCRIPTION:Title: Genericity of contracting elements in groups\nby Inhyeok Choi (Ko
rea Institute For Advanced Study) as part of World of GroupCraft III\n\n\n
Abstract\nGiven a finitely generated group G\, one can discuss the dynamic
s of each element of G via their action on the Cayley graph of G. When $G$
is hyperbolic in the sense of Gromov\, the action of an element of $G$ is
either elliptic or loxodromic\, the latter case being generic. In this ta
lk\, I will explain the converse of this statement. Namely\, we deduce the
global hyperbolicity of $G$ from the genericity of its contracting elemen
ts\, which is a natural notion that generalizes loxodromic elements. This
is based on joint work with Kunal Chawla and Giulio Tiozzo.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier De la Nuez Gonzalez (Korea Institute For Advanced Study)
DTSTART:20230904T060000Z
DTEND:20230904T063000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/12
DESCRIPTION:Title: Minimality of the compact-open topology on homeomorphism and diffeomo
rphism groups of manifolds\nby Javier De la Nuez Gonzalez (Korea Insti
tute For Advanced Study) as part of World of GroupCraft III\n\n\nAbstract\
nWe discuss recent work in which we prove that in almost all dimensions th
e compact open topology on the diffeomorphism or homeomorphism group of a
smooth manifold is minimal\, i.e. the group does not admit a strictly coar
ser Hausdorff group topology.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tejbir Lohan (IISER Mohali)
DTSTART:20230904T070000Z
DTEND:20230904T073000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/13
DESCRIPTION:Title: Product of two involutions in special linear groups\nby Tejbir L
ohan (IISER Mohali) as part of World of GroupCraft III\n\n\nAbstract\nReve
rsible or real elements in a group are those elements that are conjugate t
o their own inverses. They are closely related to strongly reversible or s
trongly real elements\, which can be expressed as a product of two involut
ions. It has been a problem of broad interest to classify reversible and s
trongly reversible elements in a group. In this talk\, we will provide a c
omplete count of reversible and strongly reversible elements in the specia
l linear groups $SL(n\, \\mathbb{C})$ and $SL(n\, \\mathbb{H})$. This is j
oint work with Krishnendu Gongopadhyay and Chandan Maity.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amrutha P (Chennai Mathematical Institute)
DTSTART:20230904T073000Z
DTEND:20230904T080000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/14
DESCRIPTION:Title: Cyclic characters of alternating group\nby Amrutha P (Chennai Mat
hematical Institute) as part of World of GroupCraft III\n\n\nAbstract\nThe
cyclic characters of a group $G$ are the characters induced from the cycl
ic subgroups of $G$. In the case of classical Coxeter groups\, Kraskiewicz
and Weyman worked out the decomposition into irreducible characters of c
haracters induced from the cyclic subgroup generated by a Coxeter element
. Jöllenbeck and Schocker gave a general approach for the case of symmetr
ic group $S_n$ by considering the cyclic group generated by any element of
$S_n$. The cyclic characters of $S_n$ are described in terms of a statist
ic on the Young tableaux called the multi major index. In this talk\, we w
ill see a description of the cyclic characters of the alternating group. T
his is joint work with Amritanshu Prasad and Velmurugan S.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lokenath Kundu (SRM University)
DTSTART:20230904T080000Z
DTEND:20230904T083000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/15
DESCRIPTION:Title: Growth of a family of finite groups\nby Lokenath Kundu (SRM Unive
rsity) as part of World of GroupCraft III\n\n\nAbstract\nLet $G$ be a fini
tely generated group. The growth of a group measures the growth\nof a $n$
−radius ball centered at the identity element. The notion of the growth
of\na family of finite groups was introduced by Prof. Sarah Black. It is k
nown that\nthe growth of any group is independent of its generating sets.
Contrasting to\nthe previous fact the growth of any family of finite group
s depends on its family\nof generating sets. Prof. Black conjectured that
the growth of any family of\nfinite simple groups has exponential growth.
In this talk\, we will find a positive\nanswer to the mentioned conjecture
.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aparajita Karmakar (Indian Statistical Institute\, Kolkata)
DTSTART:20230904T090000Z
DTEND:20230904T093000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/16
DESCRIPTION:Title: Results on equivariant cohomology of projective spaces\nby Aparaj
ita Karmakar (Indian Statistical Institute\, Kolkata) as part of World of
GroupCraft III\n\n\nAbstract\nIn this talk I will discuss some basic notio
ns in equivariant cohomology theory to finally present our work where we h
ave calculated the equivariant additive homology decompositions of complex
projective spaces. Following Lewis's approach we have been able to calcul
ate the equivariant cohomology ring structure of projective spaces with in
teger coefficients. I will try to present these results and some of its ap
plications.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Partha Sarathi Ghosh (Presidency University\, Kolkata)
DTSTART:20230904T093000Z
DTEND:20230904T100000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/17
DESCRIPTION:Title: Stability of the Haagerup property under Graph products\nby Parth
a Sarathi Ghosh (Presidency University\, Kolkata) as part of World of Grou
pCraft III\n\n\nAbstract\nI will recall what is the Haagerup property for
finitely generated groups. Then we discuss what is a graph product of a co
llection of groups (basically it is in some sense a generalization of free
products). Next I want to briefly mention the proof in the case of free p
roducts. Thereafter we will discuss the proof of the main result i.e. the
graph products of Haagerup groups again have the Haagerup property.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rakesh Halder (IISER Mohali)
DTSTART:20230904T100000Z
DTEND:20230904T103000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/18
DESCRIPTION:Title: Cannon-Thurston (CT) maps in trees of hyperbolic metric spaces\nb
y Rakesh Halder (IISER Mohali) as part of World of GroupCraft III\n\n\nAbs
tract\nThe CT-map was originally defined by Mahan Mitra in the context of
hyperbolic spaces\, based on a result of Cannon and Thurston. Mitra genera
lized and provided a new proof (in the coarse geometric setting) of their
result to any short exact sequence of hyperbolic groups. A proper map betw
een proper hyperbolic geodesic spaces admits a CT-map if it induces a cont
inuous map on their Gromov boundaries. In this talk\, I will introduce hyp
erbolic spaces\, groups\, their Gromov boundaries\, and discuss a recent r
esult on the existence of CT-map for subtrees of hyperbolic subspaces in t
rees of hyperbolic spaces generalizing earlier known results. This is join
t work with my supervisor Dr. Pranab Sardar.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Hyde (U. Copenhagen)
DTSTART:20230904T113000Z
DTEND:20230904T120000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/19
DESCRIPTION:Title: Embedding Q into a finitely presented group\nby James Hyde (U. Co
penhagen) as part of World of GroupCraft III\n\n\nAbstract\nI will define
Thompson's group T and it's lift to the line and then describe joint work
with Jim Belk and Francesco Matucci in which we give an embedding of the a
dditive group Q into the lift of T to the line.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgii Veprev (Université de Genève)
DTSTART:20230904T110000Z
DTEND:20230904T113000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/20
DESCRIPTION:Title: Limit of Rauzy digraphs of languages with subexponential complexity\nby Georgii Veprev (Université de Genève) as part of World of GroupCr
aft III\n\n\nAbstract\nTo a subshift over a finite alphabet\, one can natu
rally associate an infinite family of finite graphs\, called its Rauzy gra
phs. We show that for a subshift of subexponential complexity the Rauzy gr
aphs converge to the line $\\Z$ in the sense of Benjamini-Schramm converge
nce if and only its complexity function $p(n)$ is unbounded and satisfies
$\\lim_n\\frac{p(n+1)}{p(n)}$.\nWe then apply this criterion to many examp
les of well-studied dynamical systems. If the subshift is moreover uniquel
y ergodic then we show that the limit of labelled Rauzy graphs if it exist
s can be identified with the unique invariant measure.\n\nThis is a joint
work with Paul-Henry Leemann\, Tatiana Nagnibeda and Alexandra Skripchenko
.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Fariña-Asategui (Lund University)
DTSTART:20230904T120000Z
DTEND:20230904T123000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/21
DESCRIPTION:Title: A generalization of iterated permutational wreath products and applic
ations\nby Jorge Fariña-Asategui (Lund University) as part of World o
f GroupCraft III\n\n\nAbstract\nIterated permutational wreath products ari
se naturally as profinite groups acting transitively on regular rooted tre
es. Furthermore\, they can be characterized as those profinite groups whic
h are both self-similar and branching. A well-studied generalization of it
erated wreath products is the class of regular branch profinite groups con
taining a finite-index branching subgroup. However\, the class of regular
branch profinite groups is too small compared to the one of self-similar p
rofinite groups\, as there are only countably many groups on the former\,
while the latter is uncountable.\n\n\nIn this talk we propose a new genera
lization of iterated permutational wreath products which yields an uncount
able family of groups acting on regular rooted trees with interesting prop
erties. Remarkably\, this family of groups delivers an answer to a questi
on of Grigorchuk on the Hausdorff dimension of self-similar profinite grou
ps\, which has been open for almost two decades.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Perego (University of Milan-Bicocca)
DTSTART:20230904T130000Z
DTEND:20230904T133000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/22
DESCRIPTION:Title: Rationality of the Gromov boundary of a hyperbolic group\nby Davi
de Perego (University of Milan-Bicocca) as part of World of GroupCraft III
\n\n\nAbstract\nThe Gromov boundary of a hyperbolic group is a widely stud
ied object in the field of geometric group theory. Many authors tried to p
rovide topological approximations and recursive presentations for this bou
ndary. After recalling some properties of hyperbolic groups and language t
heoretic notions\, we will describe the tree of atoms. It was originally i
ntroduced by Belk\, Bleak and Matucci in order to prove that hyperbolic gr
oups embed into the rational group of asynchronous transducers. Then\, we
will speak about its connections with the hyperbolic world and we will see
some ways to approximate and recursively present the Gromov boundary via
this tree.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thiziri Moulla (Université de Montpellier)
DTSTART:20230904T133000Z
DTEND:20230904T140000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/23
DESCRIPTION:Title: On the volume entropy of groups\nby Thiziri Moulla (Université d
e Montpellier) as part of World of GroupCraft III\n\n\nAbstract\nLet G be
a group of finite presentation and $ (K\,h)={K_i\,h_i}_{i \\in I} $ a fam
ily of finite simplicial complexes\, endowed with Riemannian metrics\, of
fundamental group G. In this presentation\, I will define an invariant of
geometric type on G called Volume Entropy by using the properties of {K_i\
,h_i}-complexes for each $ i \\in I $. If time permits\, we'll compare thi
s invariant with another of the same type.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guy Blachar (Bar-Ilan University)
DTSTART:20230904T140000Z
DTEND:20230904T143000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/24
DESCRIPTION:Title: Probabilistic Laws on Groups\nby Guy Blachar (Bar-Ilan University
) as part of World of GroupCraft III\n\n\nAbstract\nSuppose a finite group
satisfies the following property: If you take two random elements\, then
with probability bigger than 5/8 they commute. Then this group is commutat
ive.\nStarting from this well-known result\, it is natural to ask: Do simi
lar results hold for other laws (p-groups\, nilpotent groups...)? Are ther
e analogous results for infinite groups? Are there phenomena specific to t
he infinite setup?\nWe will survey known and new results in this area. New
results are joint with Gideon Amir\, Maria Gerasimova and Gady Kozma.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Rauzy (Saarland U.)
DTSTART:20230904T150000Z
DTEND:20230904T153000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/25
DESCRIPTION:Title: Computability on the space of marked groups\nby Emmanuel Rauzy (S
aarland U.) as part of World of GroupCraft III\n\n\nAbstract\nIn the space
of marked groups\, marked groups are « close » when they satisfy the sa
me small relations. This topology allows us to classify group properties i
n a Borel hierarchy: « being abelian » is clopen\, « being nilpotent »
is open\, and so on. \n\nI will explain why it is relevant to look at thi
s topology from the point of view of computability\, now classifying prope
rties as « computably open » or « computably closed ». \n\nI will fina
lly explain how results that concern computability on the space of marked
groups provide\, via the Higman-Clapham-Valiev Theorem\, results about fin
itely presented groups with solvable word problem.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Gorazd (U. Newcastle\, Australia)
DTSTART:20230904T153000Z
DTEND:20230904T160000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/26
DESCRIPTION:Title: Universal Covers of trees and their Higman-Thompson groups\nby Ro
man Gorazd (U. Newcastle\, Australia) as part of World of GroupCraft III\n
\n\nAbstract\nThe famous Thompson group V is one famous example of finitel
y presented simple groups. Higman expanded it into a infinite group of fin
itely presented simple groups\, that can be seen as subgroups of the Almos
t Automorphism Group of regular trees (Neretin’s Group). In this talk I
will introduce analogous subgroups of the Almost Automorphism group of uni
versal covering trees of directed rooted graphs. I will look at the isomor
phism problem between these groups\, looking first at when covering trees
are almost isomorphic to each other and then at how one can embed these gr
oups in the Leavitt path module of the graph. Additionally I will also loo
k at the action of this group on the boundary of the tree and show how dif
ferent connectivity properties of the tree translate into different proper
ties of the action.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Mandel (U. Basque Country)
DTSTART:20230904T160000Z
DTEND:20230904T163000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/27
DESCRIPTION:Title: The quadratic Diophantine problem in Baumslag-Solitar groups\nby
Richard Mandel (U. Basque Country) as part of World of GroupCraft III\n\n\
nAbstract\nThe Diophantine problem for a finitely generated group $G$ is t
he algorithmic problem of determining whether a given equation has a solut
ion in $G$. The restriction of this problem to the class of quadratic equa
tions (where each variable appears exactly twice) is an important variatio
n which has been extensively studied in various classes of groups (free\,
hyperbolic\, free metabelian etc.). In this talk\, I will discuss some dec
idability and complexity results for the quadratic Diophantine problem ove
r the Baumslag-Solitar groups\, with an emphasis on the groups $\\operator
name{BS}(1\,n)$ and $\\operatorname{BS}(n\,\\pm n)$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominik Francoeur (U. Newcastle)
DTSTART:20230904T170000Z
DTEND:20230904T173000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/28
DESCRIPTION:Title: Lamplighter groups and bireversible automata\nby Dominik Francoeu
r (U. Newcastle) as part of World of GroupCraft III\n\n\nAbstract\nBirever
sible automata are combinatorial objects that can be used to describe cert
ain groups with self-similar actions on rooted trees. Groups defined by su
ch automata are interesting from the point of view of group theory\, since
they have connections\, among others\, with CAT(0) square complexes and c
ommensurators of free groups in the automorphism groups of regular trees.
However\, we currently know very little about the groups that can be gener
ated by bireversible automata\, and finding more examples is the subject o
f active research. In this talk\, after reviewing the necessary notions\,
we will show that every group of the form A≀Z with A finite and abelian
can be generated by a bireversible automaton\, thus generalising a result
of Skipper and Steinberg.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ismael Morales (U. Oxford)
DTSTART:20230904T173000Z
DTEND:20230904T180000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/29
DESCRIPTION:Title: Virtual homological invariants and profinite rigidity\nby Ismael
Morales (U. Oxford) as part of World of GroupCraft III\n\n\nAbstract\nThe
virtual second betti number of a free group (resp. surface group) is equal
to zero (resp. one). We will discuss the conjecture that these elementary
properties should\, in fact\, characterise such groups among finitely gen
erated residually finite groups. We also provide some evidence for these c
onjectures\, since they are true among limit groups and hyperbolic fundame
ntal groups of graphs of free groups with cyclic edge subgroups. Finally\,
we relate these conjectures with several questions on profinite rigidity.
This is based on joint work with Jonathan Fruchter.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gemma Crowe (Heriot-Watt U.)
DTSTART:20230904T180000Z
DTEND:20230904T183000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/30
DESCRIPTION:Title: Conjugacy\, languages and groups\nby Gemma Crowe (Heriot-Watt U.)
as part of World of GroupCraft III\n\n\nAbstract\nFormal language theory
has found surprising applications recently in geometric group theory. One
historical example was found by Cannon in hyperbolic groups\, where geodes
ics were studied in order to find the nature of the standard growth series
of hyperbolic groups. In this talk we will introduce languages associated
to conjugacy classes. This will lead us to define the conjugacy growth se
ries of a group\, which compared to standard growth is in general a far mo
re mysterious series. By studying properties of these languages\, we will
explore what this might tell us about conjugacy growth. Finally\, we will
consider if and when these properties can extend via quasi-isometries\, in
cluding recent work on virtual right-angled Artin groups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aidan Lorenz (Vanderbilt University)
DTSTART:20230904T190000Z
DTEND:20230904T193000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/31
DESCRIPTION:Title: Fibered 3-manifolds and pseudo-Anosov homeomorphisms\nby Aidan Lo
renz (Vanderbilt University) as part of World of GroupCraft III\n\n\nAbstr
act\nA result of Thurston's says that a fibered 3-manifold is hyperbolic i
f and only if it has a pseudo-Anosov monodromy. Moreover\, if the second h
omology of the 3-manifold has dimension larger than or equal to 2\, there
are infinitely many different ways in which the manifold fibers and hence
infinitely many pseudo-Anosov monodromies. Thus one can study families of
pseudo-Anosov homeomorphisms and in particular their dilatations by way of
hyperbolic fibered 3-manifolds. In this talk we will discuss techniques t
o do so and progress towards some related results about minimal dilatation
pseudo-Anosovs.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yandi Wu (U. Wisconsin)
DTSTART:20230904T193000Z
DTEND:20230904T200000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/32
DESCRIPTION:Title: Marked Length Spectrum Rigidity for Certain Quotients of the Davis Co
mplex\nby Yandi Wu (U. Wisconsin) as part of World of GroupCraft III\n
\n\nAbstract\nThe marked length spectrum of a negatively curved metric spa
ce can be thought of as a length assignment to every closed geodesic in th
e space. A celebrated result by Otal says that metrics on negatively curve
d closed surfaces are determined completely by their marked length spectra
. In my talk\, I will discuss my work towards extending Otal’s result to
a large class of surface amalgams\, which can arise as quotients of model
geometries of right-angled Coxeter groups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Koichi Oyakawa (Vanderbilt University)
DTSTART:20230904T200000Z
DTEND:20230904T203000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/33
DESCRIPTION:Title: Small cancellation groups are bi-exact\nby Koichi Oyakawa (Vander
bilt University) as part of World of GroupCraft III\n\n\nAbstract\nBi-exac
tness is an analytic property of groups defined by Ozawa and of fundamenta
l importance to the study of operator algebras. In this talk\, I discuss m
y recent result that any finitely generated (not necessarily finitely pres
ented) C′(1/33)-group is bi-exact. This is a new class of bi-exact group
s.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nima Hoda (Cornell)
DTSTART:20230904T210000Z
DTEND:20230904T213000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/34
DESCRIPTION:Title: Constructing bisimplices\nby Nima Hoda (Cornell) as part of World
of GroupCraft III\n\n\nAbstract\nI will describe the construction of an i
nfinite family of cells called\nbisimplices and their application to the c
onstruction of classifying\nspaces of quadric groups. The 1-skeleta of the
se cells are complete\nbipartite graphs\, making them well suited to the c
onstruction of\nhigher skeleta of certain families of bipartite graphs. Th
e\nconstruction of bisimplices poses special challenges since\, unlike\nsi
mplices and cubes\, they cannot be realized as polyhedra. An\nessential co
mponent of the construction is an application of the\ndiscrete Morse theor
y of Forman to the recognition of spheres.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sahana Balasubramanya (Lafayette)
DTSTART:20230904T213000Z
DTEND:20230904T220000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/36
DESCRIPTION:Title: Non-recognizing spaces for stable subgroups\nby Sahana Balasubram
anya (Lafayette) as part of World of GroupCraft III\n\n\nAbstract\nWe say
an action of a group on a space recognizes all stable subgroups if every
stable subgroup of G is quasi-isometrically embedded in the action on . T
he problem of constructing or identifying such spaces has been extensively
studied for many groups\, including mapping class groups and right angled
Artin groups- these are well known examples of acylindrically hyperbolic
groups. In these cases\, the recognizing spaces are the largest acylindric
al actions for the group. One can therefore ask the question if a largest
acylindrical action of an acylindrically hyperbolic group (if it exists) i
s a recognizing space for stable subgroups in general. We answer this ques
tion in the negative by producing an example of a relatively hyperbolic gr
oup whose largest acylindrical action fails to recognize all stable subgro
ups. This is joint work with Marissa Chesser\, Alice Kerr\, Johanna Mangah
as and Marie Trin.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Margolis (Ohio State U.)
DTSTART:20230904T220000Z
DTEND:20230904T223000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/37
DESCRIPTION:Title: Model geometries dominated by locally finite graphs\nby Alex Marg
olis (Ohio State U.) as part of World of GroupCraft III\n\n\nAbstract\nThe
central theme of geometric group theory is to study groups via their acti
ons on metric spaces. A model geometry of a finitely generated group is a
proper geodesic metric space admitting a geometric group action. Every fin
itely generated group has a model geometry that is a locally finite graph\
, namely its Cayley graph with respect to a finite generating set. In this
talk\, I investigate which finitely generated groups G have the property
that all model geometries of G are (essentially) locally finite graphs.\n
\nI introduce the notion of domination of metric spaces and give necessary
and sufficient conditions for all model geometries of a finitely generate
d group to be dominated by a locally finite graph. This characterizes fini
tely generated groups that embed as uniform lattices in locally compact gr
oups that are not compact-by-(totally disconnected). Among groups of cohom
ological dimension two\, the only such groups are surface groups and gener
alized Baumslag-Solitar groups.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mengfan Lyu (University of Technology Sydney)
DTSTART:20230903T230000Z
DTEND:20230903T233000Z
DTSTAMP:20260406T091838Z
UID:GroupCraft3/38
DESCRIPTION:Title: Multiple Context-free Languages and a Swapping Lemma\nby Mengfan
Lyu (University of Technology Sydney) as part of World of GroupCraft III\n
\n\nAbstract\nThe talk begins with an introduction to the basic concepts a
nd examples of multiple context-free languages(MCFL)\, which represent a c
aptivating and powerful extension beyond the well-known context-free langu
ages(CFL). We then proceed to introduce a new swapping lemma as an analogu
e of the pumping lemma for context-free languages. By applying the Swappin
g Lemma\, we can demonstrate how some languages fail to meet the criteria
for being multiple context-free.\n
LOCATION:https://researchseminars.org/talk/GroupCraft3/38/
END:VEVENT
END:VCALENDAR