BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Federico Berlai (University of the Basque Country)
DTSTART:20200605T050000Z
DTEND:20200605T060000Z
DTSTAMP:20260404T111136Z
UID:SiN/1
DESCRIPTION:Title: From hyperbolicity to hierarchical hyperbolicity\nby Federico Berla
i (University of the Basque Country) as part of Symmetry in Newcastle\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SiN/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Hagen (University of Bristol)
DTSTART:20200605T063000Z
DTEND:20200605T073000Z
DTSTAMP:20260404T111136Z
UID:SiN/2
DESCRIPTION:Title: Hierarchical hyperbolicity from actions on simplicial complexes\nby
Mark Hagen (University of Bristol) as part of Symmetry in Newcastle\n\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SiN/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Verret (The University of Auckland\, New Zealand)
DTSTART:20200918T050000Z
DTEND:20200918T060000Z
DTSTAMP:20260404T111136Z
UID:SiN/3
DESCRIPTION:Title: Local actions in vertex-transitive graphs\nby Gabriel Verret (The U
niversity of Auckland\, New Zealand) as part of Symmetry in Newcastle\n\n\
nAbstract\nA graph is vertex-transitive if its group of automorphism acts
transitively on its vertices. A very important concept in the study of the
se graphs is that of local action\, that is\, the permutation group induce
d by a vertex-stabiliser on the corresponding neighbourhood. I will explai
n some of its importance and discuss some attempts to generalise it to the
case of directed graphs.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Giudici (The University of Western Australia\, Australia)
DTSTART:20200918T063000Z
DTEND:20200918T073000Z
DTSTAMP:20260404T111136Z
UID:SiN/4
DESCRIPTION:Title: The synchronisation hierarchy for permutation groups\nby Michael Gi
udici (The University of Western Australia\, Australia) as part of Symmetr
y in Newcastle\n\n\nAbstract\nThe concept of a synchronising permutation g
roup was introduced nearly 15 years ago as a possible way of approaching T
he \\v{C}ern\\'y Conjecture. Such groups must be primitive. In an attempt
to understand synchronising groups\, a whole hierarchy of properties for a
permutation group has been developed\, namely\, 2-transitive groups\, $\\
mathbb{Q}$I-groups\, spreading\, separating\, synchronising\, almost synch
ronising and primitive. Many surprising connections with other areas of m
athematics such as finite geometry\, graph theory\, and design theory have
arisen in the study of these properties. In this survey talk I will give
an overview of the hierarchy and discuss what is known about which groups
lie where.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandra Garrido (Universidad Autónoma de Madrid)
DTSTART:20201002T060000Z
DTEND:20201002T070000Z
DTSTAMP:20260404T111136Z
UID:SiN/5
DESCRIPTION:Title: When is a piecewise (a.k.a topological) full group locally compact?
\nby Alejandra Garrido (Universidad Autónoma de Madrid) as part of Symmet
ry in Newcastle\n\n\nAbstract\nQuestion: When is a piecewise (a.k.a topolo
gical) full group locally compact? \n\nAnswer: Only when it's an ample gro
up in the sense of Krieger (in particular\, discrete\, countable and local
ly finite) and has a Bratteli diagram satisfying certain conditions. \n\nC
omplaint: Wait\, isn't Neretin's group a non-discrete\, locally compact\,
topological full group? \n\nRetort: It is\, but you need to use the correc
t topology!\n\nA fleshed-out version of the above conversation will be giv
en in the talk. Based on joint work with Colin Reid.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feyisayo Olukoya (University of Aberdeen)
DTSTART:20201002T073000Z
DTEND:20201002T083000Z
DTSTAMP:20260404T111136Z
UID:SiN/6
DESCRIPTION:Title: The group of automorphisms of the shift dynamical system and the Higman
-Thompson groups\nby Feyisayo Olukoya (University of Aberdeen) as part
of Symmetry in Newcastle\n\n\nAbstract\nWe give a survey of recent result
s exploring connections between the Higman-Thompson groups and their autom
orphism groups and the group of automorphisms of the shift dynamical syste
m. Our survey takes us from dynamical systems to group theory via groups o
f homeomorphisms with a segue through combinatorics\, in particular\, de B
ruijn graphs.\n\nJoint work with Collin Bleak and Peter Cameron.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Skipper (Ohio State University)
DTSTART:20201015T230000Z
DTEND:20201016T000000Z
DTSTAMP:20260404T111136Z
UID:SiN/7
DESCRIPTION:Title: Maximal Subgroups of Thompson's group V\nby Rachel Skipper (Ohio St
ate University) as part of Symmetry in Newcastle\n\n\nAbstract\nThere has
been a long interest in embedding and non-embedding results for groups in
the Thompson family. One way to get at results of this form is to classify
maximal subgroups. In this talk\, we will define certain labelings of bin
ary trees and use them to produce a large family of new maximal subgroups
of Thompson's group V. We also relate them to a conjecture about Thompson'
s group T.\nThis is joint\, ongoing work with Jim Belk\, Collin Bleak\, an
d Martyn Quick at the University of Saint Andrews.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawrence Reeves (The University of Melbourne)
DTSTART:20201016T003000Z
DTEND:20201016T013000Z
DTSTAMP:20260404T111136Z
UID:SiN/8
DESCRIPTION:Title: Irrational-slope versions of Thompson’s groups T and V\nby Lawren
ce Reeves (The University of Melbourne) as part of Symmetry in Newcastle\n
\n\nAbstract\nWe consider irrational slope versions of T and V\, We give i
nfinite presentations for these groups and show how they can be represente
d by tree-pair diagrams. We also show that they have index-2 normal subgro
ups that are simple. \nThis is joint work with Brita Nucinkis and Pep Buri
llo.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Bradford (University of Cambridge)
DTSTART:20201109T090000Z
DTEND:20201109T100000Z
DTSTAMP:20260404T111136Z
UID:SiN/9
DESCRIPTION:Title: Quantitative LEF and topological full groups\nby Henry Bradford (Un
iversity of Cambridge) as part of Symmetry in Newcastle\n\n\nAbstract\nTop
ological full groups of minimal subshifts are an important source of exoti
c examples in geometric group theory\, as well as being powerful invariant
s of symbolic dynamical systems. In 2011\, Grigorchuk and Medynets proved
that TFGs are LEF\, that is\, every finite subset of the multiplication ta
ble occurs in the multiplication table of some finite group. In this talk
we explore some ways in which asymptotic properties of the finite groups w
hich occur reflect asymptotic properties of the associated subshift. Joint
work with Daniele Dona.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Hautekiet (Université libre de Bruxelles\, Belgium)
DTSTART:20201123T073000Z
DTEND:20201123T083000Z
DTSTAMP:20260404T111136Z
UID:SiN/10
DESCRIPTION:Title: Automorphism groups of transcendental field extensions\nby William
Hautekiet (Université libre de Bruxelles\, Belgium) as part of Symmetry
in Newcastle\n\n\nAbstract\nIt is well-known that the Galois group of an (
infinite) algebraic field extension is a profinite group. When the extensi
on is transcendental\, the automorphism group is no longer compact\, but h
as a totally disconnected locally compact structure (TDLC for short). The
study of TDLC groups was initiated by van Dantzig in 1936 and then restart
ed by Willis in 1994. In this talk some of Willis' concepts\, such as tidy
subgroups\, the scale function\, flat subgroups and directions are introd
uced and applied to examples of automorphism groups of transcendental fiel
d extensions. It remains unknown whether there exist conditions that a TDL
C group must satisfy to be a Galois group. A suggestion of such a conditio
n is made.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Breuer (University of Newcastle\, Australia)
DTSTART:20201123T090000Z
DTEND:20201123T100000Z
DTSTAMP:20260404T111136Z
UID:SiN/11
DESCRIPTION:Title: Realising general linear groups as Galois groups\nby Florian Breue
r (University of Newcastle\, Australia) as part of Symmetry in Newcastle\n
\n\nAbstract\nI will show how to construct field extensions with Galois gr
oups isomorphic to general linear groups (with entries in various rings an
d fields) from the torsion of elliptic curves and Drinfeld modules. No pri
or knowledge of these structures is assumed.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:François Le Maître (Université de Paris)
DTSTART:20210125T073000Z
DTEND:20210125T083000Z
DTSTAMP:20260404T111136Z
UID:SiN/12
DESCRIPTION:Title: Dense totipotent free subgroups of full groups\nby François Le Ma
ître (Université de Paris) as part of Symmetry in Newcastle\n\n\nAbstrac
t\nIn this talk\, we will be interested in measure-preserving actions of c
ountable groups on standard probability spaces\, and more precisely in the
partitions of the space into orbits that they induce\, also called measur
e-preserving equivalence relations. In 2000\, Gaboriau obtained a characte
rization of the ergodic equivalence relations which come from non-free act
ions of the free group on $n > 1$ generators: these are exactly the equiva
lence relations of cost less than n. A natural question is: how non-free c
an these actions be made\, and what does the action on each orbit look lik
e? We will obtain a satisfactory answer by showing that the action on each
orbit can be made totipotent\, which roughly means "as rich as possible"\
, and furthermore that the free group can be made dense in the ambient ful
l group of the equivalence relation.\n\nThis is joint work with Alessandro
Carderi and Damien Gaboriau.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Cox (University of Bristol)
DTSTART:20210125T090000Z
DTEND:20210125T100000Z
DTSTAMP:20260404T111136Z
UID:SiN/13
DESCRIPTION:Title: Spread and infinite groups\nby Charles Cox (University of Bristol)
as part of Symmetry in Newcastle\n\n\nAbstract\nMy recent work has involv
ed taking questions asked for finite groups and considering them for infin
ite groups. There are various natural directions with this. In finite grou
p theory\, there exist many beautiful results regarding generation propert
ies. One such notion is that of spread\, and Scott Harper and Casey Donove
n have raised several intriguing questions for spread for infinite groups
(in https://arxiv.org/abs/1907.05498). A group $G$ has spread $k$ if for e
very $g_1\, \\dots\, g_k \\in G$ we can find an $h \\in G$ such that $\\la
ngle g_i\, h \\rangle = G$. For any group we can say that if it has a prop
er quotient that is non-cyclic\, then it has spread 0. In the finite world
there is then the astounding result - which is the work of many authors -
that this condition on proper quotients is not just a necessary condition
for positive spread\, but is also a sufficient one. Harper-Donoven’s fi
rst question is therefore: is this the case for infinite groups? Well\, no
. But that’s for the trivial reason that we have infinite simple groups
that are not 2-generated (and they point out that 3-generated examples are
also known). But if we restrict ourselves to 2-generated groups\, what ha
ppens? In this talk we’ll see the answer to this question. The arguments
will be concrete (*) and accessible to a general audience.\n\n(*) at the
risk of ruining the punchline\, we will find a 2-generated group that has
every proper quotient cyclic but that has spread zero.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Henry-Leemann (University of Neuchatel)
DTSTART:20210222T073000Z
DTEND:20210222T083000Z
DTSTAMP:20260404T111136Z
UID:SiN/14
DESCRIPTION:Title: Cayley graphs with few automorphisms\nby Paul Henry-Leemann (Unive
rsity of Neuchatel) as part of Symmetry in Newcastle\n\n\nAbstract\nLet G
be a group and S a generating set. Then the group G naturally acts on the
Cayley graph Cay(G\,S) by left multiplications. The group G is said to be
rigid if there exists an S such that the only automorphisms of Cay(G\,S) a
re the ones coming from the action of G.\nWhile the classification of fini
te rigid groups was achieved in 1981\, few results were known about infini
te groups. In a recent work\, with M. de la Salle we gave a complete class
ification of infinite finitely generated rigid groups. As a consequence\,
we also obtain that every finitely generated group admits a Cayley graph w
ith countable automorphism group.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giles Gardam (WWU Muenster)
DTSTART:20210222T090000Z
DTEND:20210222T100000Z
DTSTAMP:20260404T111136Z
UID:SiN/15
DESCRIPTION:Title: Kaplansky's conjectures\nby Giles Gardam (WWU Muenster) as part of
Symmetry in Newcastle\n\n\nAbstract\nKaplansky made various related conje
ctures about group rings\, especially for torsion-free groups. For example
\, the zero divisors conjecture predicts that if K is a field and G is a t
orsion-free group\, then the group ring K[G] has no zero divisors. I will
survey what is known about the conjectures\, including their relationships
to each other and to other group properties such as orderability\, and pr
esent some recent progress.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoe Chatzidakis (CNRS - ENS)
DTSTART:20210419T063000Z
DTEND:20210419T073000Z
DTSTAMP:20260404T111136Z
UID:SiN/16
DESCRIPTION:Title: A new invariant for difference fields\nby Zoe Chatzidakis (CNRS -
ENS) as part of Symmetry in Newcastle\n\n\nAbstract\nIf $(K\,f)$ is a diff
erence field\, and a is a finite tuple in some difference field extending
$K$\, and such that $f(a)$ in $K(a)^{alg}$\, then we define $dd(a/K)=\\mat
hop{lim}[K(f^k(a)\,a):K(a)]^{1/k}$\, the distant degree of $a$ over $K$. T
his is an invariant of the difference field extension $K(a)^{alg}/K$. We s
how that there is some $b$ in the difference field generated by $a$ over $
K$\, which is equi-algebraic with $a$ over $K$\, and such that $dd(a/K)=[K
(f(b)\,b):K(b)]$\, i.e.: for every $k>0$\, $f(b) \\in K(b\,f^k(b))$.\n\nVi
ewing $\\mathop{Aut}(K(a)^{alg}/K)$ as a locally compact group\, this resu
lt is connected to results of Goerge Willis on scales of automorphisms of
locally compact totally disconnected groups. I will explicit the correspon
dence between the two sets of results.\n(Joint with E. Hrushovski)\n
LOCATION:https://stable.researchseminars.org/talk/SiN/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Ciobanu (Herriot Watt)
DTSTART:20210419T080000Z
DTEND:20210419T090000Z
DTSTAMP:20260404T111136Z
UID:SiN/17
DESCRIPTION:Title: Free group homomorphisms and the Post Correspondence Problem\nby L
aura Ciobanu (Herriot Watt) as part of Symmetry in Newcastle\n\n\nAbstract
\nThe Post Correspondence Problem (PCP) is a classical problem in computer
science that can be stated as: is it decidable whether given two morphism
s $g$ and $h$ between two free semigroups $A$ and $B$\, there is any nontr
ivial $x$ in $A$ such that $g(x)=h(x)$? This question can be phrased in te
rms of equalisers\, asked in the context of free groups\, and expanded: if
the `equaliser' of $g$ and $h$ is defined to be the subgroup consisting o
f all $x$ where $g(x)=h(x)$\, it is natural to wonder not only whether the
equaliser is trivial\, but what its rank or basis might be.\n\nWhile the
PCP for semigroups is famously insoluble and acts as a source of undecidab
ility in many areas of computer science\, the PCP for free groups is open\
, as are the related questions about rank\, basis\, or further generalisat
ions. However\, in this talk we will show that there are links and surpris
ing equivalences between these problems in free groups\, and classes of ma
ps for which we can give complete answers. This is joint work with Alan Lo
gan.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yago Antolin (Universidad Complutense de Madrid)
DTSTART:20210510T063000Z
DTEND:20210510T073000Z
DTSTAMP:20260404T111136Z
UID:SiN/18
DESCRIPTION:Title: Geometry and Complexity of positive cones in groups.\nby Yago Anto
lin (Universidad Complutense de Madrid) as part of Symmetry in Newcastle\n
\n\nAbstract\nA positive cone on a group $G$ is a subsemigroup $P$\, such
that $G$ is the disjoint union of $P$\, $P^{-1}$ and the trivial element.
Positive cones codify naturally $G$-left-invariant total orders on $G$. Wh
en $G$ is a finitely generated group\, we will discuss whether or not a po
sitive cone can be described by a regular language over the generators and
how the ambient geometry of $G$ influences the geometry of a positive con
e.\n\nThis will be based on joint works with Juan Alonso\, Joaquin Brum\,
Cristobal Rivas and Hang Lu Su.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Kropholler (Universität Münster)
DTSTART:20210510T080000Z
DTEND:20210510T090000Z
DTSTAMP:20260404T111136Z
UID:SiN/19
DESCRIPTION:Title: Groups of type FP_2 over fields but not over the integers\nby Robe
rt Kropholler (Universität Münster) as part of Symmetry in Newcastle\n\n
\nAbstract\nBeing of type $\\mathop{FP}_2$ is an algebraic shadow of being
finitely presented. A long standing question was whether these two classe
s are equivalent. This was shown to be false in the work of Bestvina and B
rady. More recently\, there are many new examples of groups of type $\\mat
hop{FP}_2$ coming with various interesting properties. I will begin with a
n introduction to the finiteness property $\\mathop{FP}_2$. I will end by
giving a construction to find groups that are of type $\\mathop{FP}_2(F)$
for all fields $F$ but not $\\mathop{FP}_2(\\mathbb{Z})$\n
LOCATION:https://stable.researchseminars.org/talk/SiN/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Libor Barto (Charles University in Prague)
DTSTART:20210524T063000Z
DTEND:20210524T073000Z
DTSTAMP:20260404T111136Z
UID:SiN/20
DESCRIPTION:Title: CSPs and Symmetries\nby Libor Barto (Charles University in Prague)
as part of Symmetry in Newcastle\n\n\nAbstract\nHow difficult is to solve
a given computational problem? In a large class of computational problems
\, including the fixed-template Constraint Satisfaction Problems (CSPs)\,
this fundamental question has a simple and beautiful answer: the more symm
etrical the problem is\, the easier is to solve it. The tight connection b
etween the complexity of a CSP and a certain concept that captures its sym
metry has fueled much of the progress in the area in the last 20 years. I
will talk about this connection and some of the many tools that have been
used to analyze the symmetries. The tools involve rather diverse areas of
mathematics including algebra\, analysis\, combinatorics\, logic\, probab
ility\, and topology.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoe Chatzidakis (CNRS - ENS)
DTSTART:20210524T080000Z
DTEND:20210524T090000Z
DTSTAMP:20260404T111136Z
UID:SiN/21
DESCRIPTION:Title: A new invariant for difference fields\nby Zoe Chatzidakis (CNRS -
ENS) as part of Symmetry in Newcastle\n\n\nAbstract\nIf $(K\,f)$ is a diff
erence field\, and $a$ is a finite tuple in some difference field extendin
g $K$\, and such that $f(a) \\in K(a)^{alg}$\, then we define $dd(a/K)=\\l
im[K(f^k(a)\,a):K(a)]^{1/k}$\, the distant degree of $a$ over $K$. This is
an invariant of the difference field extension $K(a)^{alg}/K$. We show th
at there is some $b$ in the difference field generated by $a$ over $K$\, w
hich is equi-algebraic with $a$ over $K$\, and such that $dd(a/K)=[K(f(b)\
,b):K(b)]$\, i.e.: for every $k>0$\, $f(b) \\in K(b\,f^k(b))$.\n\nViewing
$\\mathop{Aut}(K(a)^{alg}/K)$ as a locally compact group\, this result is
connected to results of Goerge Willis on scales of automorphisms of locall
y compact totally disconnected groups. I will explicit the correspondence
between the two sets of results.\n(Joint with E. Hrushovski)\n
LOCATION:https://stable.researchseminars.org/talk/SiN/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Waldemar Hołubowski (Silesian University of Technology)
DTSTART:20210607T063000Z
DTEND:20210607T073000Z
DTSTAMP:20260404T111136Z
UID:SiN/22
DESCRIPTION:Title: Normal subgroups in the group of column-finite infinite matrices\n
by Waldemar Hołubowski (Silesian University of Technology) as part of Sym
metry in Newcastle\n\n\nAbstract\nThe classical result\, due to Jordan\, B
urnside\, Dickson\, says that every normal subgroup of $GL(n\, K)$ ($K$ -
a field\, $n \\geq 3$) which is not contained in the center\, contains $SL
(n\, K)$. A. Rosenberg gave description of normal subgroups of $GL(V)$\, w
here $V$ is a vector space of any infinite cardinality dimension over a di
vision ring. However\, when he considers subgroups of the direct product o
f the center and the group of linear transformations $g$ such that $g-id_V
$ has finite dimensional range the proof is not complete. We fill this gap
for countably dimensional $V$ giving description of the lattice of normal
subgroups in the group of infinite column-finite matrices indexed by posi
tive integers over any field. Similar results for Lie algebras of matrices
will be surveyed.\n\nThe talks is based on results presented in https://a
rxiv.org/abs/1808.06873 and https://arxiv.org/abs/1806.01099.\n\n(joint wo
rk with Martyna Maciaszczyk and Sebastian Zurek.)\n
LOCATION:https://stable.researchseminars.org/talk/SiN/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yves Stadler (Université Clermont Auvergne)
DTSTART:20210621T063000Z
DTEND:20210621T073000Z
DTSTAMP:20260404T111136Z
UID:SiN/23
DESCRIPTION:Title: Highly transitive groups among groups acting on trees\nby Yves Sta
dler (Université Clermont Auvergne) as part of Symmetry in Newcastle\n\n\
nAbstract\nHighly transitive groups\, i.e. groups admitting an embedding i
n Sym(N) with dense image\, form a wide class of groups. For instance\, M.
Hull and D. Osin proved that it contains all countable acylindrically hyp
erbolic groups with trivial finite radical. After an introduction to high
transitiviy\, I will present a theorem (from joint work with P. Fima\, F.
Le Maître and S. Moon) showing that many groups acting on trees are highl
y transitive. On the one hand\, this theorem gives new examples of highly
transitive groups. On the other hand\, it is sharp because of results by A
. Le Boudec and N. Matte Bon.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Castellano (University of Milan - Bicoca)
DTSTART:20210621T080000Z
DTEND:20210621T090000Z
DTSTAMP:20260404T111136Z
UID:SiN/24
DESCRIPTION:Title: The Euler characteristic and the zeta-functions of a totally disconnec
ted locally compact group\nby Ilaria Castellano (University of Milan -
Bicoca) as part of Symmetry in Newcastle\n\n\nAbstract\nThe Euler charact
eristic and the zeta-functions of a totally disconnected locally compact g
roup\nAbstract: The Euler-Poincaré characteristic of a discrete group is
an important (but also quite mysterious) invariant. It is usually just an
integer or a rational number and reflects many quite significant propertie
s. The realm of totally disconnected locally compact groups admits an anal
ogue of the Euler-Poincaré characteristic which surprisingly is no longer
just an integer\, or a rational number\, but a rational multiple of a Haa
r measure. Warning: in order to gain such an invariant the group has to be
unimodular and satisfy some cohomological finiteness conditions. Examples
of groups satisfying these additional conditions are the fundamental grou
ps of finite trees of profinite groups. What arouses our curiosity is the
fact that - in some cases - the Euler-Poincaré characteristic turns out t
o be miraculously related to a zeta-function. A large part of the talk wil
l be devoted to the introduction of the just-cited objects. We aim at conc
luding the presentation by facing the concrete example of the group of F-p
oints of a split semisimple simply connected algebraic group G over F (whe
re F denotes a non-archimedean locally compact field of residue characteri
stic p).\nJoint work with Gianmarco Chinello and Thomas Weigel.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lancelot Semal (UC Louvain)
DTSTART:20200705T080000Z
DTEND:20200705T090000Z
DTSTAMP:20260404T111136Z
UID:SiN/25
DESCRIPTION:Title: Unitary representations of totally disconnected locally compact groups
satisfying Ol'shanskii's factorization\nby Lancelot Semal (UC Louvain
) as part of Symmetry in Newcastle\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SiN/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lancelot Semal (UC Louvain)
DTSTART:20210705T080000Z
DTEND:20210705T090000Z
DTSTAMP:20260404T111136Z
UID:SiN/26
DESCRIPTION:Title: Unitary representations of totally disconnected locally compact groups
satisfying Ol'shanskii's factorization\nby Lancelot Semal (UC Louvain
) as part of Symmetry in Newcastle\n\n\nAbstract\nWe provide a new axiomat
ic framework\, inspired by the work of Ol'shanskii\, to describe explicitl
y certain irreducible unitary representations of second-countable non-disc
rete unimodular totally disconnected locally compact groups. We show that
this setup applies to various families of automorphism groups of locally f
inite semiregular trees and right-angled buildings.\n\nThe talk is based o
n material presented in https://arxiv.org/abs/2106.05730\n
LOCATION:https://stable.researchseminars.org/talk/SiN/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Raum (Stockholm University)
DTSTART:20210809T063000Z
DTEND:20210809T073000Z
DTSTAMP:20260404T111136Z
UID:SiN/27
DESCRIPTION:Title: Locally compact groups acting on trees\, the type I conjecture and non
-amenable von Neumann algebras\nby Sven Raum (Stockholm University) as
part of Symmetry in Newcastle\n\n\nAbstract\nn the 90's\, Nebbia conjectu
red that a group of tree automorphisms acting transitively on the tree's b
oundary must be of type I\, that is\, its unitary representations can in p
rincipal be classified. For key examples\, such as Burger-Mozes groups\,
this conjecture is verified. Aiming for a better understanding of Nebbia'
s conjecture and a better understanding of representation theory of groups
acting on trees\, it is natural to ask whether there is a characterisatio
n of type I groups acting on trees. In 2016\, we introduced in collaborati
on with Cyril Houdayer a refinement of Nebbia's conjecture to a trichotomy
\, opposing type I groups with groups whose von Neumann algebra is non-ame
nable. For large classes of groups\, including Burger-Mozes groups\, we c
ould verify this trichotomy.\nIn this talk\, I will motivate and introduce
the conjecture trichotomy for groups acting on tress and explain how von
Neumann algebraic techniques enter the picture.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Parkinson (University of Sydney)
DTSTART:20210809T080000Z
DTEND:20210809T090000Z
DTSTAMP:20260404T111136Z
UID:SiN/28
DESCRIPTION:Title: Automata for Coxeter groups\nby James Parkinson (University of Syd
ney) as part of Symmetry in Newcastle\n\n\nAbstract\nIn 1993 Brink and How
lett proved that finitely generated Coxeter groups are automatic. In parti
cular\, they constructed a finite state automaton recognising the language
of reduced words in the Coxeter group. This automaton is constructed in t
erms of the remarkable set of "elementary roots" in the associated root sy
stem.\nIn this talk we outline the construction of Brink and Howlett. We a
lso describe the minimal automaton recognising the language of reduced wor
ds\, and prove necessary and sufficient conditions for the Brink-Howlett a
utomaton to coincide with this minimal automaton. This resolves a conjectu
re of Hohlweg\, Nadeau\, and Williams\, and is joint work with Yeeka Yau.\
n
LOCATION:https://stable.researchseminars.org/talk/SiN/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Willis (University of Newcastle)
DTSTART:20210830T080000Z
DTEND:20210830T090000Z
DTSTAMP:20260404T111136Z
UID:SiN/29
DESCRIPTION:Title: Constructing groups with flat-rank greater than 1\nby George Willi
s (University of Newcastle) as part of Symmetry in Newcastle\n\n\nAbstract
\nThe contraction subgroup for $x$ in the locally compact group\, $G$\, $\
\mathop{con}(x) = \\left\\{ g\\in G \\mid x^ngx^{-n} \\to 1\\text{ as }n\\
to\\infty \\right\\}$\, and the Levi subgroup is $\\mathop{lev}(x) = \\lef
t\\{ g\\in G \\mid \\{x^ngx^{-n}\\}_{n\\in\\mathbb{Z}} \\text{ has compact
closure}\\right\\}$. The following will be shown.\n\nLet $G$ be a totally
disconnected\, locally compact group and $x\\in G$. Let $y\\in{\\sf lev}(
x)$. Then there are $x'\\in G$ and a compact subgroup\, $K\\leq G$ such th
at: $K$ is normalised by $x'$ and $y$\, $\\mathop{con}(x') = \\mathop{con}
(x)$ and $\\mathop{lev}(x') = \\mathop{lev}(x)$\, and the group $\\langle
x'\,y\,K\\rangle$ is abelian modulo $K$\, and hence flat.\n\n\nIf no compa
ct open subgroup of $G$ normalised by $x$ and no compact open subgroup of
$\\mathop{lev}(x)$ normalised by $y$\, then the flat-rank of $\\langle x'\
,y\,K\\rangle$ is equal to $2$.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siegfried Echterhoff (University of Münster)
DTSTART:20210927T063000Z
DTEND:20210927T073000Z
DTSTAMP:20260404T111136Z
UID:SiN/30
DESCRIPTION:Title: Amenable group actions on C*-algebras and the weak containment problem
\nby Siegfried Echterhoff (University of Münster) as part of Symmetry
in Newcastle\n\n\nAbstract\nThe notion of amenable actions by discrete gr
oups on C*-algebras has been introduced by Claire Amantharaman-Delaroche m
ore than thirty years ago\, and has become a well understood theory with m
any applications. So it is somewhat surprising that an established theory
of amenable actions by general locally compact groups has been missed for
a very long time. We now present a theory which extends the discrete case
and unifies several notions of approximation properties of actions which h
ave been discussed in the literature. We also discuss the weak containment
problem which asks wether an action $\\alpha:G\\to \\Aut(A)$ is amenable
if and only if the maximal and reduced crossed products coincide.\n\nIn th
is lecture we report on joint work with Alcides Buss and Rufus Willett\n
LOCATION:https://stable.researchseminars.org/talk/SiN/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim de Laat (University of Münster)
DTSTART:20210927T080000Z
DTEND:20210927T090000Z
DTSTAMP:20260404T111136Z
UID:SiN/31
DESCRIPTION:Title: Gelfand pairs\, spherical functions and exotic group C*-algebras\n
by Tim de Laat (University of Münster) as part of Symmetry in Newcastle\n
\n\nAbstract\nFor a non-amenable group $G$\, there can be many group C*-al
gebras that lie naturally between the universal and the reduced C*-algebra
of $G$. These are called exotic group C*-algebras. After a short introduc
tion\, I will explain that if $G$ is a simple Lie group or an appropriate
locally compact group acting on a tree\, the $L^p$-integrability propertie
s of different spherical functions on $G$ (relative to a maximal compact s
ubgroup) can be used to distinguish between exotic group C*-algebras. This
recovers results of Samei and Wiersma. Additionally\, I will explain that
under certain natural assumptions\, the aforementioned exotic group C*-al
gebras are the only ones coming from $G$-invariant ideals in the Fourier-S
tieltjes algebra of $G$.\n\nThis is based on joint work with Dennis Heinig
and Timo Siebenand.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sanghyun Kim (KIAS)
DTSTART:20211101T063000Z
DTEND:20211101T073000Z
DTSTAMP:20260404T111136Z
UID:SiN/32
DESCRIPTION:Title: Optimal regularity of mapping class group actions on the circle\nb
y Sanghyun Kim (KIAS) as part of Symmetry in Newcastle\n\n\nAbstract\nWe p
rove that for each finite index subgroup $H$ of the mapping class group of
a closed hyperbolic surface\, and for each real number $r>0$ there does n
ot exist a faithful $C^{1+r}$--action of $H$ on a circle. (Joint with Thom
as Koberda and Cristobal Rivas)\n
LOCATION:https://stable.researchseminars.org/talk/SiN/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francois Thilmany (UC Louvain)
DTSTART:20211101T080000Z
DTEND:20211101T090000Z
DTSTAMP:20260404T111136Z
UID:SiN/33
DESCRIPTION:Title: Uniform discreteness of arithmetic groups and the Lehmer conjecture\nby Francois Thilmany (UC Louvain) as part of Symmetry in Newcastle\n\n\
nAbstract\nThe famous Lehmer problem asks whether there is a gap between 1
and the Mahler measure of algebraic integers which are not roots of unity
. Asked in 1933\, this deep question concerning number theory has since th
en been connected to several other subjects. After introducing the concept
s involved\, we will briefly describe a few of these connections with the
theory of linear groups. Then\, we will discuss the equivalence of a weak
form of the Lehmer conjecture and the "uniform discreteness" of cocompact
lattices in semisimple Lie groups (conjectured by Margulis).\n\nJoint work
with Lam Pham.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Thomas (University of Sydney)
DTSTART:20220204T010000Z
DTEND:20220204T020000Z
DTSTAMP:20260404T111136Z
UID:SiN/34
DESCRIPTION:Title: A gallery model for affine flag varieties via chimney retractions\
nby Anne Thomas (University of Sydney) as part of Symmetry in Newcastle\n\
nLecture held in SR118\, Callaghan Campus.\n\nAbstract\nA gallery model fo
r affine flag varieties via chimney retractions\nWe provide a unified comb
inatorial framework to study orbits in affine flag varieties via the assoc
iated Bruhat-Tits buildings. We first formulate\, for arbitrary affine bui
ldings\, the notion of a chimney retraction. This simultaneously generalis
es the two well-known notions of retractions in affine buildings: retracti
ons from chambers at infinity and retractions from alcoves. We then presen
t a recursive formula for computing the images of certain minimal gallerie
s in the building under chimney retractions\, using purely combinatorial t
ools associated to the underlying affine Weyl group. Finally\, for Bruhat-
Tits buildings\, we relate these retractions and their effect on certain m
inimal galleries to double coset intersections in the corresponding affine
flag variety. This is joint work with Elizabeth Milicevic\, Yusra Naqvi a
nd Petra Schwer.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Bischof (Uni Giesen)
DTSTART:20220204T033000Z
DTEND:20220204T043000Z
DTSTAMP:20260404T111136Z
UID:SiN/35
DESCRIPTION:Title: (Twin) Buildings and groups\nby Sebastian Bischof (Uni Giesen) as
part of Symmetry in Newcastle\n\nLecture held in SR118\, Callaghan Campus.
\n\nAbstract\nBuildings have been introduced by Tits in order to study sem
i-simple algebraic groups from a geometrical point of view. One of the mos
t important results in the theory of buildings is the classification of th
ick irreducible spherical buildings of rank at least 3. In particular\, an
y such building comes from an RGD-system. The decisive tool in this classi
fication is the Extension theorem for spherical buildings\, i.e. a local i
sometry extends to the whole building.\nTwin buildings were introduced by
Ronan and Tits in the late 1980s. Their definition was motivated by the th
eory of Kac-Moody groups over fields. Each such group acts naturally on a
pair of buildings and the action preserves an opposition relation between
the chambers of the two buildings. This opposition relation shares many im
portant properties with the opposition relation on the chambers of a spher
ical building. Thus\, twin buildings appear to be natural generalizations
of spherical buildings with infinite Weyl group. Since the notion of RGD-s
ystems exists not only in the spherical case\, one can ask whether any twi
n building (satisfying some further conditions) comes from an RGD-system.
In 1992 Tits proves several results that are inspired by his strategy in t
he spherical case and he discusses several obstacles for obtaining a simil
ar Extension theorem for twin buildings. In this talk I will speak about t
he history and developments of the Extension theorem for twin buildings.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Ferov (University of Newcastle)
DTSTART:20220304T010000Z
DTEND:20220304T020000Z
DTSTAMP:20260404T111136Z
UID:SiN/36
DESCRIPTION:Title: Automorphism groups of Cayley graphs of Coxeter groups: when are they
discrete?\nby Michal Ferov (University of Newcastle) as part of Symmet
ry in Newcastle\n\nLecture held in SR118\, University Drive\, Callaghan.\n
\nAbstract\nGroup of automorphisms of a connected locally finite graph is
naturally a totally disconnected locally compact topological group\, when
equipped with the permutation topology. It therefore makes sense to ask fo
r which graphs is the topology not discrete. We show that in case of Cayle
y graphs of Coxeter groups\, one can fully characterise the discrete ones
in terms of the symmetries of the corresponding Coxeter system. Joint work
with Federico Berlai.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeroen Schillewaert (The University of Auckland)
DTSTART:20220304T033000Z
DTEND:20220304T043000Z
DTSTAMP:20260404T111136Z
UID:SiN/37
DESCRIPTION:Title: The geometries of the Freudenthal-Tits magic square\nby Jeroen Sch
illewaert (The University of Auckland) as part of Symmetry in Newcastle\n\
nLecture held in SR118\, University Drive\, Callaghan.\n\nAbstract\nI will
give an overview of a programme investigating projective embeddings of (e
xceptional) geometries which Hendrik Van Maldeghem and I started in 2010.\
n
LOCATION:https://stable.researchseminars.org/talk/SiN/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Parkinson (University of Sydney)
DTSTART:20220304T050000Z
DTEND:20220304T060000Z
DTSTAMP:20260404T111136Z
UID:SiN/38
DESCRIPTION:Title: Automorphisms and opposition in spherical buildings.\nby James Par
kinson (University of Sydney) as part of Symmetry in Newcastle\n\nLecture
held in SR118\, University Drive\, Callaghan.\n\nAbstract\nThe geometry of
elements fixed by an automorphism of a spherical building is a rich and w
ell-studied object\, intimately connected to the theory of Galois descent
in buildings. In recent years\, a complementary theory has emerged investi
gating the geometry of elements mapped onto opposite elements by a given a
utomorphism. In this talk we will give an overview of this theory. This wo
rk is joint primarily with Hendrik Van Maldeghem (along with others).\n
LOCATION:https://stable.researchseminars.org/talk/SiN/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Carter (University of Newcastle)
DTSTART:20220401T010000Z
DTEND:20220401T020000Z
DTSTAMP:20260404T111136Z
UID:SiN/39
DESCRIPTION:Title: Unitary representations and the type I property of groups acting on tr
ees\nby Max Carter (University of Newcastle) as part of Symmetry in Ne
wcastle\n\n\nAbstract\nUnitary representations are a classical and useful
tool for studying locally compact groups: motivated in part by quantum mec
hanics\, they have been studied in detail since the early-mid 1900’s wit
h much success\, and they enable group theorists to employ functional anal
ytic techniques in the study of locally compact groups. The algebras that
unitary representations generate play an important role in not only unders
tanding the representation theory of a locally compact group\, but also in
understanding properties pertaining to the group itself. This talk will g
ive a brief introduction to some of the basics of the unitary representati
on theory of locally compact groups\, with focus placed on the associated
operator algebraic structures/properties. In particular\, `type I groups'
and `CCR groups' will be the main focus. As an application\, I will discus
s some current research interests in the unitary representation theory of
groups acting on trees\, including work of myself on the unitary represent
ation theory of `scale groups’.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camila Sehnem (Victoria University of Wellington)
DTSTART:20220401T033000Z
DTEND:20220401T043000Z
DTSTAMP:20260404T111136Z
UID:SiN/40
DESCRIPTION:Title: Equilibrium on Toeplitz extensions of higher dimensional noncommutativ
e tori\nby Camila Sehnem (Victoria University of Wellington) as part o
f Symmetry in Newcastle\n\n\nAbstract\nThe C*-algebra generated by the lef
t-regular representation of $\\mathbb{N}^n$ twisted by a $2$-cocycle is a
Toeplitz extension of an $n$-dimensional noncommutative torus\, on which e
ach vector $r \\in [0\,\\infty)^n$ determines a one-parameter subgroup of
the gauge action. I will report on joint work with Z. Afsar\, J. Ramagge a
nd M. Laca\, in which we show that the equilibrium states of the resulting
C*-dynamical system are parametrised by tracial states of the noncommutat
ive torus corresponding to the restriction of the cocycle to the vanishing
coordinates of $r$. These in turn correspond to probability measures on a
classical torus whose dimension depends on a certain degeneracy index of
the restricted cocycle. Our results generalise the phase transition on the
Toeplitz noncommutative tori used as building blocks in work of Brownlow
e\, Hawkins and Sims\, and of Afsar\, an Huef\, Raeburn and Sims.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roozbeh Hazrat (University of Western Sydney)
DTSTART:20220401T050000Z
DTEND:20220401T060000Z
DTSTAMP:20260404T111136Z
UID:SiN/41
DESCRIPTION:Title: Sandpile models and Leavitt algebras\nby Roozbeh Hazrat (Universit
y of Western Sydney) as part of Symmetry in Newcastle\n\n\nAbstract\nSandp
ile models are about how things spread along a grid (think of Covid!) and
Leavitt algebras are algebras associated to graphs. We relate these two su
bjects!\n
LOCATION:https://stable.researchseminars.org/talk/SiN/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio Bravo (University of Chile)
DTSTART:20220701T000000Z
DTEND:20220701T010000Z
DTSTAMP:20260404T111136Z
UID:SiN/42
DESCRIPTION:Title: Quotients of the Bruhat-Tits tree function filed analogs of the Hecke
congruence subgroups\nby Claudio Bravo (University of Chile) as part o
f Symmetry in Newcastle\n\nLecture held in Lambert Lounge\, US 321.\n\nAbs
tract\nLet C be a smooth\, projective\, and geometrically connected curve
defined over a finite field F. For each closed point P_infty of C\, let R
be the ring of functions that are regular outside P_infty\, and let K be t
he completion path P_infty of the function field of C. In order to study g
roup of the form GL_2(R)\, Serre describes the quotient graph GL_2(R)\\T\,
where T is the Bruhat-Tits tree defined from SL_2(K). In particular\, Ser
re shows that GL_2(R)\\T is the union of a finite graph and a finite numbe
r of ray shaped subgraphs\, which are called cusps. It is not hard to see
that finite index subgroups inherit this property.\nIn this exposition we
describe the quotient graph H\\T defined from the action on T of the group
H consisting of matrices that are upper triangular modulo I\, where I is
an ideal R. More specifically\, we give an explicit formula for the cusp n
umber H\\T. Then By\, using Bass-Serre theory\, we describe the combinator
ial structure of H. These groups play\, in the function field context\, th
e same role as the Hecke Congruence subgroups of SL_2(Z). Moreover\, not t
hat the groups studied by Serre correspond to the case where the ideal I c
oincides with the ring R.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Conder (University of Auckland)
DTSTART:20220701T013000Z
DTEND:20220701T023000Z
DTSTAMP:20260404T111136Z
UID:SiN/43
DESCRIPTION:Title: Discrete two-generator subgroups of PSL(2\,Q_p)\nby Matthew Conder
(University of Auckland) as part of Symmetry in Newcastle\n\nLecture held
in Lambert Lounge\, US 321.\n\nAbstract\nDue to work of Gilman\, Rosenber
ger\, Purzitsky and many others\, discrete two-generator subgroups of PSL(
2\,R) have been completely classified by studying their action by Möbius
transformations on the hyperbolic plane. Here we aim to classify discrete
two-generator subgroups of PSL(2\,Q_p) by studying their action by isometr
ies on the Bruhat-Tits tree. We first give a general structure theorem for
two-generator groups acting by isometries on a tree\, which relies on cer
tain Klein-Maskit combination theorems. We will then discuss how this theo
rem can be applied to determine discreteness of a two-generator subgroup o
f PSL(2\,Q_p). This is ongoing work in collaboration with Jeroen Schillewa
ert.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Willis (University of Newcastle)
DTSTART:20220701T040000Z
DTEND:20220701T050000Z
DTSTAMP:20260404T111136Z
UID:SiN/44
DESCRIPTION:Title: Groups acting on regular trees and t.d.l.c. groups\nby George Will
is (University of Newcastle) as part of Symmetry in Newcastle\n\nLecture h
eld in Lambert Lounge\, US 321.\n\nAbstract\nGroups acting on regular tree
s and t.d.l.c. groups\nAbstract: Groups of automorphisms of regular trees
are an important source of examples of and intuition about totally disconn
ected\, locally compact (t.d.l.c.) groups. Indeed\, Pierre-Emmanuel Capric
e has called them a microcosm the general theory of t.d.l.c. groups. Altho
ugh much is know about them\, many questions remain open.\nThis talk will
survey some of what is known about groups of tree automorphisms and how it
relates to the general theory.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kane Townsend (University of Technology Sydney)
DTSTART:20221007T010000Z
DTEND:20221007T020000Z
DTSTAMP:20260404T111136Z
UID:SiN/45
DESCRIPTION:Title: Hyperbolic groups with $k$-geodetic Cayley graphs\nby Kane Townsen
d (University of Technology Sydney) as part of Symmetry in Newcastle\n\n\n
Abstract\nA locally-finite simple connected graph is said to be $k$-geodet
ic for some $k\\geq1$\, if there is at most $k$ distinct geodesics between
any two vertices of the graph. We investigate the properties of hyperboli
c groups with $k$-geodetic Cayley graphs. To begin\, we show that $k$-geod
etic graphs cannot have a "ladder-like" geodesic structure with unbounded
length. Using this bound\, we generalise a well-known result of Papasoglu
that states hyperbolic groups with $1$-geodetic Cayley graphs are virtuall
y-free. We then investigate which elements of the hyperbolic group with $k
$-geodetic Cayley graph commute with a given infinite order element.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Freden (Southern Utah University)
DTSTART:20221007T033000Z
DTEND:20221007T043000Z
DTSTAMP:20260404T111136Z
UID:SiN/46
DESCRIPTION:Title: Aspects of growth in Baumslag-Solitar groups\nby Eric Freden (Sout
hern Utah University) as part of Symmetry in Newcastle\n\n\nAbstract\nIn 1
997\, Grigorchuk and de la Harpe suggested computing the growth series for
the Baumslag-Solitar group BS(2\,3). After 25 years\, this is still an op
en problem. In fact\, the growth of only the solvable groups BS(1\,n) and
automatic groups BS(n\,n) are known. In this talk I will review what has s
ince been discovered about these remarkable groups and conclude with new u
npublished results concerning the exponents of growth for the subfamily BS
(2\,2n).\n
LOCATION:https://stable.researchseminars.org/talk/SiN/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volker Diekert (Universität Stuttgart)
DTSTART:20221007T050000Z
DTEND:20221007T060000Z
DTSTAMP:20260404T111136Z
UID:SiN/47
DESCRIPTION:Title: Decidability of membership problems for $2\\times 2$ matrices over $\\
mathbb{Q}$\nby Volker Diekert (Universität Stuttgart) as part of Symm
etry in Newcastle\n\n\nAbstract\nMy talk is based on a joint work with Igo
r Potapov and Pavel Semukhin (Liverpool\, UK).\nWe consider membership pro
blems in matrix semigroups. Using symbolic algorithms on words and finite
automata\, we prove various new decidability results for $2\\times 2$ matr
ices over $\\mathbb{Q}$.\nFor that\, we introduce the concept of flat rati
onal sets: if $M$ is a monoid and $N$ is\na submonoid\, then \\emph{flat r
ational sets of $M$ over $N$} are finite unions of the form $L_0g_1L_1 \\c
dots g_t L_t$ where all $L_i$'s are rational subsets of $N$ and $g_i\\in M
$. We give quite general sufficient conditions under which flat rational s
ets form an effective relative Boolean algebra. As a corollary\, we obtain
that the emptiness problem for Boolean combinations of flat rational subs
ets of $\\mathrm{GL}(2\,\\mathbb{Q})$ over $\\mathrm{GL}(2\,\\mathbb{Z})$
is decidable (in singly exponential time). It is possible that such a stro
ng decidability result cannot be pushed any further for groups sitting bet
ween\n$\\mathrm{GL}(2\,\\mathbb{Z})$ and $\\mathrm{GL}(2\,\\mathbb{Q})$.\n
\nWe also show a dichotomy for nontrivial group extension of $\\mathrm{GL}
(2\,\\mathbb{Z})$ in $\\mathrm{GL}(2\,\\mathbb{Q})$: if $G$ is a f.g.~grou
p such that $\\mathrm{GL}(2\,\\mathbb{Z}) < G \\leq \\mathrm{GL}(2\,\\math
bb{Q})$\, then either $G\\cong \\mathrm{GL}(2\,\\mathbb{Z})\\times \\mathb
b{Z}^k$\, for\nsome $k\\geq 1$\, or $G$ contains an extension of the Baums
lag-Solitar group $\\mathop\\mathrm{BS}(1\,q)$\, with $q\\geq\n2$\, of inf
inite index. In the first case of the dichotomy the membership problem for
$G$ is\ndecidable but the equality problem for rational subsets of $G$ is
undecidable. In the second case\,\ndecidability of the membership problem
for rational subsets in $G$ is open.\n\nOur improves various natural dec
idability results for $2 \\times 2$ matrices with rational entries\, and i
t also\nsupports them with concrete complexity bounds for the first time.\
n
LOCATION:https://stable.researchseminars.org/talk/SiN/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Hulpke (Colorado State University)
DTSTART:20221104T030000Z
DTEND:20221104T040000Z
DTSTAMP:20260404T111136Z
UID:SiN/48
DESCRIPTION:Title: Constructing Perfect Groups\nby Alexander Hulpke (Colorado State U
niversity) as part of Symmetry in Newcastle\n\n\nAbstract\nThe constructio
n of perfect groups of a given order can be considered as the prototype of
construction of nonsolvable groups of a given order.\nI will describe a r
ecent project to enumerate\, up to isomorphism\, the perfect groups of ord
er up to 2*10^6. It crucially relies on new tools for calculating cohmolog
y\, as well as improved implementations for isomorphism test.\n\nThis work
extends results of Holt and Plesken from 1989 and illustrates the scope o
f algorithmic improvements over the past decades.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Conder (University of Auckland)
DTSTART:20221124T230000Z
DTEND:20221125T000000Z
DTSTAMP:20260404T111136Z
UID:SiN/49
DESCRIPTION:Title: Two-generator subgroups of SL2 over local fields\nby Matthew Conde
r (University of Auckland) as part of Symmetry in Newcastle\n\n\nAbstract\
nIn this talk\, we will give an overview of some results and open problems
relating to two-generator subgroups of SL2 over a local field K. We first
consider the archimedean setting\, where certain discrete and/or free two
-generator subgroups of SL(2\,R) and SL(2\,C) can be identified by investi
gating their respective actions by Möbius transformations on the upper ha
lf plane and Riemann sphere. We then outline some recent results in the no
n-archimedean setting\, obtained by studying the analogous action of SL(2\
,K) by isometries on the corresponding Bruhat-Tits tree. Finally\, we disc
uss an application of this work to the problem of deciding whether a two-g
enerator subgroup of SL(2\,K) is dense.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armin Weiß (Universität Stuttgart)
DTSTART:20230125T040000Z
DTEND:20230125T050000Z
DTSTAMP:20260404T111136Z
UID:SiN/50
DESCRIPTION:Title: An Automaton Group with PSPACE-Complete Word Problem\nby Armin Wei
ß (Universität Stuttgart) as part of Symmetry in Newcastle\n\n\nAbstract
\nFinite automata pose an interesting alternative way to present groups an
d \nsemigroups. Some of these automaton groups became famous for their pec
uliar \nproperties and have been extensively studied. \n\nOne aspect of th
is research is the study of algorithmic properties of \nautomaton groups a
nd semigroups. While many natural algorithmic decision \nproblems have bee
n proven or are generally suspected to be undecidable for \nthese classes\
, the word problem forms a notable exception. In the group case\, \nit ask
s whether a given word in the generators is equal to the neutral element \
nin the group in question and is well-known to be decidable for automaton
\ngroups. In fact\, it was observed in a work by Steinberg published in 20
15 that \nit can be solved in nondeterministic linear space using a straig
ht-forward \nguess and check algorithm. In the same work\, he conjectured
that there is an \nautomaton group with a PSPACE-complete word problem.\n\
nIn a recent paper presented at STACS 2020\, Jan Philipp Wächter and myse
lf could\nprove that there indeed is such an automaton group. To achieve t
his\, we combined\ntwo ideas. The first one is a construction introduced b
y D'Angeli\, Rodaro and\nWächter to show that there is an inverse automat
on semigroup with a \nPSPACE-complete word problem and the second one is a
n idea already used \nby Barrington in 1989 to encode NC¹ circuits in the
group of even permutation \nover five elements. In the talk\, we will dis
cuss how Barrington's idea can be \napplied in the context of automaton gr
oups\, which will allow us to prove that \nthe uniform word problem for au
tomaton groups (were the generating automaton \nand\, thus\, the group is
part of the input) is PSPACE- complete. Afterwards\, we \nwill also discus
s the ideas underlying the construction to simulate a PSPACE-\nmachine wit
h an invertible automaton\, which allow for extending the result to \nthe
non-uniform case. Finally\, we will briefly look at related problems such
\nas the compressed word problem for automaton groups and the special case
of\nautomaton group of polynomial activity.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Brownlowe (University of Sydney)
DTSTART:20230217T000000Z
DTEND:20230217T010000Z
DTSTAMP:20260404T111136Z
UID:SiN/51
DESCRIPTION:Title: C*-algebraic approaches to self-similarity\nby Nathan Brownlowe (U
niversity of Sydney) as part of Symmetry in Newcastle\n\n\nAbstract\nIn th
is talk I will go through the basics of self-similar actions and some of t
heir generalisations. I will then introduce C*-algebras\, before surveying
the literature on how we build C*-algebras to model self-similarity.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Robertson (University of New England)
DTSTART:20230217T023000Z
DTEND:20230217T033000Z
DTSTAMP:20260404T111136Z
UID:SiN/52
DESCRIPTION:Title: Self-similar quantum groups\nby David Robertson (University of New
England) as part of Symmetry in Newcastle\n\n\nAbstract\nQuantum automorp
hism groups originated in the work of Wang in the mid 90s as an answer to
question of Connes: what are the quantum automorphisms of a space? Wang sh
owed that for a finite set with at least 4 points there are an infinite nu
mber of quantum permutations. Since then\, work on quantum automorphism gr
oups has progressed in many different directions\, including the construct
ion of the quantum automorphism group of a finite graph by Bichon in 2004
and quantum automorphisms of locally finite graphs by Rollier and Vaes in
2022. In a recent preprint with Nathan Brownlowe\, we have shown that the
quantum automorphism group of a homogeneous rooted tree is a compact qua
ntum group\, and defined when a quantum subgroup is self-similar. In this
talk I will give an overview of this construction\, and construct a numbe
r of examples through an analogue of the notion of a finitely constrained
self-similar group defined by Sunic in 2011.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aidan Sims (University of Wollongong)
DTSTART:20230217T040000Z
DTEND:20230217T050000Z
DTSTAMP:20260404T111136Z
UID:SiN/53
DESCRIPTION:Title: K-theoretic duality for self-similar groupoids\nby Aidan Sims (Uni
versity of Wollongong) as part of Symmetry in Newcastle\n\n\nAbstract\nA K
-theoretic duality for C*-algebras is\, roughly speaking\, a particularly
nice isomorphism of the K-theory groups of each with the K-homology groups
of the other. They are generalisations of Poincare duality for manifolds\
, and in that vein\, they often help to compute algebraic or analytic K-th
eory invariants in terms of more-tractable topological information. Under
some technical hypotheses\, Nekrashevych established a K-theoretic duality
between the C*-algebra of a self-similar group and a related C*-algebra a
ssociated to a limit space that resembles the way that real numbers are re
presented by decimal expansions. I will discuss how Nekrashevych’s limit
space is constructed\, focussing on elementary but instructive examples t
o keep things concrete\, and sketch out how to use it to describe a K-theo
retic duality that helps in computing K-theory for self-similar groupoid C
*-algebras. I won’t assume any background in any of this stuff. This is
joint work with Brownlowe\, Buss\, Goncalves\, Hume and Whittaker.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wibmer (TU Graz)
DTSTART:20230525T060000Z
DTEND:20230525T070000Z
DTSTAMP:20260404T111136Z
UID:SiN/54
DESCRIPTION:Title: Difference algebraic groups\nby Michael Wibmer (TU Graz) as part o
f Symmetry in Newcastle\n\n\nAbstract\nDifference algebraic groups are a g
eneralization of algebraic groups. Instead of just algebraic equations\, o
ne allows difference algebraic equations as the defining equations. Here o
ne can think of a difference equation as a discrete version of a different
ial equation. Besides their intrinsic beauty\, one of the main motivations
for studying difference algebraic groups is that they occur as Galois gro
ups in certain Galois theories.\n\nThis talk will be an introduction to di
fference algebraic groups.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wibmer (TU Graz)
DTSTART:20230525T073000Z
DTEND:20230525T083000Z
DTSTAMP:20260404T111136Z
UID:SiN/55
DESCRIPTION:Title: Expansive endomorphisms of profinite groups\nby Michael Wibmer (TU
Graz) as part of Symmetry in Newcastle\n\n\nAbstract\nÉtale algebraic gr
oups over a field k are equivalent to finite groups with a continuous acti
on of the absolute Galois group of k. The difference version of this well-
know result asserts that étale difference algebraic groups over a differe
nce field k (i.e.\, a field equipped with an endomorphism) are equivalent
to profinite groups equipped with an expansive endomorphism and a certain
compatible difference Galois action. In any case\, understanding the struc
ture of expansive endomorphisms of profinite groups seems a worthwhile end
eavor and that's what this talk is about.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dilshan Wijesena (University of New South Wales)
DTSTART:20230809T040000Z
DTEND:20230809T050000Z
DTSTAMP:20260404T111136Z
UID:SiN/56
DESCRIPTION:Title: Irreducible Pythagorean representations of Thompson’s groups\nby
Dilshan Wijesena (University of New South Wales) as part of Symmetry in N
ewcastle\n\n\nAbstract\nRichard Thompson’s groups $F$\, $T$ and $V$ are
one of the most fascinating discrete infinite groups for their several unu
sual properties and their analytical properties have been challenging expe
rts for many decades. One reason for this is because very little is known
about its representation theory. Luckily\, thanks to the novel technology
of Jones\, a rich family of so-called Pythagorean unitary representation o
f Thompson’s groups can be constructed by simply specifying a pair of fi
nite-dimensional operators satisfying a certain equality. These representa
tions can even be extended to the celebrated Cuntz algebra and carry a pow
erful diagrammatic calculus which we use to develop techniques to study th
eir properties. This permits to reduce very difficult questions concerning
irreducibility and equivalence of infinite-dimensional representations in
to problems in finite-dimensional linear algebra. This provides a new rich
class of irreducible representations of $F$. Moreover\, we introduce the
Pythagorean dimension which is a new invariant for all representations of
the Cuntz algebra and Pythagorean representations of $F\,T\,V$. For each d
imension $d$\, we show the irreducible classes form a moduli space of a re
al manifold of dimension $2d^2+1$.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Incerti-Medici (Universität Wien)
DTSTART:20240125T070000Z
DTEND:20240125T080000Z
DTSTAMP:20260404T111136Z
UID:SiN/57
DESCRIPTION:Title: Automorphism groups of cocompact CAT(0) cube complexes\nby Merlin
Incerti-Medici (Universität Wien) as part of Symmetry in Newcastle\n\n\nA
bstract\nGiven a cocompact CAT(0) cube complex\, we study the group of its
cubical isometries\, which frequently forms a non-discrete tdlc group. We
present a method to study these groups that is focused on our ability to
understand the stabilizer subgroups. We demonstrate the potency of this me
thod by introducing a finite\, topologically generating set and discuss an
important simple subgroup. If there is time\, we discuss some open questi
ons regarding the placement of these groups among non-discrete tdlc groups
.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Glasby (University of Western Australia)
DTSTART:20240320T010000Z
DTEND:20240320T020000Z
DTSTAMP:20260404T111136Z
UID:SiN/58
DESCRIPTION:Title: Classifying groups with three automorphism orbits\nby Stephen Glas
by (University of Western Australia) as part of Symmetry in Newcastle\n\nL
ecture held in VG10.\n\nAbstract\nWe call a group $G$ a $k$-orbit group i
f its automorphism group $Aut(G)$ acting naturally on $G$ has \nprecisely
$k$ orbits. I will describe the classification of finite 3-orbit groups af
ter surveying\nwork to classify $k$-orbit groups for small $k$ when $G$ is
finite or infinite. The finite 3-orbit groups that are not $p$-groups are
easy to classify. Apart from $Q_8$\, the finite non-abelian 3-orbit 2-gro
ups are a subset of the Suzuki 2-groups which Graham Higman [2] classified
in 1963. Determining which subset turns out to be far from easy as the au
tomorphism groups of Suzuki 2-groups are mysterious.\nAlex Bors and I clas
sified the finite 3-orbit 2-groups in [1]. In 2024 Li and Zhu [3]\, unawar
e of our work\nand using different methods\, classified the finite groups
$G$ where $Aut(G)$ is transitive on elements of order $p$. Their groups in
clude the 3-orbit Suzuki 2-groups\, the homocyclic groups $C_{p^n}^m$ of e
xponent $p^2$ and the generalised quaternion group $Q_{2^{n+1}}$.\n\nI was
able to classify all finite 3-orbit groups (including $p>2$) using Hering
's Theorem and some representation theory. However\, to my surprise Li and
Zhu [4] in March 2024 did the same.\n\n[1] Alexander Bors and S.P. Glasby
\,\nFinite 2-groups with exactly three automorphism orbits\, https://arxiv
.org/abs/2011.13016v1 (2020).\n\n[2] G. Higman\, Suzuki 2-groups\, Illinoi
s J.~Math. 7 (1963)\, 79--96.\n\n[3] Cai Heng Li and Yan Zhou Zhu\, A Proo
f of Gross' Conjecture on 2-Automorphic 2-Groups\,\nhttps://arxiv.org/abs/
2312.16416 (2024).\n\n[4] Cai Heng Li and Yan Zhou Zhu\,\nThe finite group
s with three automorphism orbits\, https://arxiv.org/abs/2403.01725 (2024)
.\n
LOCATION:https://stable.researchseminars.org/talk/SiN/58/
END:VEVENT
END:VCALENDAR