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BEGIN:VEVENT
SUMMARY:Federico Berlai (University of the Basque Country)
DTSTART;VALUE=DATE-TIME:20200605T050000Z
DTEND;VALUE=DATE-TIME:20200605T060000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/1
DESCRIPTION:Title: From
hyperbolicity to hierarchical hyperbolicity\nby Federico Berlai (Univ
ersity of the Basque Country) as part of Symmetry in Newcastle\n\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/SiN/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Hagen (University of Bristol)
DTSTART;VALUE=DATE-TIME:20200605T063000Z
DTEND;VALUE=DATE-TIME:20200605T073000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/2
DESCRIPTION:Title: Hier
archical hyperbolicity from actions on simplicial complexes\nby Mark H
agen (University of Bristol) as part of Symmetry in Newcastle\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/SiN/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Verret (The University of Auckland\, New Zealand)
DTSTART;VALUE=DATE-TIME:20200918T050000Z
DTEND;VALUE=DATE-TIME:20200918T060000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/3
DESCRIPTION:Title: Loca
l actions in vertex-transitive graphs\nby Gabriel Verret (The Universi
ty of Auckland\, New Zealand) as part of Symmetry in Newcastle\n\n\nAbstra
ct\nA graph is vertex-transitive if its group of automorphism acts transit
ively on its vertices. A very important concept in the study of these grap
hs is that of local action\, that is\, the permutation group induced by a
vertex-stabiliser on the corresponding neighbourhood. I will explain some
of its importance and discuss some attempts to generalise it to the case o
f directed graphs.\n
LOCATION:https://researchseminars.org/talk/SiN/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Giudici (The University of Western Australia\, Australia)
DTSTART;VALUE=DATE-TIME:20200918T063000Z
DTEND;VALUE=DATE-TIME:20200918T073000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/4
DESCRIPTION:Title: The
synchronisation hierarchy for permutation groups\nby Michael Giudici (
The University of Western Australia\, Australia) as part of Symmetry in Ne
wcastle\n\n\nAbstract\nThe concept of a synchronising permutation group wa
s introduced nearly 15 years ago as a possible way of approaching The \\v{
C}ern\\'y Conjecture. Such groups must be primitive. In an attempt to unde
rstand synchronising groups\, a whole hierarchy of properties for a permut
ation group has been developed\, namely\, 2-transitive groups\, $\\mathbb{
Q}$I-groups\, spreading\, separating\, synchronising\, almost synchronisin
g and primitive. Many surprising connections with other areas of mathemat
ics 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 over
view of the hierarchy and discuss what is known about which groups lie whe
re.\n
LOCATION:https://researchseminars.org/talk/SiN/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandra Garrido (Universidad Autónoma de Madrid)
DTSTART;VALUE=DATE-TIME:20201002T060000Z
DTEND;VALUE=DATE-TIME:20201002T070000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/5
DESCRIPTION:Title: When
is a piecewise (a.k.a topological) full group locally compact?\nby Al
ejandra Garrido (Universidad Autónoma de Madrid) as part of Symmetry in N
ewcastle\n\n\nAbstract\nQuestion: When is a piecewise (a.k.a topological)
full group locally compact? \n\nAnswer: Only when it's an ample group in t
he sense of Krieger (in particular\, discrete\, countable and locally fini
te) and has a Bratteli diagram satisfying certain conditions. \n\nComplain
t: Wait\, isn't Neretin's group a non-discrete\, locally compact\, topolog
ical full group? \n\nRetort: It is\, but you need to use the correct topol
ogy!\n\nA fleshed-out version of the above conversation will be given in t
he talk. Based on joint work with Colin Reid.\n
LOCATION:https://researchseminars.org/talk/SiN/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feyisayo Olukoya (University of Aberdeen)
DTSTART;VALUE=DATE-TIME:20201002T073000Z
DTEND;VALUE=DATE-TIME:20201002T083000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/6
DESCRIPTION:Title: The
group of automorphisms of the shift dynamical system and the Higman-Thomps
on groups\nby Feyisayo Olukoya (University of Aberdeen) as part of Sym
metry in Newcastle\n\n\nAbstract\nWe give a survey of recent results explo
ring connections between the Higman-Thompson groups and their automorphism
groups and the group of automorphisms of the shift dynamical system. Our
survey takes us from dynamical systems to group theory via groups of homeo
morphisms with a segue through combinatorics\, in particular\, de Bruijn g
raphs.\n\nJoint work with Collin Bleak and Peter Cameron.\n
LOCATION:https://researchseminars.org/talk/SiN/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Skipper (Ohio State University)
DTSTART;VALUE=DATE-TIME:20201015T230000Z
DTEND;VALUE=DATE-TIME:20201016T000000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/7
DESCRIPTION:Title: Maxi
mal Subgroups of Thompson's group V\nby Rachel Skipper (Ohio State Uni
versity) 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 Tho
mpson family. One way to get at results of this form is to classify maxima
l subgroups. In this talk\, we will define certain labelings of binary tre
es and use them to produce a large family of new maximal subgroups of Thom
pson'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\, and Marty
n Quick at the University of Saint Andrews.\n
LOCATION:https://researchseminars.org/talk/SiN/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawrence Reeves (The University of Melbourne)
DTSTART;VALUE=DATE-TIME:20201016T003000Z
DTEND;VALUE=DATE-TIME:20201016T013000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/8
DESCRIPTION:Title: Irra
tional-slope versions of Thompson’s groups T and V\nby Lawrence Reev
es (The University of Melbourne) as part of Symmetry in Newcastle\n\n\nAbs
tract\nWe consider irrational slope versions of T and V\, We give infinite
presentations for these groups and show how they can be represented by tr
ee-pair diagrams. We also show that they have index-2 normal subgroups tha
t are simple. \nThis is joint work with Brita Nucinkis and Pep Burillo.\n
LOCATION:https://researchseminars.org/talk/SiN/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Bradford (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20201109T090000Z
DTEND;VALUE=DATE-TIME:20201109T100000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/9
DESCRIPTION:Title: Quan
titative LEF and topological full groups\nby Henry Bradford (Universit
y of Cambridge) as part of Symmetry in Newcastle\n\n\nAbstract\nTopologica
l full groups of minimal subshifts are an important source of exotic examp
les in geometric group theory\, as well as being powerful invariants of sy
mbolic dynamical systems. In 2011\, Grigorchuk and Medynets proved that TF
Gs are LEF\, that is\, every finite subset of the multiplication table occ
urs in the multiplication table of some finite group. In this talk we expl
ore some ways in which asymptotic properties of the finite groups which oc
cur reflect asymptotic properties of the associated subshift. Joint work w
ith Daniele Dona.\n
LOCATION:https://researchseminars.org/talk/SiN/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Hautekiet (Université libre de Bruxelles\, Belgium)
DTSTART;VALUE=DATE-TIME:20201123T073000Z
DTEND;VALUE=DATE-TIME:20201123T083000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/10
DESCRIPTION:Title: Aut
omorphism groups of transcendental field extensions\nby William Hautek
iet (Université libre de Bruxelles\, Belgium) as part of Symmetry in Newc
astle\n\n\nAbstract\nIt is well-known that the Galois group of an (infinit
e) algebraic field extension is a profinite group. When the extension is t
ranscendental\, the automorphism group is no longer compact\, but has a to
tally disconnected locally compact structure (TDLC for short). The study o
f TDLC groups was initiated by van Dantzig in 1936 and then restarted by W
illis in 1994. In this talk some of Willis' concepts\, such as tidy subgro
ups\, the scale function\, flat subgroups and directions are introduced an
d applied to examples of automorphism groups of transcendental field exten
sions. It remains unknown whether there exist conditions that a TDLC group
must satisfy to be a Galois group. A suggestion of such a condition is ma
de.\n
LOCATION:https://researchseminars.org/talk/SiN/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Breuer (University of Newcastle\, Australia)
DTSTART;VALUE=DATE-TIME:20201123T090000Z
DTEND;VALUE=DATE-TIME:20201123T100000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/11
DESCRIPTION:Title: Rea
lising general linear groups as Galois groups\nby Florian Breuer (Univ
ersity of Newcastle\, Australia) as part of Symmetry in Newcastle\n\n\nAbs
tract\nI will show how to construct field extensions with Galois groups is
omorphic to general linear groups (with entries in various rings and field
s) from the torsion of elliptic curves and Drinfeld modules. No prior know
ledge of these structures is assumed.\n
LOCATION:https://researchseminars.org/talk/SiN/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:François Le Maître (Université de Paris)
DTSTART;VALUE=DATE-TIME:20210125T073000Z
DTEND;VALUE=DATE-TIME:20210125T083000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/12
DESCRIPTION:Title: Den
se totipotent free subgroups of full groups\nby François Le Maître (
Université de Paris) as part of Symmetry in Newcastle\n\n\nAbstract\nIn t
his talk\, we will be interested in measure-preserving actions of countabl
e groups on standard probability spaces\, and more precisely in the partit
ions of the space into orbits that they induce\, also called measure-prese
rving equivalence relations. In 2000\, Gaboriau obtained a characterizatio
n of the ergodic equivalence relations which come from non-free actions of
the free group on $n > 1$ generators: these are exactly the equivalence r
elations of cost less than n. A natural question is: how non-free can thes
e actions be made\, and what does the action on each orbit look like? We w
ill obtain a satisfactory answer by showing that the action on each orbit
can be made totipotent\, which roughly means "as rich as possible"\, and f
urthermore that the free group can be made dense in the ambient full group
of the equivalence relation.\n\nThis is joint work with Alessandro Carder
i and Damien Gaboriau.\n
LOCATION:https://researchseminars.org/talk/SiN/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Cox (University of Bristol)
DTSTART;VALUE=DATE-TIME:20210125T090000Z
DTEND;VALUE=DATE-TIME:20210125T100000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/13
DESCRIPTION:Title: Spr
ead and infinite groups\nby Charles Cox (University of Bristol) as par
t of Symmetry in Newcastle\n\n\nAbstract\nMy recent work has involved taki
ng questions asked for finite groups and considering them for infinite gro
ups. There are various natural directions with this. In finite group theor
y\, there exist many beautiful results regarding generation properties. On
e such notion is that of spread\, and Scott Harper and Casey Donoven have
raised several intriguing questions for spread for infinite groups (in htt
ps://arxiv.org/abs/1907.05498). A group $G$ has spread $k$ if for every $g
_1\, \\dots\, g_k \\in G$ we can find an $h \\in G$ such that $\\langle g_
i\, h \\rangle = G$. For any group we can say that if it has a proper quot
ient 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 t
his condition on proper quotients is not just a necessary condition for po
sitive spread\, but is also a sufficient one. Harper-Donoven’s first que
stion is therefore: is this the case for infinite groups? Well\, no. But t
hat’s for the trivial reason that we have infinite simple groups that ar
e not 2-generated (and they point out that 3-generated examples are also k
nown). But if we restrict ourselves to 2-generated groups\, what happens?
In this talk we’ll see the answer to this question. The arguments will b
e 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 p
roper quotient cyclic but that has spread zero.\n
LOCATION:https://researchseminars.org/talk/SiN/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Henry-Leemann (University of Neuchatel)
DTSTART;VALUE=DATE-TIME:20210222T073000Z
DTEND;VALUE=DATE-TIME:20210222T083000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/14
DESCRIPTION:Title: Cay
ley graphs with few automorphisms\nby Paul Henry-Leemann (University o
f Neuchatel) as part of Symmetry in Newcastle\n\n\nAbstract\nLet G be a gr
oup 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 i
f there exists an S such that the only automorphisms of Cay(G\,S) are the
ones coming from the action of G.\nWhile the classification of finite rigi
d groups was achieved in 1981\, few results were known about infinite grou
ps. In a recent work\, with M. de la Salle we gave a complete classificati
on of infinite finitely generated rigid groups. As a consequence\, we also
obtain that every finitely generated group admits a Cayley graph with cou
ntable automorphism group.\n
LOCATION:https://researchseminars.org/talk/SiN/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giles Gardam (WWU Muenster)
DTSTART;VALUE=DATE-TIME:20210222T090000Z
DTEND;VALUE=DATE-TIME:20210222T100000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/15
DESCRIPTION:Title: Kap
lansky's conjectures\nby Giles Gardam (WWU Muenster) as part of Symmet
ry in Newcastle\n\n\nAbstract\nKaplansky made various related conjectures
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 torsion-
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 eac
h other and to other group properties such as orderability\, and present s
ome recent progress.\n
LOCATION:https://researchseminars.org/talk/SiN/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoe Chatzidakis (CNRS - ENS)
DTSTART;VALUE=DATE-TIME:20210419T063000Z
DTEND;VALUE=DATE-TIME:20210419T073000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/16
DESCRIPTION:Title: A n
ew invariant for difference fields\nby Zoe Chatzidakis (CNRS - ENS) as
part of Symmetry in Newcastle\n\n\nAbstract\nIf $(K\,f)$ is a difference
field\, and a is a finite tuple in some difference field extending $K$\, a
nd such that $f(a)$ in $K(a)^{alg}$\, then we define $dd(a/K)=\\mathop{lim
}[K(f^k(a)\,a):K(a)]^{1/k}$\, the distant degree of $a$ over $K$. This is
an invariant of the difference field extension $K(a)^{alg}/K$. We show tha
t there is some $b$ in the difference field generated by $a$ over $K$\, wh
ich 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 c
onnected to results of Goerge Willis on scales of automorphisms of locally
compact totally disconnected groups. I will explicit the correspondence b
etween the two sets of results.\n(Joint with E. Hrushovski)\n
LOCATION:https://researchseminars.org/talk/SiN/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Ciobanu (Herriot Watt)
DTSTART;VALUE=DATE-TIME:20210419T080000Z
DTEND;VALUE=DATE-TIME:20210419T090000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/17
DESCRIPTION:Title: Fre
e group homomorphisms and the Post Correspondence Problem\nby Laura Ci
obanu (Herriot Watt) as part of Symmetry in Newcastle\n\n\nAbstract\nThe P
ost Correspondence Problem (PCP) is a classical problem in computer scienc
e that can be stated as: is it decidable whether given two morphisms $g$ a
nd $h$ between two free semigroups $A$ and $B$\, there is any nontrivial $
x$ in $A$ such that $g(x)=h(x)$? This question can be phrased in terms of
equalisers\, asked in the context of free groups\, and expanded: if the `e
qualiser' of $g$ and $h$ is defined to be the subgroup consisting of all $
x$ where $g(x)=h(x)$\, it is natural to wonder not only whether the equali
ser 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 undecidability i
n many areas of computer science\, the PCP for free groups is open\, as ar
e the related questions about rank\, basis\, or further generalisations. H
owever\, in this talk we will show that there are links and surprising equ
ivalences between these problems in free groups\, and classes of maps for
which we can give complete answers. This is joint work with Alan Logan.\n
LOCATION:https://researchseminars.org/talk/SiN/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yago Antolin (Universidad Complutense de Madrid)
DTSTART;VALUE=DATE-TIME:20210510T063000Z
DTEND;VALUE=DATE-TIME:20210510T073000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/18
DESCRIPTION:Title: Geo
metry and Complexity of positive cones in groups.\nby Yago Antolin (Un
iversidad Complutense de Madrid) as part of Symmetry in Newcastle\n\n\nAbs
tract\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. Positiv
e cones codify naturally $G$-left-invariant total orders on $G$. When $G$
is a finitely generated group\, we will discuss whether or not a positive
cone can be described by a regular language over the generators and how th
e ambient geometry of $G$ influences the geometry of a positive cone.\n\nT
his will be based on joint works with Juan Alonso\, Joaquin Brum\, Cristob
al Rivas and Hang Lu Su.\n
LOCATION:https://researchseminars.org/talk/SiN/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Kropholler (Universität Münster)
DTSTART;VALUE=DATE-TIME:20210510T080000Z
DTEND;VALUE=DATE-TIME:20210510T090000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/19
DESCRIPTION:Title: Gro
ups of type FP_2 over fields but not over the integers\nby Robert Krop
holler (Universität Münster) as part of Symmetry in Newcastle\n\n\nAbstr
act\nBeing of type $\\mathop{FP}_2$ is an algebraic shadow of being finite
ly presented. A long standing question was whether these two classes are e
quivalent. This was shown to be false in the work of Bestvina and Brady. M
ore recently\, there are many new examples of groups of type $\\mathop{FP}
_2$ coming with various interesting properties. I will begin with an intro
duction 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://researchseminars.org/talk/SiN/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Libor Barto (Charles University in Prague)
DTSTART;VALUE=DATE-TIME:20210524T063000Z
DTEND;VALUE=DATE-TIME:20210524T073000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/20
DESCRIPTION:Title: CSP
s and Symmetries\nby Libor Barto (Charles University in Prague) as par
t of Symmetry in Newcastle\n\n\nAbstract\nHow difficult is to solve a give
n computational problem? In a large class of computational problems\, incl
uding the fixed-template Constraint Satisfaction Problems (CSPs)\, this fu
ndamental question has a simple and beautiful answer: the more symmetrical
the problem is\, the easier is to solve it. The tight connection between
the complexity of a CSP and a certain concept that captures its symmetry h
as fueled much of the progress in the area in the last 20 years. I will ta
lk about this connection and some of the many tools that have been used to
analyze the symmetries. The tools involve rather diverse areas of mathema
tics including algebra\, analysis\, combinatorics\, logic\, probability\,
and topology.\n
LOCATION:https://researchseminars.org/talk/SiN/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoe Chatzidakis (CNRS - ENS)
DTSTART;VALUE=DATE-TIME:20210524T080000Z
DTEND;VALUE=DATE-TIME:20210524T090000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/21
DESCRIPTION:Title: A n
ew invariant for difference fields\nby Zoe Chatzidakis (CNRS - ENS) as
part of Symmetry in Newcastle\n\n\nAbstract\nIf $(K\,f)$ is a difference
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 $dd(a/K)=\\lim[K(f^
k(a)\,a):K(a)]^{1/k}$\, the distant degree of $a$ over $K$. This is an inv
ariant of the difference field extension $K(a)^{alg}/K$. We show that ther
e 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\nViewing $\\math
op{Aut}(K(a)^{alg}/K)$ as a locally compact group\, this result is connect
ed to results of Goerge Willis on scales of automorphisms of locally compa
ct totally disconnected groups. I will explicit the correspondence between
the two sets of results.\n(Joint with E. Hrushovski)\n
LOCATION:https://researchseminars.org/talk/SiN/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Waldemar Hołubowski (Silesian University of Technology)
DTSTART;VALUE=DATE-TIME:20210607T063000Z
DTEND;VALUE=DATE-TIME:20210607T073000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/22
DESCRIPTION:Title: Nor
mal subgroups in the group of column-finite infinite matrices\nby Wald
emar Hołubowski (Silesian University of Technology) as part of Symmetry i
n Newcastle\n\n\nAbstract\nThe classical result\, due to Jordan\, Burnside
\, 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 $GL(V)$\, where $V
$ is a vector space of any infinite cardinality dimension over a division
ring. However\, when he considers subgroups of the direct product of the c
enter and the group of linear transformations $g$ such that $g-id_V$ has f
inite dimensional range the proof is not complete. We fill this gap for co
untably dimensional $V$ giving description of the lattice of normal subgro
ups in the group of infinite column-finite matrices indexed by positive in
tegers over any field. Similar results for Lie algebras of matrices will b
e surveyed.\n\nThe talks is based on results presented in https://arxiv.or
g/abs/1808.06873 and https://arxiv.org/abs/1806.01099.\n\n(joint work with
Martyna Maciaszczyk and Sebastian Zurek.)\n
LOCATION:https://researchseminars.org/talk/SiN/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yves Stadler (Université Clermont Auvergne)
DTSTART;VALUE=DATE-TIME:20210621T063000Z
DTEND;VALUE=DATE-TIME:20210621T073000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/23
DESCRIPTION:Title: Hig
hly transitive groups among groups acting on trees\nby Yves Stadler (U
niversité Clermont Auvergne) as part of Symmetry in Newcastle\n\n\nAbstra
ct\nHighly transitive groups\, i.e. groups admitting an embedding in Sym(N
) with dense image\, form a wide class of groups. For instance\, M. Hull a
nd D. Osin proved that it contains all countable acylindrically hyperbolic
groups with trivial finite radical. After an introduction to high transit
iviy\, I will present a theorem (from joint work with P. Fima\, F. Le Maî
tre and S. Moon) showing that many groups acting on trees are highly trans
itive. On the one hand\, this theorem gives new examples of highly transit
ive groups. On the other hand\, it is sharp because of results by A. Le Bo
udec and N. Matte Bon.\n
LOCATION:https://researchseminars.org/talk/SiN/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Castellano (University of Milan - Bicoca)
DTSTART;VALUE=DATE-TIME:20210621T080000Z
DTEND;VALUE=DATE-TIME:20210621T090000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/24
DESCRIPTION:Title: The
Euler characteristic and the zeta-functions of a totally disconnected loc
ally compact group\nby Ilaria Castellano (University of Milan - Bicoca
) as part of Symmetry in Newcastle\n\n\nAbstract\nThe Euler characteristic
and the zeta-functions of a totally disconnected locally compact group\nA
bstract: The Euler-Poincaré characteristic of a discrete group is an impo
rtant (but also quite mysterious) invariant. It is usually just an integer
or a rational number and reflects many quite significant properties. The
realm of totally disconnected locally compact groups admits an analogue of
the Euler-Poincaré characteristic which surprisingly is no longer just a
n integer\, or a rational number\, but a rational multiple of a Haar measu
re. Warning: in order to gain such an invariant the group has to be unimod
ular and satisfy some cohomological finiteness conditions. Examples of gro
ups satisfying these additional conditions are the fundamental groups of f
inite trees of profinite groups. What arouses our curiosity is the fact th
at - in some cases - the Euler-Poincaré characteristic turns out to be mi
raculously related to a zeta-function. A large part of the talk will be de
voted to the introduction of the just-cited objects. We aim at concluding
the presentation by facing the concrete example of the group of F-points o
f a split semisimple simply connected algebraic group G over F (where F de
notes a non-archimedean locally compact field of residue characteristic p)
.\nJoint work with Gianmarco Chinello and Thomas Weigel.\n
LOCATION:https://researchseminars.org/talk/SiN/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lancelot Semal (UC Louvain)
DTSTART;VALUE=DATE-TIME:20200705T080000Z
DTEND;VALUE=DATE-TIME:20200705T090000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/25
DESCRIPTION:Title: Uni
tary representations of totally disconnected locally compact groups satisf
ying Ol'shanskii's factorization\nby Lancelot Semal (UC Louvain) as pa
rt of Symmetry in Newcastle\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SiN/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lancelot Semal (UC Louvain)
DTSTART;VALUE=DATE-TIME:20210705T080000Z
DTEND;VALUE=DATE-TIME:20210705T090000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/26
DESCRIPTION:Title: Uni
tary representations of totally disconnected locally compact groups satisf
ying Ol'shanskii's factorization\nby Lancelot Semal (UC Louvain) as pa
rt of Symmetry in Newcastle\n\n\nAbstract\nWe provide a new axiomatic fram
ework\, inspired by the work of Ol'shanskii\, to describe explicitly certa
in irreducible unitary representations of second-countable non-discrete un
imodular totally disconnected locally compact groups. We show that this se
tup applies to various families of automorphism groups of locally finite s
emiregular trees and right-angled buildings.\n\nThe talk is based on mater
ial presented in https://arxiv.org/abs/2106.05730\n
LOCATION:https://researchseminars.org/talk/SiN/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Raum (Stockholm University)
DTSTART;VALUE=DATE-TIME:20210809T063000Z
DTEND;VALUE=DATE-TIME:20210809T073000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/27
DESCRIPTION:Title: Loc
ally compact groups acting on trees\, the type I conjecture and non-amenab
le von Neumann algebras\nby Sven Raum (Stockholm University) as part o
f Symmetry in Newcastle\n\n\nAbstract\nn the 90's\, Nebbia conjectured tha
t a group of tree automorphisms acting transitively on the tree's boundary
must be of type I\, that is\, its unitary representations can in principa
l be classified. For key examples\, such as Burger-Mozes groups\, this co
njecture is verified. Aiming for a better understanding of Nebbia's conje
cture and a better understanding of representation theory of groups acting
on trees\, it is natural to ask whether there is a characterisation of ty
pe I groups acting on trees. In 2016\, we introduced in collaboration with
Cyril Houdayer a refinement of Nebbia's conjecture to a trichotomy\, oppo
sing type I groups with groups whose von Neumann algebra is non-amenable.
For large classes of groups\, including Burger-Mozes groups\, we could ve
rify this trichotomy.\nIn this talk\, I will motivate and introduce the co
njecture trichotomy for groups acting on tress and explain how von Neumann
algebraic techniques enter the picture.\n
LOCATION:https://researchseminars.org/talk/SiN/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Parkinson (University of Sydney)
DTSTART;VALUE=DATE-TIME:20210809T080000Z
DTEND;VALUE=DATE-TIME:20210809T090000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/28
DESCRIPTION:Title: Aut
omata for Coxeter groups\nby James Parkinson (University of Sydney) as
part of Symmetry in Newcastle\n\n\nAbstract\nIn 1993 Brink and Howlett pr
oved that finitely generated Coxeter groups are automatic. In particular\,
they constructed a finite state automaton recognising the language of red
uced words in the Coxeter group. This automaton is constructed in terms of
the remarkable set of "elementary roots" in the associated root system.\n
In this talk we outline the construction of Brink and Howlett. We also des
cribe the minimal automaton recognising the language of reduced words\, an
d prove necessary and sufficient conditions for the Brink-Howlett automato
n to coincide with this minimal automaton. This resolves a conjecture of H
ohlweg\, Nadeau\, and Williams\, and is joint work with Yeeka Yau.\n
LOCATION:https://researchseminars.org/talk/SiN/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Willis (University of Newcastle)
DTSTART;VALUE=DATE-TIME:20210830T080000Z
DTEND;VALUE=DATE-TIME:20210830T090000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/29
DESCRIPTION:Title: Con
structing groups with flat-rank greater than 1\nby George Willis (Univ
ersity of Newcastle) as part of Symmetry in Newcastle\n\n\nAbstract\nThe c
ontraction subgroup for $x$ in the locally compact group\, $G$\, $\\mathop
{con}(x) = \\left\\{ g\\in G \\mid x^ngx^{-n} \\to 1\\text{ as }n\\to\\inf
ty \\right\\}$\, and the Levi subgroup is $\\mathop{lev}(x) = \\left\\{ g\
\in G \\mid \\{x^ngx^{-n}\\}_{n\\in\\mathbb{Z}} \\text{ has compact closur
e}\\right\\}$. The following will be shown.\n\nLet $G$ be a totally discon
nected\, locally compact group and $x\\in G$. Let $y\\in{\\sf lev}(x)$. Th
en there are $x'\\in G$ and a compact subgroup\, $K\\leq G$ such that: $K$
is normalised by $x'$ and $y$\, $\\mathop{con}(x') = \\mathop{con}(x)$ an
d $\\mathop{lev}(x') = \\mathop{lev}(x)$\, and the group $\\langle x'\,y\,
K\\rangle$ is abelian modulo $K$\, and hence flat.\n\n\nIf no compact open
subgroup of $G$ normalised by $x$ and no compact open subgroup of $\\math
op{lev}(x)$ normalised by $y$\, then the flat-rank of $\\langle x'\,y\,K\\
rangle$ is equal to $2$.\n
LOCATION:https://researchseminars.org/talk/SiN/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siegfried Echterhoff (University of Münster)
DTSTART;VALUE=DATE-TIME:20210927T063000Z
DTEND;VALUE=DATE-TIME:20210927T073000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/30
DESCRIPTION:Title: Ame
nable group actions on C*-algebras and the weak containment problem\nb
y Siegfried Echterhoff (University of Münster) as part of Symmetry in New
castle\n\n\nAbstract\nThe notion of amenable actions by discrete groups on
C*-algebras has been introduced by Claire Amantharaman-Delaroche more tha
n thirty years ago\, and has become a well understood theory with many app
lications. So it is somewhat surprising that an established theory of amen
able 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 uni
fies several notions of approximation properties of actions which have bee
n discussed in the literature. We also discuss the weak containment proble
m 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 this lect
ure we report on joint work with Alcides Buss and Rufus Willett\n
LOCATION:https://researchseminars.org/talk/SiN/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim de Laat (University of Münster)
DTSTART;VALUE=DATE-TIME:20210927T080000Z
DTEND;VALUE=DATE-TIME:20210927T090000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/31
DESCRIPTION:Title: Gel
fand pairs\, spherical functions and exotic group C*-algebras\nby Tim
de Laat (University of Münster) as part of Symmetry in Newcastle\n\n\nAbs
tract\nFor a non-amenable group $G$\, there can be many group C*-algebras
that lie naturally between the universal and the reduced C*-algebra of $G$
. These are called exotic group C*-algebras. After a short introduction\,
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 properties of di
fferent spherical functions on $G$ (relative to a maximal compact subgroup
) can be used to distinguish between exotic group C*-algebras. This recove
rs results of Samei and Wiersma. Additionally\, I will explain that under
certain natural assumptions\, the aforementioned exotic group C*-algebras
are the only ones coming from $G$-invariant ideals in the Fourier-Stieltje
s algebra of $G$.\n\nThis is based on joint work with Dennis Heinig and Ti
mo Siebenand.\n
LOCATION:https://researchseminars.org/talk/SiN/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sanghyun Kim (KIAS)
DTSTART;VALUE=DATE-TIME:20211101T063000Z
DTEND;VALUE=DATE-TIME:20211101T073000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/32
DESCRIPTION:Title: Opt
imal regularity of mapping class group actions on the circle\nby Sangh
yun Kim (KIAS) as part of Symmetry in Newcastle\n\n\nAbstract\nWe prove th
at for each finite index subgroup $H$ of the mapping class group of a clos
ed hyperbolic surface\, and for each real number $r>0$ there does not exis
t a faithful $C^{1+r}$--action of $H$ on a circle. (Joint with Thomas Kobe
rda and Cristobal Rivas)\n
LOCATION:https://researchseminars.org/talk/SiN/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francois Thilmany (UC Louvain)
DTSTART;VALUE=DATE-TIME:20211101T080000Z
DTEND;VALUE=DATE-TIME:20211101T090000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/33
DESCRIPTION:Title: Uni
form discreteness of arithmetic groups and the Lehmer conjecture\nby F
rancois Thilmany (UC Louvain) as part of Symmetry in Newcastle\n\n\nAbstra
ct\nThe famous Lehmer problem asks whether there is a gap between 1 and th
e Mahler measure of algebraic integers which are not roots of unity. Asked
in 1933\, this deep question concerning number theory has since then been
connected to several other subjects. After introducing the concepts invol
ved\, 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 lattice
s in semisimple Lie groups (conjectured by Margulis).\n\nJoint work with L
am Pham.\n
LOCATION:https://researchseminars.org/talk/SiN/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Thomas (University of Sydney)
DTSTART;VALUE=DATE-TIME:20220204T010000Z
DTEND;VALUE=DATE-TIME:20220204T020000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/34
DESCRIPTION:Title: A g
allery model for affine flag varieties via chimney retractions\nby Ann
e Thomas (University of Sydney) as part of Symmetry in Newcastle\n\nLectur
e held in SR118\, Callaghan Campus.\n\nAbstract\nA gallery model for affin
e flag varieties via chimney retractions\nWe provide a unified combinatori
al framework to study orbits in affine flag varieties via the associated B
ruhat-Tits buildings. We first formulate\, for arbitrary affine buildings\
, the notion of a chimney retraction. This simultaneously generalises the
two well-known notions of retractions in affine buildings: retractions fro
m chambers at infinity and retractions from alcoves. We then present a rec
ursive formula for computing the images of certain minimal galleries in th
e building under chimney retractions\, using purely combinatorial tools as
sociated to the underlying affine Weyl group. Finally\, for Bruhat-Tits bu
ildings\, we relate these retractions and their effect on certain minimal
galleries to double coset intersections in the corresponding affine flag v
ariety. This is joint work with Elizabeth Milicevic\, Yusra Naqvi and Petr
a Schwer.\n
LOCATION:https://researchseminars.org/talk/SiN/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Bischof (Uni Giesen)
DTSTART;VALUE=DATE-TIME:20220204T033000Z
DTEND;VALUE=DATE-TIME:20220204T043000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/35
DESCRIPTION:Title: (Tw
in) Buildings and groups\nby Sebastian Bischof (Uni Giesen) as part of
Symmetry in Newcastle\n\nLecture held in SR118\, Callaghan Campus.\n\nAbs
tract\nBuildings have been introduced by Tits in order to study semi-simpl
e algebraic groups from a geometrical point of view. One of the most impor
tant results in the theory of buildings is the classification of thick irr
educible spherical buildings of rank at least 3. In particular\, any such
building comes from an RGD-system. The decisive tool in this classificatio
n is the Extension theorem for spherical buildings\, i.e. a local isometry
extends to the whole building.\nTwin buildings were introduced by Ronan a
nd Tits in the late 1980s. Their definition was motivated by the theory 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 cha
mbers of the two buildings. This opposition relation shares many important
properties with the opposition relation on the chambers of a spherical bu
ilding. Thus\, twin buildings appear to be natural generalizations of sphe
rical buildings with infinite Weyl group. Since the notion of RGD-systems
exists not only in the spherical case\, one can ask whether any twin build
ing (satisfying some further conditions) comes from an RGD-system. In 1992
Tits proves several results that are inspired by his strategy in the sphe
rical case and he discusses several obstacles for obtaining a similar Exte
nsion theorem for twin buildings. In this talk I will speak about the hist
ory and developments of the Extension theorem for twin buildings.\n
LOCATION:https://researchseminars.org/talk/SiN/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Ferov (University of Newcastle)
DTSTART;VALUE=DATE-TIME:20220304T010000Z
DTEND;VALUE=DATE-TIME:20220304T020000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/36
DESCRIPTION:Title: Aut
omorphism groups of Cayley graphs of Coxeter groups: when are they discret
e?\nby Michal Ferov (University of Newcastle) as part of Symmetry in N
ewcastle\n\nLecture held in SR118\, University Drive\, Callaghan.\n\nAbstr
act\nGroup of automorphisms of a connected locally finite graph is natural
ly a totally disconnected locally compact topological group\, when equippe
d with the permutation topology. It therefore makes sense to ask for which
graphs is the topology not discrete. We show that in case of Cayley graph
s of Coxeter groups\, one can fully characterise the discrete ones in term
s of the symmetries of the corresponding Coxeter system. Joint work with F
ederico Berlai.\n
LOCATION:https://researchseminars.org/talk/SiN/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeroen Schillewaert (The University of Auckland)
DTSTART;VALUE=DATE-TIME:20220304T033000Z
DTEND;VALUE=DATE-TIME:20220304T043000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/37
DESCRIPTION:Title: The
geometries of the Freudenthal-Tits magic square\nby Jeroen Schillewae
rt (The University of Auckland) as part of Symmetry in Newcastle\n\nLectur
e held in SR118\, University Drive\, Callaghan.\n\nAbstract\nI will give a
n overview of a programme investigating projective embeddings of (exceptio
nal) geometries which Hendrik Van Maldeghem and I started in 2010.\n
LOCATION:https://researchseminars.org/talk/SiN/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Parkinson (University of Sydney)
DTSTART;VALUE=DATE-TIME:20220304T050000Z
DTEND;VALUE=DATE-TIME:20220304T060000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/38
DESCRIPTION:Title: Aut
omorphisms and opposition in spherical buildings.\nby James Parkinson
(University of Sydney) as part of Symmetry in Newcastle\n\nLecture held in
SR118\, University Drive\, Callaghan.\n\nAbstract\nThe geometry of elemen
ts fixed by an automorphism of a spherical building is a rich and well-stu
died object\, intimately connected to the theory of Galois descent in buil
dings. In recent years\, a complementary theory has emerged investigating
the geometry of elements mapped onto opposite elements by a given automorp
hism. In this talk we will give an overview of this theory. This work is j
oint primarily with Hendrik Van Maldeghem (along with others).\n
LOCATION:https://researchseminars.org/talk/SiN/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Carter (University of Newcastle)
DTSTART;VALUE=DATE-TIME:20220401T010000Z
DTEND;VALUE=DATE-TIME:20220401T020000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/39
DESCRIPTION:Title: Uni
tary representations and the type I property of groups acting on trees
\nby Max Carter (University of Newcastle) as part of Symmetry in Newcastle
\n\n\nAbstract\nUnitary representations are a classical and useful tool fo
r studying locally compact groups: motivated in part by quantum mechanics\
, they have been studied in detail since the early-mid 1900’s with much
success\, and they enable group theorists to employ functional analytic te
chniques in the study of locally compact groups. The algebras that unitary
representations generate play an important role in not only understanding
the representation theory of a locally compact group\, but also in unders
tanding properties pertaining to the group itself. This talk will give a b
rief introduction to some of the basics of the unitary representation theo
ry of locally compact groups\, with focus placed on the associated operato
r algebraic structures/properties. In particular\, `type I groups' and `CC
R groups' will be the main focus. As an application\, I will discuss some
current research interests in the unitary representation theory of groups
acting on trees\, including work of myself on the unitary representation t
heory of `scale groups’.\n
LOCATION:https://researchseminars.org/talk/SiN/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camila Sehnem (Victoria University of Wellington)
DTSTART;VALUE=DATE-TIME:20220401T033000Z
DTEND;VALUE=DATE-TIME:20220401T043000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/40
DESCRIPTION:Title: Equ
ilibrium on Toeplitz extensions of higher dimensional noncommutative tori<
/a>\nby Camila Sehnem (Victoria University of Wellington) as part of Symme
try in Newcastle\n\n\nAbstract\nThe C*-algebra generated by the left-regul
ar representation of $\\mathbb{N}^n$ twisted by a $2$-cocycle is a Toeplit
z extension of an $n$-dimensional noncommutative torus\, on which each vec
tor $r \\in [0\,\\infty)^n$ determines a one-parameter subgroup of the gau
ge action. I will report on joint work with Z. Afsar\, J. Ramagge and M. L
aca\, in which we show that the equilibrium states of the resulting C*-dyn
amical system are parametrised by tracial states of the noncommutative tor
us corresponding to the restriction of the cocycle to the vanishing coordi
nates of $r$. These in turn correspond to probability measures on a classi
cal torus whose dimension depends on a certain degeneracy index of the res
tricted cocycle. Our results generalise the phase transition on the Toepli
tz noncommutative tori used as building blocks in work of Brownlowe\, Haw
kins and Sims\, and of Afsar\, an Huef\, Raeburn and Sims.\n
LOCATION:https://researchseminars.org/talk/SiN/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roozbeh Hazrat (University of Western Sydney)
DTSTART;VALUE=DATE-TIME:20220401T050000Z
DTEND;VALUE=DATE-TIME:20220401T060000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/41
DESCRIPTION:Title: San
dpile models and Leavitt algebras\nby Roozbeh Hazrat (University of We
stern Sydney) as part of Symmetry in Newcastle\n\n\nAbstract\nSandpile mod
els are about how things spread along a grid (think of Covid!) and Leavitt
algebras are algebras associated to graphs. We relate these two subjects!
\n
LOCATION:https://researchseminars.org/talk/SiN/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio Bravo (University of Chile)
DTSTART;VALUE=DATE-TIME:20220701T000000Z
DTEND;VALUE=DATE-TIME:20220701T010000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/42
DESCRIPTION:Title: Quo
tients of the Bruhat-Tits tree function filed analogs of the Hecke congrue
nce subgroups\nby Claudio Bravo (University of Chile) as part of Symme
try in Newcastle\n\nLecture held in Lambert Lounge\, US 321.\n\nAbstract\n
Let 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 the comp
letion path P_infty of the function field of C. In order to study group 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\, Serre show
s that GL_2(R)\\T is the union of a finite graph and a finite number of ra
y shaped subgraphs\, which are called cusps. It is not hard to see that fi
nite index subgroups inherit this property.\nIn this exposition we describ
e the quotient graph H\\T defined from the action on T of the group H cons
isting of matrices that are upper triangular modulo I\, where I is an idea
l R. More specifically\, we give an explicit formula for the cusp number H
\\T. Then By\, using Bass-Serre theory\, we describe the combinatorial str
ucture of H. These groups play\, in the function field context\, the same
role as the Hecke Congruence subgroups of SL_2(Z). Moreover\, not that the
groups studied by Serre correspond to the case where the ideal I coincide
s with the ring R.\n
LOCATION:https://researchseminars.org/talk/SiN/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Conder (University of Auckland)
DTSTART;VALUE=DATE-TIME:20220701T013000Z
DTEND;VALUE=DATE-TIME:20220701T023000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/43
DESCRIPTION:Title: Dis
crete two-generator subgroups of PSL(2\,Q_p)\nby Matthew Conder (Unive
rsity of Auckland) as part of Symmetry in Newcastle\n\nLecture held in Lam
bert Lounge\, US 321.\n\nAbstract\nDue to work of Gilman\, Rosenberger\, P
urzitsky and many others\, discrete two-generator subgroups of PSL(2\,R) h
ave been completely classified by studying their action by Möbius transfo
rmations on the hyperbolic plane. Here we aim to classify discrete two-gen
erator subgroups of PSL(2\,Q_p) by studying their action by isometries on
the Bruhat-Tits tree. We first give a general structure theorem for two-ge
nerator groups acting by isometries on a tree\, which relies on certain Kl
ein-Maskit combination theorems. We will then discuss how this theorem can
be applied to determine discreteness of a two-generator subgroup of PSL(2
\,Q_p). This is ongoing work in collaboration with Jeroen Schillewaert.\n
LOCATION:https://researchseminars.org/talk/SiN/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Willis (University of Newcastle)
DTSTART;VALUE=DATE-TIME:20220701T040000Z
DTEND;VALUE=DATE-TIME:20220701T050000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/44
DESCRIPTION:Title: Gro
ups acting on regular trees and t.d.l.c. groups\nby George Willis (Uni
versity of Newcastle) as part of Symmetry in Newcastle\n\nLecture held in
Lambert Lounge\, US 321.\n\nAbstract\nGroups acting on regular trees and t
.d.l.c. groups\nAbstract: Groups of automorphisms of regular trees are an
important source of examples of and intuition about totally disconnected\,
locally compact (t.d.l.c.) groups. Indeed\, Pierre-Emmanuel Caprice has c
alled them a microcosm the general theory of t.d.l.c. groups. Although muc
h 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 relate
s to the general theory.\n
LOCATION:https://researchseminars.org/talk/SiN/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kane Townsend (University of Technology Sydney)
DTSTART;VALUE=DATE-TIME:20221007T010000Z
DTEND;VALUE=DATE-TIME:20221007T020000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/45
DESCRIPTION:Title: Hyp
erbolic groups with $k$-geodetic Cayley graphs\nby Kane Townsend (Univ
ersity of Technology Sydney) as part of Symmetry in Newcastle\n\n\nAbstrac
t\nA locally-finite simple connected graph is said to be $k$-geodetic for
some $k\\geq1$\, if there is at most $k$ distinct geodesics between any tw
o vertices of the graph. We investigate the properties of hyperbolic group
s with $k$-geodetic Cayley graphs. To begin\, we show that $k$-geodetic gr
aphs cannot have a "ladder-like" geodesic structure with unbounded length.
Using this bound\, we generalise a well-known result of Papasoglu that st
ates hyperbolic groups with $1$-geodetic Cayley graphs are virtually-free.
We then investigate which elements of the hyperbolic group with $k$-geode
tic Cayley graph commute with a given infinite order element.\n
LOCATION:https://researchseminars.org/talk/SiN/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Freden (Southern Utah University)
DTSTART;VALUE=DATE-TIME:20221007T033000Z
DTEND;VALUE=DATE-TIME:20221007T043000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/46
DESCRIPTION:Title: Asp
ects of growth in Baumslag-Solitar groups\nby Eric Freden (Southern Ut
ah University) as part of Symmetry in Newcastle\n\n\nAbstract\nIn 1997\, G
rigorchuk and de la Harpe suggested computing the growth series for the Ba
umslag-Solitar group BS(2\,3). After 25 years\, this is still an open prob
lem. In fact\, the growth of only the solvable groups BS(1\,n) and automat
ic groups BS(n\,n) are known. In this talk I will review what has since be
en discovered about these remarkable groups and conclude with new unpublis
hed results concerning the exponents of growth for the subfamily BS(2\,2n)
.\n
LOCATION:https://researchseminars.org/talk/SiN/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volker Diekert (Universität Stuttgart)
DTSTART;VALUE=DATE-TIME:20221007T050000Z
DTEND;VALUE=DATE-TIME:20221007T060000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/47
DESCRIPTION:Title: Dec
idability of membership problems for $2\\times 2$ matrices over $\\mathbb{
Q}$\nby Volker Diekert (Universität Stuttgart) as part of Symmetry in
Newcastle\n\n\nAbstract\nMy talk is based on a joint work with Igor Potap
ov and Pavel Semukhin (Liverpool\, UK).\nWe consider membership problems i
n matrix semigroups. Using symbolic algorithms on words and finite automat
a\, we prove various new decidability results for $2\\times 2$ matrices ov
er $\\mathbb{Q}$.\nFor that\, we introduce the concept of flat rational se
ts: if $M$ is a monoid and $N$ is\na submonoid\, then \\emph{flat rational
sets of $M$ over $N$} are finite unions of the form $L_0g_1L_1 \\cdots g_
t L_t$ where all $L_i$'s are rational subsets of $N$ and $g_i\\in M$. We g
ive quite general sufficient conditions under which flat rational sets for
m an effective relative Boolean algebra. As a corollary\, we obtain that t
he emptiness problem for Boolean combinations of flat rational subsets of
$\\mathrm{GL}(2\,\\mathbb{Q})$ over $\\mathrm{GL}(2\,\\mathbb{Z})$ is deci
dable (in singly exponential time). It is possible that such a strong deci
dability result cannot be pushed any further for groups sitting between\n$
\\mathrm{GL}(2\,\\mathbb{Z})$ and $\\mathrm{GL}(2\,\\mathbb{Q})$.\n\nWe al
so show a dichotomy for nontrivial group extension of $\\mathrm{GL}(2\,\\m
athbb{Z})$ in $\\mathrm{GL}(2\,\\mathbb{Q})$: if $G$ is a f.g.~group such
that $\\mathrm{GL}(2\,\\mathbb{Z}) < G \\leq \\mathrm{GL}(2\,\\mathbb{Q})$
\, then either $G\\cong \\mathrm{GL}(2\,\\mathbb{Z})\\times \\mathbb{Z}^k$
\, for\nsome $k\\geq 1$\, or $G$ contains an extension of the Baumslag-Sol
itar group $\\mathop\\mathrm{BS}(1\,q)$\, with $q\\geq\n2$\, of infinite i
ndex. In the first case of the dichotomy the membership problem for $G$ is
\ndecidable but the equality problem for rational subsets of $G$ is undeci
dable. In the second case\,\ndecidability of the membership problem for ra
tional subsets in $G$ is open.\n\nOur improves various natural decidabili
ty results for $2 \\times 2$ matrices with rational entries\, and it also\
nsupports them with concrete complexity bounds for the first time.\n
LOCATION:https://researchseminars.org/talk/SiN/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Hulpke (Colorado State University)
DTSTART;VALUE=DATE-TIME:20221104T030000Z
DTEND;VALUE=DATE-TIME:20221104T040000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/48
DESCRIPTION:Title: Con
structing Perfect Groups\nby Alexander Hulpke (Colorado State Universi
ty) as part of Symmetry in Newcastle\n\n\nAbstract\nThe construction of pe
rfect groups of a given order can be considered as the prototype of constr
uction of nonsolvable groups of a given order.\nI will describe a recent p
roject to enumerate\, up to isomorphism\, the perfect groups of order up t
o 2*10^6. It crucially relies on new tools for calculating cohmology\, as
well as improved implementations for isomorphism test.\n\nThis work extend
s results of Holt and Plesken from 1989 and illustrates the scope of algor
ithmic improvements over the past decades.\n
LOCATION:https://researchseminars.org/talk/SiN/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Conder (University of Auckland)
DTSTART;VALUE=DATE-TIME:20221124T230000Z
DTEND;VALUE=DATE-TIME:20221125T000000Z
DTSTAMP;VALUE=DATE-TIME:20221209T133736Z
UID:SiN/49
DESCRIPTION:Title: Two
-generator subgroups of SL2 over local fields\nby Matthew Conder (Univ
ersity of Auckland) as part of Symmetry in Newcastle\n\n\nAbstract\nIn thi
s talk\, we will give an overview of some results and open problems relati
ng to two-generator subgroups of SL2 over a local field K. We first consid
er the archimedean setting\, where certain discrete and/or free two-genera
tor subgroups of SL(2\,R) and SL(2\,C) can be identified by investigating
their respective actions by Möbius transformations on the upper half plan
e and Riemann sphere. We then outline some recent results in the non-archi
medean setting\, obtained by studying the analogous action of SL(2\,K) by
isometries on the corresponding Bruhat-Tits tree. Finally\, we discuss an
application of this work to the problem of deciding whether a two-generato
r subgroup of SL(2\,K) is dense.\n
LOCATION:https://researchseminars.org/talk/SiN/49/
END:VEVENT
END:VCALENDAR