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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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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:20210616T213941Z
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\nInteract
ive livestream: https://uonewcastle.zoom.us/j/82596235512\n\nAbstract\nHig
hly transitive groups\, i.e. groups admitting an embedding in Sym(N) with
dense image\, form a wide class of groups. For instance\, M. Hull and D. O
sin proved that it contains all countable acylindrically hyperbolic 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 highly transitive.
On the one hand\, this theorem gives new examples of highly transitive gro
ups. On the other hand\, it is sharp because of results by A. Le Boudec an
d N. Matte Bon.\n
LOCATION:https://researchseminars.org/talk/SiN/23/
URL:https://uonewcastle.zoom.us/j/82596235512
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:20210616T213941Z
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\nInteractive livestream: https://uone
wcastle.zoom.us/j/82596235512\n\nAbstract\nThe Euler characteristic and th
e zeta-functions of a totally disconnected locally compact group\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 r
ational number and reflects many quite significant properties. The realm o
f totally disconnected locally compact groups admits an analogue of the Eu
ler-Poincaré characteristic which surprisingly is no longer just an integ
er\, or a rational number\, but a rational multiple of a Haar measure. War
ning: in order to gain such an invariant the group has to be unimodular an
d satisfy some cohomological finiteness conditions. Examples of groups sat
isfying these additional conditions are the fundamental groups of finite t
rees of profinite groups. What arouses our curiosity is the fact that - in
some cases - the Euler-Poincaré characteristic turns out to be miraculou
sly related to a zeta-function. A large part of the talk will be devoted t
o the introduction of the just-cited objects. We aim at concluding the pre
sentation by facing the concrete example of the group of F-points of a spl
it semisimple simply connected algebraic group G over F (where F denotes a
non-archimedean locally compact field of residue characteristic p).\nJoin
t work with Gianmarco Chinello and Thomas Weigel.\n
LOCATION:https://researchseminars.org/talk/SiN/24/
URL:https://uonewcastle.zoom.us/j/82596235512
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