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BEGIN:VEVENT
SUMMARY:Alex Lubotzky (Hebrew University of Jerusalem)
DTSTART:20210816T143000Z
DTEND:20210816T151500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/1
DESCRIPTION:Title: Stability and testability of permutations' equations\nby Alex Lub
otzky (Hebrew University of Jerusalem) as part of BIRS workshop: Totally D
isconnected Locally Compact Groups via Group Actions\n\n\nAbstract\nLet $A
$ and $B$ be two permutations in $Sym(n)$ which "almost commute"- are they
a small deformation of permutations that truly commute? More generally\,
if $R$ is a system of wards-equations in variables $X=x_1\,\\dots\,x_d$ an
d \n$A_1\,\\dots\,A_d$ permutations which are nearly solution\; are they n
ear true solutions? It turns out that the answer to this question depends
only on the group presented by the generators $X$ and relations $R$. This
leads to the notions of \n"stable groups" and "testable groups". We wil
l present a few results and methods which were developed in recent years t
o check whether a group is stable\\testable. We will also describe the con
nection of this subject with property testing in computer science\, with
the long-standing problem of whether every group is sofic and with IRS's (
=invariant random subgroups).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariapia Moscatiello (University of Bologna)
DTSTART:20210816T151500Z
DTEND:20210816T161000Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/2
DESCRIPTION:Title: Bases of permutation groups and IBIS groups\nby Mariapia Moscatie
llo (University of Bologna) as part of BIRS workshop: Totally Disconnected
Locally Compact Groups via Group Actions\n\n\nAbstract\nLet $G$ be a perm
utation group acting on a finite set $\\Omega$. A subset $\\mathcal{B}$ of
$\\Omega$ is called a base for $G$ if the pointwise stabilizer of $\\math
cal{B}$ in $G$ is trivial. \n\nIn the 19th century\, bounding the order o
f a finite primitive permutation group $G$ was a problem that attracted a
lot of attention.\n Early investigations of bases then arose because such
a problem reduces to that of bounding the minimal size of a base of $G$. \
n Some other far-reaching applications across Pure Mathematics led the stu
dy of the base size to be a crucial area of current research in permutatio
n groups. In this part of the talk\, we will investigate some of these app
lications and review some results about base size. We will present a recen
t improvement of a famous estimation due to Liebeck that estimates the bas
e size of a primitive permutation group in terms of its degree.\n\n\n\n\nI
n the second part of the talk\, we will define the concept of irredundant
bases of $G$ and the concept of IBIS groups. Whereas bases of minimal size
have been well studied\, irredundant bases and IBIS groups have not yet r
eceived a similar degree of attention. Indeed\, Cameron and Fon-Der-Flaas\
, already in 1995\, defined such groups and proposed to classify some mean
ingful families. But only this year\, a systematic investigation of primit
ive permutation IBIS groups has been started. We will discuss how we reduc
ed the classification of primitive IBIS groups to the almost simple groups
and affine groups. Eventually\, we will conclude by mentioning recent adv
ances towards a complete classification.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Liebeck (Imperial College)
DTSTART:20210816T163000Z
DTEND:20210816T171500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/3
DESCRIPTION:Title: Cherlin's conjecture on binary groups\nby Martin Liebeck (Imperia
l College) as part of BIRS workshop: Totally Disconnected Locally Compact
Groups via Group Actions\n\n\nAbstract\nA permutation group $G$ on a set $
X$ is called binary if the following condition holds: if $r > 2$ and \n$x\
,y\\in X^r$ are $2$-equivalent $r$-tuples\, then $x$ and $y$ must be in th
e same $G$-orbit. Here we say $x = (x_1\,\\dots\,x_r)$ and $y = (y_1\,\\cd
ots\,y_r)$ are $2$-equivalent if any pair $(x_i\,x_j)$ can be mapped to th
e corresponding pair $(y_i\,y_j)$ by an element of $G$. The definition was
coined by Gregory Cherlin as part of his theory of homogeneous structures
in model theory. Over 20 years ago\, Cherlin conjectured that the all the
finite primitive binary groups fall into three families: the full symmetr
ic groups $Sym(X)$\; cyclic groups of prime order\; and a certain class of
affine groups of dimension $1$ or $2$. In joint work with Nick Gill and P
ablo Spiga\, we have completed the proof of this conjecture.\nIn the talk
I will try to explain the point of the binary definition in relation to mo
del theory\, discuss various examples of binary groups\, and indicate some
of the strategies of the proof of the conjecture.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Tracey (University of Oxford)
DTSTART:20210816T173000Z
DTEND:20210816T181500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/4
DESCRIPTION:Title: On the Fitting height and insoluble length of a finite group\nby
Gareth Tracey (University of Oxford) as part of BIRS workshop: Totally Dis
connected Locally Compact Groups via Group Actions\n\n\nAbstract\nA classi
cal result of Baer states that an element $x$ of a finite group $G$ is con
tained in\nthe Fitting subgroup $F(G)$ of $G$ if and only if $x$ is a left
Engel element of $G$. That is\, $x \\in F (G)$\nif and only if there exis
ts a positive integer $k$ such that $[g\,_k x] := [g\, x\, . . . \, x]$ (w
ith $x$ appearing\nk times\, and using the convention $[x_1 \, x_2 \, x_3
. . . \, x_k ] := [[. . . [[x_1 \, x_2 ]\, x_3 ]\, . . .]\, x_k ]$) is tri
vial for\nall $g \\in G$. The result was generalised by E. Khukhro and P.
Shumyatsky in a 2013 paper via\nan analysis of the sets\n$$E_{G\,k }(x) :=
\\{[g\,_k x] : g \\in G\\}.$$\nIn this talk\, we will continue to study t
he properties of these sets\, concluding with the proof\nof two conjecture
s made in said paper. As a by-product of our methods\, we also prove a\nge
neralisation of a result of Flavell\, which itself generalises Wielandt’
s Zipper Lemma and\nprovides a characterisation of subgroups contained in
a unique maximal subgroup. We also\nderive a number of consequences of our
theorems\, including some applications to the set of odd\norder elements
of a finite group inverted by an involutory automorphism.\nWe will finish
the talk with some related work on the question: Which finite groups $G$ c
an\nhave an element contained in a unique maximal subgroup of $G$? All of
this is joint work with\nR. M. Guralnick.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Reid (University of Newcastle)
DTSTART:20210816T190000Z
DTEND:20210816T194500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/5
DESCRIPTION:Title: In search of well-foundedness principles for totally disconnected loc
ally compact groups\nby Colin Reid (University of Newcastle) as part o
f BIRS workshop: Totally Disconnected Locally Compact Groups via Group Act
ions\n\n\nAbstract\nFor some classes of groups\, there is a natural notion
of rank\, which can be used to argue by induction or sometimes even class
ify the groups: for example\, the order of a finite group\, or the dimensi
on of a Lie group. Closely related is the pervasive theme of decomposing
a group into "basic" or "irreducible" factors. How far can we get with th
is approach in the class of totally disconnected locally compact second-co
untable (t.d.l.c.s.c.) groups?\n\nI will describe a certain approach to st
ructural complexity of t.d.l.c.s.c. groups that is inspired by development
s in the area over the last ten years\, particularly the class of elementa
ry groups introduced P. Wesolek in his 2014 PhD thesis. The latter work s
hows that one can get a surprising amount of information from descending c
hain conditions on subgroups\, and associated ordinal-valued rank function
s\, from a perspective that takes all compact groups and discrete groups a
s having small rank. I will give an example of a class of "well-founded"
groups with good closure properties that properly contains the elementary
groups\, including for example all locally linear groups and many examples
of compactly generated simple groups acting on trees with Tits' independe
nce property\, but then also give a family of t.d.l.c.s.c. groups that do
not belong to this class.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Smith (University of Lincoln)
DTSTART:20210816T203000Z
DTEND:20210816T211500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/6
DESCRIPTION:by Simon Smith (University of Lincoln) as part of BIRS worksho
p: Totally Disconnected Locally Compact Groups via Group Actions\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Bamberg (University of Western Australia)
DTSTART:20210817T010000Z
DTEND:20210817T014500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/7
DESCRIPTION:Title: Orbits of Sylow p-subgroups of finite permutation groups\nby John
Bamberg (University of Western Australia) as part of BIRS workshop: Total
ly Disconnected Locally Compact Groups via Group Actions\n\n\nAbstract\nWe
say that a finite group G acting on a set X has Property (*)_p for a prim
e p if the stabiliser of x in P is a Sylow p-subgroup of the stabiliser of
x in G\, for all x in X and Sylow p-subgroups P of G. Property (*)_p aros
e in the recent work of Tornier (2018) on local Sylow p-subgroups of Burge
r-Mozes groups\, and he determined the values of p for which the alternati
ng and symmetric groups in their natural actions have Property (*)_p. In t
his talk\, we will explore the various properties of groups satisfying (*)
_p and extensions of Tornier's result\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Giudici (The University of Western Australia)
DTSTART:20210817T020000Z
DTEND:20210817T024500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/8
DESCRIPTION:Title: 2-closed groups and automorphism groups of digraphs\nby Michael G
iudici (The University of Western Australia) as part of BIRS workshop: Tot
ally Disconnected Locally Compact Groups via Group Actions\n\n\nAbstract\n
Wielandt introduced the notion of the 2-closure of a permutation group $G$
on a set $\\Omega$. This is the largest subgroup of $\\mathrm{Sym}(\\Omeg
a)$ with the same set of orbits on ordered pairs as $G$. We say that $G$ i
s 2-closed if $G$ is equal to its 2-closure. The automorphism group of a g
raph or digraph is a 2-closed group. In this talk I will discuss some rece
nt work with Luke Morgan and Jin-Xin Zhou on 2-closed groups that are not
the automorphism group of a graph or digraph.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Ferov (The University of Newcastle)
DTSTART:20210817T143000Z
DTEND:20210817T151500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/9
DESCRIPTION:Title: Automorphism groups of Cayley graphs of Coxeter groups - when are the
y discrete?\nby Michal Ferov (The University of Newcastle) as part of
BIRS workshop: Totally Disconnected Locally Compact Groups via Group Actio
ns\n\n\nAbstract\nWe give a full characterisation\, in term of symmetries
of the defining Coxeter system\, of finitely generated Coxeter groups for
which the group of automorphisms of the Cayley graph (with respect to the
standard generating set) is uncountable and therefore non-discrete with th
e permutation topology.\nI will sketch the main ideas of the proof and\, t
ime permitting\, I will mention results on rigidity.\n(Joint work with Fed
erico Berlai)\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Castellano (University of Milano-Bicocca)
DTSTART:20210817T153000Z
DTEND:20210817T161500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/10
DESCRIPTION:Title: The Euler characteristic and the zeta-functions of a totally disconn
ected locally compact group\nby Ilaria Castellano (University of Milan
o-Bicocca) as part of BIRS workshop: Totally Disconnected Locally Compact
Groups via Group Actions\n\n\nAbstract\nThe aim of this talk is to introdu
ce the Euler-Poincaré characteristic in the context of totally disconnect
ed locally compact (= TDLC) groups. For discrete groups\, such a character
istic is just an integer or a rational number but\, for TDLC-groups\, it b
ecomes a rational multiple of a Haar measure. This important invariant is
also (mysteriously) related to the value in -1 of a double-coset zeta func
tion that can be attached to a TDLC-group whenever a compact open subgroup
is selected. We will discuss the definition of this type of zeta-function
in detail.\nJoint work with Gianmarco Chinello and Thomas Weigel.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoran Sunic (Hofstra University)
DTSTART:20210817T163000Z
DTEND:20210817T171500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/11
DESCRIPTION:Title: Iterated monodromy groups of conservative polynomials (\nby Zora
n Sunic (Hofstra University) as part of BIRS workshop: Totally Disconnecte
d Locally Compact Groups via Group Actions\n\n\nAbstract\nThe notion of an
iterated monodromy group\, introduced by Nekrashevych\, is a natural exte
nsion of the classical monodromy group of a covering. A particularly inter
esting source of examples comes from post-critically finite rational/polyn
omial maps. In this talk\, we will recall the necessary definitions\, alon
g with a few well known examples\, and then present a treatment of the cla
ss of conservative polynomials\, introduced by Smale in his work on the Fu
ndamental Theorem of Algebra. Some of the iterated monodoromy groups of co
nservative polynomials are finitely generated\, dense subgroups in iterate
d wreath products of finite alternating groups and are branching over them
selves (that is\, as abstract groups\, they are finitely generated permuta
tional wreath products of themselves with an alternating group\, G=Alt(d)x
x(GxGx...xG))\, while the others are branching over a subgroup of index 2
(a parity issue related to the multiplicities of the critical points of th
e polynomial).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Skipper (Ohio State)
DTSTART:20210817T190000Z
DTEND:20210817T194500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/12
DESCRIPTION:Title: The scale function on Neretin’s group\nby Rachel Skipper (Ohio
State) as part of BIRS workshop: Totally Disconnected Locally Compact Gro
ups via Group Actions\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Waltraud Lederle (UCLouvain)
DTSTART:20210817T200000Z
DTEND:20210817T204500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/13
DESCRIPTION:Title: Conjugacy and dynamics in the almost automorphism group of a tree\nby Waltraud Lederle (UCLouvain) as part of BIRS workshop: Totally Disco
nnected Locally Compact Groups via Group Actions\n\n\nAbstract\nThe almost
automorphism group of a regular tree is one of the most important example
s in the theory of totally disconnected\, locally compact groups. In this
talk\, we explain how to determine whether two of its elements are conjuga
te or not\, combining results by Belk--Matucci and Gawron--Nekrashevych--S
ushchanskii.\nThis is joint work with Gil Goffer from the Weizmann Institu
te.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyi Zheng (UC San Diego)
DTSTART:20210817T210000Z
DTEND:20210817T214500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/14
DESCRIPTION:by Tianyi Zheng (UC San Diego) as part of BIRS workshop: Total
ly Disconnected Locally Compact Groups via Group Actions\n\nAbstract: TBA\
n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Segal (Oxford University)
DTSTART:20210818T143000Z
DTEND:20210818T151500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/15
DESCRIPTION:Title: Groups\, rings\, logic\nby Dan Segal (Oxford University) as part
of BIRS workshop: Totally Disconnected Locally Compact Groups via Group A
ctions\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aristotelis Panagiotopoulos (University of Münster)
DTSTART:20210818T153000Z
DTEND:20210818T161500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/16
DESCRIPTION:Title: Ulam stability for quotients of the p-adic groups\nby Aristoteli
s Panagiotopoulos (University of Münster) as part of BIRS workshop: Total
ly Disconnected Locally Compact Groups via Group Actions\n\n\nAbstract\nBa
sed on an earlier work of Shelah concerning the relationship \nof the cont
inuum hypothesis to the cardinality of the set of automorphisms \nof $\\ma
thcal{P}(\\omega)/\\mathrm{fin}$\, Velickovic showed that if such an \naut
omorphism admits a Borel lift $\\mathcal{P}(\\omega)\\to \n\\mathcal{P}(\\
omega)$\, then it is of a certain "trivial" form. Similarly\, \nKanovei an
d Reeken showed that if $N\,M$ are countable dense subgroups of \n$\\mathb
b{R}$\, then every homomorphism $\\mathbb{R}/N\\to \\mathbb{R}/M$ with \na
Borel lift $\\mathbb{R}\\to \\mathbb{R}$\, is of a certain "trivial" form
. \nKanovei and Reeken asked whether quotients of the $p$-adic groups sati
sfy \nsimilar "Ulam stability" phenomena. In this talk\, we will settle th
is \nquestion by providing Ulam-stability phenomena for definable homomorp
hisms \n$G/N\\to H/M$ when $G\,H$ are arbitrary abelian non-archimedean Po
lish \ngroups and $N\,M$ are Polishable subgroups. \n\nThis is joint work
with Jeffrey Bergfalk and Martino Lupini.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eilidh Mckemmie (Hebrew University of Jerusalem)
DTSTART:20210819T143000Z
DTEND:20210819T151500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/21
DESCRIPTION:Title: The probability of generating invariably a finite simple group\n
by Eilidh Mckemmie (Hebrew University of Jerusalem) as part of BIRS worksh
op: Totally Disconnected Locally Compact Groups via Group Actions\n\n\nAbs
tract\nWe say a group is invariably generated by a subset if every tuple i
n the product of conjugacy classes of elements in that subset is a generat
ing tuple.\nWe discuss the history of computational Galois theory and prob
abilistic generation problems to motivate some results about the probabili
ty of generating invariably a finite simple group\, joint work with Daniel
e Garzoni. We also highlight some methods for studying probabilistic invar
iable generation.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Thomas (Warwick University)
DTSTART:20210819T153000Z
DTEND:20210819T161500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/22
DESCRIPTION:Title: The classification of extremely primitive groups\nby Adam Thomas
(Warwick University) as part of BIRS workshop: Totally Disconnected Local
ly Compact Groups via Group Actions\n\n\nAbstract\nLet $G$ be a finite pri
mitive permutation group acting on a set $X$ with nontrivial point stabili
ser $G_x$. We say that $G$ is extremely primitive if $G_x$ acts primitivel
y on every orbit in $X\\setminus\\{x\\}$. These groups arise naturally in
several different contexts and their study can be traced back to work of M
anning in the 1920s. After surveying previous results\, we will discuss jo
int work with Tim Burness towards completing this classification dealing w
ith the almost simple groups with socle an exceptional group of Lie type.
We will describe the various techniques used in the proof and\, discuss th
e results we proved on bases for primitive actions of exceptional groups.\
n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aluna Rizzoli (University of Cambridge)
DTSTART:20210819T163000Z
DTEND:20210819T171500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/23
DESCRIPTION:Title: A double coset problem for classical groups\nby Aluna Rizzoli (U
niversity of Cambridge) as part of BIRS workshop: Totally Disconnected Loc
ally Compact Groups via Group Actions\n\n\nAbstract\nBuilding on the class
ification of modules for algebraic groups with finitely many orbits on sub
spaces\, we determine all irreducible modules for simple algebraic groups
that are self-dual and have finitely many orbits on totally singular $k$-s
paces ($k=1$ or $k=2$). This question is naturally connected with the prob
lem of finding for which pairs of subgroups $H$\, $J$ of an algebraic grou
p $G$ there are finitely many $(H\,J)$-double cosets. We provide a solutio
n to the question when $J$ is a maximal parabolic subgroup $P_k$ of a clas
sical group.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Stewart (Newcastle University)
DTSTART:20210819T173000Z
DTEND:20210819T181500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/24
DESCRIPTION:Title: The Jacobson–Morozov theorem (and characteristic 2)\nby David
Stewart (Newcastle University) as part of BIRS workshop: Totally Disconnec
ted Locally Compact Groups via Group Actions\n\n\nAbstract\n(jt with Adam
Thomas) The classical Jacobson–Morozov theorem guarantees that any nilpo
tent element $e$ in a semisimple complex Lie algebra $\\mathfrak g$ can be
extended to an $sl_2$-triple $(e\,h\,f)$ with $[h\,e]=2e$\, $[h\,f]=-2f$
and $[e\,f]=h$. This is a very useful theorem—for example in defining a
Slodowy slice. A theorem of Kostant tells you the $sl_2$-triple is even un
ique up to conjugacy by the simple complex algebraic group $G$ with $\\mat
hfrak g=\\rm{Lie}(G)$. Building on previous work of Pommerening\, Carter a
nd others\, Thomas and I gave precise conditions on the odd characteristic
for these results to hold. The appropriate analogue in characteristic $2$
is subtle since an $sl_2$-triple generates a (nilpotent) Heisenberg algeb
ra\; one can also consider a $pgl_2$-triple with $[h\,e]=e$\, $[h\,f]=f$ a
nd $[e\,f]=0$ having a $2$-dimensional abelian ideal\; lastly\, in charact
eristic $2$ there is a simple $3$-dimensional Lie algebra with $[e\,f]=h$\
, $[h\,e]=e$ and $[h\,f]=f$—‘fake $sl_2$’. We give complete answers
on the embeddings of $e$ into such subalgebras in all cases. An interestin
g waypoint is to classify the nilpotent elements admitting toral elements
$h$ with $[h\,e]=e$\, in other words\, to find the dimension of $$n_{\\mat
hfrak g}({\\rm span}(e))/c_{\\mathfrak g}(e)\,$$ which is an interesting p
roblem only in characteristic $2$.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Rosendal (University of Maryland)
DTSTART:20210819T203000Z
DTEND:20210819T211500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/25
DESCRIPTION:Title: Finite conjugacy classes and split exact cochain complexes\nby C
hristian Rosendal (University of Maryland) as part of BIRS workshop: Total
ly Disconnected Locally Compact Groups via Group Actions\n\n\nAbstract\nWe
will present the theory behind and new results on the cohomology of super
-reflexive Banach G-modules X\, where G is a countable discrete group. In
particular\, we shall show how the cohomology is controlled by the FC-cent
re of G\, that is\, the subgroup of elements having finite conjugacy class
es. For example\, using purely cohomological tools\, we show that when X i
s an isometric super-reflexive Banach G-module so that X has no almost inv
ariant unit vectors under the action of the FC-centre\, then the associate
d cochain complex is split exact. Further connections to the work of Bader
-Furman-Gelander-Monod\, Nowak\, and Bader-Rosendal-Sauer will be presente
d. We aim to start out slowly so that the talk should be accessible to the
general analyst\, geometer or group theorist.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Harper (University of Bristol)
DTSTART:20210820T143000Z
DTEND:20210820T151500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/26
DESCRIPTION:Title: Spread\, subgroups and Shintani descent\nby Scott Harper (Univer
sity of Bristol) as part of BIRS workshop: Totally Disconnected Locally Co
mpact Groups via Group Actions\n\n\nAbstract\nMany interesting and surpris
ing results have arisen from studying generating sets for groups. For exam
ple\, every finite simple group has a generating pair\, and\, moreover\, e
very nontrivial element is contained in a generating pair. I will discuss
recent work with Burness and Guralnick that completely classifies the fini
te groups where every nontrivial element is contained in a generating pair
and answers a 1975 question of Brenner and Wiegold. I will explain how th
is generation problem is related to interesting questions about subgroup s
tructure and how these questions can be addressed via the technique of Shi
ntani descent.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Burness (University of Bristol)
DTSTART:20210820T153000Z
DTEND:20210820T161500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/27
DESCRIPTION:Title: Bases for primitive permutation groups with restricted stabilisers\nby Tim Burness (University of Bristol) as part of BIRS workshop: Total
ly Disconnected Locally Compact Groups via Group Actions\n\n\nAbstract\nLe
t G be a finite primitive permutation group on a set X with point stabilis
er H and recall that a subset of X is a base if its pointwise stabiliser i
s trivial. The base size of G\, denoted b(G)\, is the minimal size of a ba
se. In this talk\, I will present several new results that give bounds on
b(G) under various structural restrictions on H. For example\, a theorem o
f Seress from 1996 states that if G is soluble then b(G) is at most 4 and
I have recently proved that b(G) is at most 5 if one only assumes that H i
s soluble (both bounds are best possible). I will report on some natural e
xtensions in joint work with Aner Shalev and time permitting\, I will pres
ent new results with Hongyi Huang on the Saxl graphs of base-two primitive
groups with soluble stabilisers.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anitha Thillaisundaram (University of Lincoln)
DTSTART:20210820T163000Z
DTEND:20210820T171500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/28
DESCRIPTION:Title: Maximal subgroups of groups acting on rooted trees\nby Anitha Th
illaisundaram (University of Lincoln) as part of BIRS workshop: Totally Di
sconnected Locally Compact Groups via Group Actions\n\n\nAbstract\nGroups
acting on rooted trees\, especially the so-called branch groups\, have bee
n vastly studied over the past few decades\, owing to their exotic propert
ies - in particular\, branch groups have been used to answer important ope
n problems and disprove conjectures. The study of maximal subgroups of bra
nch groups has recently picked up speed\, with new developments by Francoe
ur enabling one to study the maximal subgroups of the larger class of weak
ly branch groups. A prominent example of a weakly branch\, but not branch\
, group is the Basilica group. This was the first example of an amenable g
roup which is not subexponentially amenable. In this talk\, I will present
results concerning maximal subgroups of a family of generalised Basilica
groups. This is joint work with Karthika Rajeev.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Craven (University of Birmingham)
DTSTART:20210820T173000Z
DTEND:20210820T181500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/29
DESCRIPTION:Title: Maximal subgroups of finite simple groups\nby David Craven (Univ
ersity of Birmingham) as part of BIRS workshop: Totally Disconnected Local
ly Compact Groups via Group Actions\n\n\nAbstract\nIn this talk we will di
scuss the structure of maximal subgroups of\nfinite simple groups\, partic
ularly groups of Lie type. We will discuss\nsubgroups of exceptional group
s of Lie type\, and a version of Ennola\nduality that exists for groups of
Lie type\, which relates untwisted\nand twisted groups of Lie type.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Lee (University of Auckland)
DTSTART:20210818T010000Z
DTEND:20210818T014500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/30
DESCRIPTION:by Melissa Lee (University of Auckland) as part of BIRS worksh
op: Totally Disconnected Locally Compact Groups via Group Actions\n\nAbstr
act: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:C.R.E. Raja (Indian Statistical Institute)
DTSTART:20210818T020000Z
DTEND:20210818T024500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/31
DESCRIPTION:Title: Group actions and power maps\nby C.R.E. Raja (Indian Statistical
Institute) as part of BIRS workshop: Totally Disconnected Locally Compact
Groups via Group Actions\n\n\nAbstract\nLet Pk be the power map x↦xk on
a group G. We consider groups for which Pk has dense image or Pk is surje
ctive. We study the structure such groups via linear representations using
scale function and distality apart from general results from algebraic gr
oups/linear algebra/tdlc groups.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephan Tornier (The University of Newcastle)
DTSTART:20210819T213000Z
DTEND:20210819T221500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/32
DESCRIPTION:Title: A GAP package for self-replicating groups\nby Stephan Tornier (T
he University of Newcastle) as part of BIRS workshop: Totally Disconnected
Locally Compact Groups via Group Actions\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andre Nies (The University of Auckland)
DTSTART:20210820T010000Z
DTEND:20210820T014500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/33
DESCRIPTION:by Andre Nies (The University of Auckland) as part of BIRS wor
kshop: Totally Disconnected Locally Compact Groups via Group Actions\n\nAb
stract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Thomas (The University of Sydney)
DTSTART:20210819T010000Z
DTEND:20210819T014500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/34
DESCRIPTION:by Anne Thomas (The University of Sydney) as part of BIRS work
shop: Totally Disconnected Locally Compact Groups via Group Actions\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Saul Freedman (University of St Andrews)
DTSTART:20210819T020000Z
DTEND:20210819T024500Z
DTSTAMP:20260422T185106Z
UID:BIRS-21w5151/35
DESCRIPTION:Title: Non-commuting\, non-generating graphs of groups\nby Saul Freedma
n (University of St Andrews) as part of BIRS workshop: Totally Disconnecte
d Locally Compact Groups via Group Actions\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5151/35/
END:VEVENT
END:VCALENDAR