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BEGIN:VEVENT
SUMMARY:Alex Lubotzky (Hebrew University of Jerusalem)
DTSTART:20210816T143000Z
DTEND:20210816T151500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/1
DESCRIPTION:Title: Stability and testability of permutations' equations\nby A
lex Lubotzky (Hebrew University of Jerusalem) as part of BIRS workshop: To
tally Disconnected Locally Compact Groups via Group Actions\n\n\nAbstract\
nLet $A$ and $B$ be two permutations in $Sym(n)$ which "almost commute"- a
re they a small deformation of permutations that truly commute? More gener
ally\, if $R$ is a system of wards-equations in variables $X=x_1\,\\dots\,
x_d$ and \n$A_1\,\\dots\,A_d$ permutations which are nearly solution\; are
they near 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 will present a few results and methods which were developed in recent
years to check whether a group is stable\\testable. We will also describe
the connection 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://stable.researchseminars.org/talk/BIRS-21w5151/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariapia Moscatiello (University of Bologna)
DTSTART:20210816T151500Z
DTEND:20210816T161000Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/2
DESCRIPTION:Title: Bases of permutation groups and IBIS groups\nby Mariapia M
oscatiello (University of Bologna) as part of BIRS workshop: Totally Disco
nnected Locally Compact Groups via Group Actions\n\n\nAbstract\nLet $G$ be
a permutation group acting on a finite set $\\Omega$. A subset $\\mathcal
{B}$ of $\\Omega$ is called a base for $G$ if the pointwise stabilizer of
$\\mathcal{B}$ in $G$ is trivial. \n\nIn the 19th century\, bounding the
order of a finite primitive permutation group $G$ was a problem that attra
cted a lot of attention.\n Early investigations of bases then arose becaus
e 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 study of the base size to be a crucial area of current research in per
mutation groups. In this part of the talk\, we will investigate some of th
ese applications and review some results about base size. We will present
a recent improvement of a famous estimation due to Liebeck that estimates
the base size of a primitive permutation group in terms of its degree.\n\n
\n\n\nIn the second part of the talk\, we will define the concept of irred
undant bases of $G$ and the concept of IBIS groups. Whereas bases of minim
al size have been well studied\, irredundant bases and IBIS groups have no
t yet received a similar degree of attention. Indeed\, Cameron and Fon-Der
-Flaas\, already in 1995\, defined such groups and proposed to classify so
me meaningful families. But only this year\, a systematic investigation of
primitive permutation IBIS groups has been started. We will discuss how w
e reduced the classification of primitive IBIS groups to the almost simple
groups and affine groups. Eventually\, we will conclude by mentioning rec
ent advances towards a complete classification.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Liebeck (Imperial College)
DTSTART:20210816T163000Z
DTEND:20210816T171500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/3
DESCRIPTION:Title: Cherlin's conjecture on binary groups\nby Martin Liebeck (
Imperial College) as part of BIRS workshop: Totally Disconnected Locally C
ompact Groups via Group Actions\n\n\nAbstract\nA permutation group $G$ on
a set $X$ is called binary if the following condition holds: if $r > 2$ an
d \n$x\,y\\in X^r$ are $2$-equivalent $r$-tuples\, then $x$ and $y$ must b
e in the same $G$-orbit. Here we say $x = (x_1\,\\dots\,x_r)$ and $y = (y_
1\,\\cdots\,y_r)$ are $2$-equivalent if any pair $(x_i\,x_j)$ can be mappe
d to the corresponding pair $(y_i\,y_j)$ by an element of $G$. The definit
ion was coined by Gregory Cherlin as part of his theory of homogeneous str
uctures in model theory. Over 20 years ago\, Cherlin conjectured that the
all the finite primitive binary groups fall into three families: the full
symmetric groups $Sym(X)$\; cyclic groups of prime order\; and a certain c
lass of affine groups of dimension $1$ or $2$. In joint work with Nick Gil
l and Pablo Spiga\, we have completed the proof of this conjecture.\nIn th
e talk I will try to explain the point of the binary definition in relatio
n to model theory\, discuss various examples of binary groups\, and indica
te some of the strategies of the proof of the conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Tracey (University of Oxford)
DTSTART:20210816T173000Z
DTEND:20210816T181500Z
DTSTAMP:20260404T041448Z
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: Tota
lly Disconnected Locally Compact Groups via Group Actions\n\n\nAbstract\nA
classical result of Baer states that an element $x$ of a finite group $G$
is contained 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 the
re exists a positive integer $k$ such that $[g\,_k x] := [g\, x\, . . . \,
x]$ (with $x$ appearing\nk times\, and using the convention $[x_1 \, x_2
\, x_3 . . . \, x_k ] := [[. . . [[x_1 \, x_2 ]\, x_3 ]\, . . .]\, x_k ]$)
is trivial 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 the properties of these sets\, concluding with the proof\nof two con
jectures made in said paper. As a by-product of our methods\, we also prov
e a\ngeneralisation of a result of Flavell\, which itself generalises Wiel
andt’s Zipper Lemma and\nprovides a characterisation of subgroups contai
ned in a unique maximal subgroup. We also\nderive a number of consequences
of our theorems\, including some applications to the set of odd\norder el
ements of a finite group inverted by an involutory automorphism.\nWe will
finish the talk with some related work on the question: Which finite group
s $G$ can\nhave an element contained in a unique maximal subgroup of $G$?
All of this is joint work with\nR. M. Guralnick.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Reid (University of Newcastle)
DTSTART:20210816T190000Z
DTEND:20210816T194500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/5
DESCRIPTION:Title: In search of well-foundedness principles for totally disconnec
ted locally compact groups\nby Colin Reid (University of Newcastle) as
part of BIRS workshop: Totally Disconnected Locally Compact Groups via Gr
oup Actions\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 eve
n classify the groups: for example\, the order of a finite group\, or the
dimension of a Lie group. Closely related is the pervasive theme of decom
posing a group into "basic" or "irreducible" factors. How far can we get
with this approach in the class of totally disconnected locally compact se
cond-countable (t.d.l.c.s.c.) groups?\n\nI will describe a certain approac
h to structural complexity of t.d.l.c.s.c. groups that is inspired by deve
lopments in the area over the last ten years\, particularly the class of e
lementary groups introduced P. Wesolek in his 2014 PhD thesis. The latter
work shows that one can get a surprising amount of information from desce
nding chain conditions on subgroups\, and associated ordinal-valued rank f
unctions\, from a perspective that takes all compact groups and discrete g
roups as having small rank. I will give an example of a class of "well-fo
unded" groups with good closure properties that properly contains the elem
entary groups\, including for example all locally linear groups and many e
xamples of compactly generated simple groups acting on trees with Tits' in
dependence property\, but then also give a family of t.d.l.c.s.c. groups t
hat do not belong to this class.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Smith (University of Lincoln)
DTSTART:20210816T203000Z
DTEND:20210816T211500Z
DTSTAMP:20260404T041448Z
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://stable.researchseminars.org/talk/BIRS-21w5151/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Bamberg (University of Western Australia)
DTSTART:20210817T010000Z
DTEND:20210817T014500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/7
DESCRIPTION:Title: Orbits of Sylow p-subgroups of finite permutation groups\n
by John Bamberg (University of Western Australia) as part of BIRS workshop
: Totally Disconnected Locally Compact Groups via Group Actions\n\n\nAbstr
act\nWe say that a finite group G acting on a set X has Property (*)_p for
a prime p if the stabiliser of x in P is a Sylow p-subgroup of the stabil
iser of x in G\, for all x in X and Sylow p-subgroups P of G. Property (*)
_p arose in the recent work of Tornier (2018) on local Sylow p-subgroups o
f Burger-Mozes groups\, and he determined the values of p for which the al
ternating and symmetric groups in their natural actions have Property (*)_
p. In this talk\, we will explore the various properties of groups satisfy
ing (*)_p and extensions of Tornier's result\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Giudici (The University of Western Australia)
DTSTART:20210817T020000Z
DTEND:20210817T024500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/8
DESCRIPTION:Title: 2-closed groups and automorphism groups of digraphs\nby Mi
chael Giudici (The University of Western Australia) as part of BIRS worksh
op: Totally Disconnected Locally Compact Groups via Group Actions\n\n\nAbs
tract\nWielandt introduced the notion of the 2-closure of a permutation gr
oup $G$ on a set $\\Omega$. This is the largest subgroup of $\\mathrm{Sym}
(\\Omega)$ with the same set of orbits on ordered pairs as $G$. We say tha
t $G$ is 2-closed if $G$ is equal to its 2-closure. The automorphism group
of a graph or digraph is a 2-closed group. In this talk I will discuss so
me recent work with Luke Morgan and Jin-Xin Zhou on 2-closed groups that a
re not the automorphism group of a graph or digraph.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Ferov (The University of Newcastle)
DTSTART:20210817T143000Z
DTEND:20210817T151500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/9
DESCRIPTION:Title: Automorphism groups of Cayley graphs of Coxeter groups - when
are they discrete?\nby Michal Ferov (The University of Newcastle) as p
art of BIRS workshop: Totally Disconnected Locally Compact Groups via Grou
p Actions\n\n\nAbstract\nWe give a full characterisation\, in term of symm
etries of the defining Coxeter system\, of finitely generated Coxeter grou
ps for which the group of automorphisms of the Cayley graph (with respect
to the standard generating set) is uncountable and therefore non-discrete
with the permutation topology.\nI will sketch the main ideas of the proof
and\, time permitting\, I will mention results on rigidity.\n(Joint work w
ith Federico Berlai)\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Castellano (University of Milano-Bicocca)
DTSTART:20210817T153000Z
DTEND:20210817T161500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/10
DESCRIPTION:Title: The Euler characteristic and the zeta-functions of a totally
disconnected locally compact group\nby Ilaria Castellano (University o
f Milano-Bicocca) as part of BIRS workshop: Totally Disconnected Locally C
ompact Groups via Group Actions\n\n\nAbstract\nThe aim of this talk is to
introduce the Euler-Poincaré characteristic in the context of totally dis
connected locally compact (= TDLC) groups. For discrete groups\, such a ch
aracteristic is just an integer or a rational number but\, for TDLC-groups
\, it becomes a rational multiple of a Haar measure. This important invari
ant is also (mysteriously) related to the value in -1 of a double-coset ze
ta function that can be attached to a TDLC-group whenever a compact open s
ubgroup is selected. We will discuss the definition of this type of zeta-f
unction in detail.\nJoint work with Gianmarco Chinello and Thomas Weigel.\
n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoran Sunic (Hofstra University)
DTSTART:20210817T163000Z
DTEND:20210817T171500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/11
DESCRIPTION:Title: Iterated monodromy groups of conservative polynomials (\n
by Zoran Sunic (Hofstra University) as part of BIRS workshop: Totally Disc
onnected Locally Compact Groups via Group Actions\n\n\nAbstract\nThe notio
n of an iterated monodromy group\, introduced by Nekrashevych\, is a natur
al extension of the classical monodromy group of a covering. A particularl
y interesting source of examples comes from post-critically finite rationa
l/polynomial maps. In this talk\, we will recall the necessary definitions
\, along with a few well known examples\, and then present a treatment of
the class of conservative polynomials\, introduced by Smale in his work on
the Fundamental Theorem of Algebra. Some of the iterated monodoromy group
s of conservative polynomials are finitely generated\, dense subgroups in
iterated wreath products of finite alternating groups and are branching ov
er themselves (that is\, as abstract groups\, they are finitely generated
permutational wreath products of themselves with an alternating group\, G=
Alt(d)xx(GxGx...xG))\, while the others are branching over a subgroup of i
ndex 2 (a parity issue related to the multiplicities of the critical point
s of the polynomial).\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Skipper (Ohio State)
DTSTART:20210817T190000Z
DTEND:20210817T194500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/12
DESCRIPTION:Title: The scale function on Neretin’s group\nby Rachel Skippe
r (Ohio State) as part of BIRS workshop: Totally Disconnected Locally Comp
act Groups via Group Actions\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Waltraud Lederle (UCLouvain)
DTSTART:20210817T200000Z
DTEND:20210817T204500Z
DTSTAMP:20260404T041448Z
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: Totall
y Disconnected Locally Compact Groups via Group Actions\n\n\nAbstract\nThe
almost automorphism group of a regular tree is one of the most important
examples in the theory of totally disconnected\, locally compact groups. I
n this talk\, we explain how to determine whether two of its elements are
conjugate or not\, combining results by Belk--Matucci and Gawron--Nekrashe
vych--Sushchanskii.\nThis is joint work with Gil Goffer from the Weizmann
Institute.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyi Zheng (UC San Diego)
DTSTART:20210817T210000Z
DTEND:20210817T214500Z
DTSTAMP:20260404T041448Z
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://stable.researchseminars.org/talk/BIRS-21w5151/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Segal (Oxford University)
DTSTART:20210818T143000Z
DTEND:20210818T151500Z
DTSTAMP:20260404T041448Z
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 Actions\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aristotelis Panagiotopoulos (University of Münster)
DTSTART:20210818T153000Z
DTEND:20210818T161500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/16
DESCRIPTION:Title: Ulam stability for quotients of the p-adic groups\nby Ari
stotelis Panagiotopoulos (University of Münster) as part of BIRS workshop
: Totally Disconnected Locally Compact Groups via Group Actions\n\n\nAbstr
act\nBased on an earlier work of Shelah concerning the relationship \nof t
he continuum hypothesis to the cardinality of the set of automorphisms \no
f $\\mathcal{P}(\\omega)/\\mathrm{fin}$\, Velickovic showed that if such a
n \nautomorphism admits a Borel lift $\\mathcal{P}(\\omega)\\to \n\\mathca
l{P}(\\omega)$\, then it is of a certain "trivial" form. Similarly\, \nKan
ovei and Reeken showed that if $N\,M$ are countable dense subgroups of \n$
\\mathbb{R}$\, then every homomorphism $\\mathbb{R}/N\\to \\mathbb{R}/M$ w
ith \na Borel lift $\\mathbb{R}\\to \\mathbb{R}$\, is of a certain "trivia
l" form. \nKanovei and Reeken asked whether quotients of the $p$-adic grou
ps satisfy \nsimilar "Ulam stability" phenomena. In this talk\, we will se
ttle this \nquestion by providing Ulam-stability phenomena for definable h
omomorphisms \n$G/N\\to H/M$ when $G\,H$ are arbitrary abelian non-archime
dean Polish \ngroups and $N\,M$ are Polishable subgroups. \n\nThis is join
t work with Jeffrey Bergfalk and Martino Lupini.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eilidh Mckemmie (Hebrew University of Jerusalem)
DTSTART:20210819T143000Z
DTEND:20210819T151500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/21
DESCRIPTION:Title: The probability of generating invariably a finite simple grou
p\nby Eilidh Mckemmie (Hebrew University of Jerusalem) as part of BIRS
workshop: Totally Disconnected Locally Compact Groups via Group Actions\n
\n\nAbstract\nWe say a group is invariably generated by a subset if every
tuple in the product of conjugacy classes of elements in that subset is a
generating tuple.\nWe discuss the history of computational Galois theory a
nd probabilistic generation problems to motivate some results about the pr
obability of generating invariably a finite simple group\, joint work with
Daniele Garzoni. We also highlight some methods for studying probabilisti
c invariable generation.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Thomas (Warwick University)
DTSTART:20210819T153000Z
DTEND:20210819T161500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/22
DESCRIPTION:Title: The classification of extremely primitive groups\nby Adam
Thomas (Warwick University) as part of BIRS workshop: Totally Disconnecte
d Locally Compact Groups via Group Actions\n\n\nAbstract\nLet $G$ be a fin
ite primitive permutation group acting on a set $X$ with nontrivial point
stabiliser $G_x$. We say that $G$ is extremely primitive if $G_x$ acts pri
mitively on every orbit in $X\\setminus\\{x\\}$. These groups arise natura
lly in several different contexts and their study can be traced back to wo
rk of Manning in the 1920s. After surveying previous results\, we will dis
cuss joint work with Tim Burness towards completing this classification de
aling with the almost simple groups with socle an exceptional group of Lie
type. We will describe the various techniques used in the proof and\, dis
cuss the results we proved on bases for primitive actions of exceptional g
roups.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aluna Rizzoli (University of Cambridge)
DTSTART:20210819T163000Z
DTEND:20210819T171500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/23
DESCRIPTION:Title: A double coset problem for classical groups\nby Aluna Riz
zoli (University of Cambridge) as part of BIRS workshop: Totally Disconnec
ted Locally Compact Groups via Group Actions\n\n\nAbstract\nBuilding on th
e classification of modules for algebraic groups with finitely many orbits
on subspaces\, we determine all irreducible modules for simple algebraic
groups that are self-dual and have finitely many orbits on totally singula
r $k$-spaces ($k=1$ or $k=2$). This question is naturally connected with t
he problem of finding for which pairs of subgroups $H$\, $J$ of an algebra
ic group $G$ there are finitely many $(H\,J)$-double cosets. We provide a
solution to the question when $J$ is a maximal parabolic subgroup $P_k$ of
a classical group.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Stewart (Newcastle University)
DTSTART:20210819T173000Z
DTEND:20210819T181500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/24
DESCRIPTION:Title: The Jacobson–Morozov theorem (and characteristic 2)\nby
David Stewart (Newcastle University) as part of BIRS workshop: Totally Di
sconnected Locally Compact Groups via Group Actions\n\n\nAbstract\n(jt wit
h Adam Thomas) The classical Jacobson–Morozov theorem guarantees that an
y nilpotent 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 defi
ning a Slodowy slice. A theorem of Kostant tells you the $sl_2$-triple is
even unique up to conjugacy by the simple complex algebraic group $G$ with
$\\mathfrak g=\\rm{Lie}(G)$. Building on previous work of Pommerening\, C
arter and others\, Thomas and I gave precise conditions on the odd charact
eristic for these results to hold. The appropriate analogue in characteris
tic $2$ is subtle since an $sl_2$-triple generates a (nilpotent) Heisenber
g algebra\; one can also consider a $pgl_2$-triple with $[h\,e]=e$\, $[h\,
f]=f$ and $[e\,f]=0$ having a $2$-dimensional abelian ideal\; lastly\, in
characteristic $2$ 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 a
nswers on the embeddings of $e$ into such subalgebras in all cases. An int
eresting waypoint is to classify the nilpotent elements admitting toral el
ements $h$ with $[h\,e]=e$\, in other words\, to find the dimension of $$n
_{\\mathfrak g}({\\rm span}(e))/c_{\\mathfrak g}(e)\,$$ which is an intere
sting problem only in characteristic $2$.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Rosendal (University of Maryland)
DTSTART:20210819T203000Z
DTEND:20210819T211500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/25
DESCRIPTION:Title: Finite conjugacy classes and split exact cochain complexes\nby Christian Rosendal (University of Maryland) as part of BIRS workshop
: Totally Disconnected Locally Compact Groups via Group Actions\n\n\nAbstr
act\nWe will present the theory behind and new results on the cohomology o
f super-reflexive Banach G-modules X\, where G is a countable discrete gro
up. In particular\, we shall show how the cohomology is controlled by the
FC-centre of G\, that is\, the subgroup of elements having finite conjugac
y classes. For example\, using purely cohomological tools\, we show that w
hen X is an isometric super-reflexive Banach G-module so that X has no alm
ost invariant unit vectors under the action of the FC-centre\, then the as
sociated cochain complex is split exact. Further connections to the work o
f Bader-Furman-Gelander-Monod\, Nowak\, and Bader-Rosendal-Sauer will be p
resented. We aim to start out slowly so that the talk should be accessible
to the general analyst\, geometer or group theorist.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Harper (University of Bristol)
DTSTART:20210820T143000Z
DTEND:20210820T151500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/26
DESCRIPTION:Title: Spread\, subgroups and Shintani descent\nby Scott Harper
(University of Bristol) as part of BIRS workshop: Totally Disconnected Loc
ally Compact Groups via Group Actions\n\n\nAbstract\nMany interesting and
surprising results have arisen from studying generating sets for groups. F
or example\, every finite simple group has a generating pair\, and\, moreo
ver\, every nontrivial element is contained in a generating pair. I will d
iscuss recent work with Burness and Guralnick that completely classifies t
he finite groups where every nontrivial element is contained in a generati
ng pair and answers a 1975 question of Brenner and Wiegold. I will explain
how this generation problem is related to interesting questions about sub
group structure and how these questions can be addressed via the technique
of Shintani descent.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Burness (University of Bristol)
DTSTART:20210820T153000Z
DTEND:20210820T161500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/27
DESCRIPTION:Title: Bases for primitive permutation groups with restricted stabil
isers\nby Tim Burness (University of Bristol) as part of BIRS workshop
: Totally Disconnected Locally Compact Groups via Group Actions\n\n\nAbstr
act\nLet G be a finite primitive permutation group on a set X with point s
tabiliser H and recall that a subset of X is a base if its pointwise stabi
liser is trivial. The base size of G\, denoted b(G)\, is the minimal size
of a base. In this talk\, I will present several new results that give bou
nds on b(G) under various structural restrictions on H. For example\, a th
eorem of 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 t
hat H is soluble (both bounds are best possible). I will report on some na
tural extensions in joint work with Aner Shalev and time permitting\, I wi
ll present new results with Hongyi Huang on the Saxl graphs of base-two pr
imitive groups with soluble stabilisers.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anitha Thillaisundaram (University of Lincoln)
DTSTART:20210820T163000Z
DTEND:20210820T171500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/28
DESCRIPTION:Title: Maximal subgroups of groups acting on rooted trees\nby An
itha Thillaisundaram (University of Lincoln) as part of BIRS workshop: Tot
ally Disconnected Locally Compact Groups via Group Actions\n\n\nAbstract\n
Groups acting on rooted trees\, especially the so-called branch groups\, h
ave been vastly studied over the past few decades\, owing to their exotic
properties - in particular\, branch groups have been used to answer import
ant open problems and disprove conjectures. The study of maximal subgroups
of branch groups has recently picked up speed\, with new developments by
Francoeur enabling one to study the maximal subgroups of the larger class
of weakly branch groups. A prominent example of a weakly branch\, but not
branch\, group is the Basilica group. This was the first example of an ame
nable group which is not subexponentially amenable. In this talk\, I will
present results concerning maximal subgroups of a family of generalised Ba
silica groups. This is joint work with Karthika Rajeev.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Craven (University of Birmingham)
DTSTART:20210820T173000Z
DTEND:20210820T181500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/29
DESCRIPTION:Title: Maximal subgroups of finite simple groups\nby David Crave
n (University of Birmingham) as part of BIRS workshop: Totally Disconnecte
d Locally Compact Groups via Group Actions\n\n\nAbstract\nIn this talk we
will discuss the structure of maximal subgroups of\nfinite simple groups\,
particularly groups of Lie type. We will discuss\nsubgroups of exceptiona
l groups of Lie type\, and a version of Ennola\nduality that exists for gr
oups of Lie type\, which relates untwisted\nand twisted groups of Lie type
.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Lee (University of Auckland)
DTSTART:20210818T010000Z
DTEND:20210818T014500Z
DTSTAMP:20260404T041448Z
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://stable.researchseminars.org/talk/BIRS-21w5151/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:C.R.E. Raja (Indian Statistical Institute)
DTSTART:20210818T020000Z
DTEND:20210818T024500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/31
DESCRIPTION:Title: Group actions and power maps\nby C.R.E. Raja (Indian Stat
istical 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 surjective. We study the structure such groups via linear representatio
ns using scale function and distality apart from general results from alge
braic groups/linear algebra/tdlc groups.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephan Tornier (The University of Newcastle)
DTSTART:20210819T213000Z
DTEND:20210819T221500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/32
DESCRIPTION:Title: A GAP package for self-replicating groups\nby Stephan Tor
nier (The University of Newcastle) as part of BIRS workshop: Totally Disco
nnected Locally Compact Groups via Group Actions\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andre Nies (The University of Auckland)
DTSTART:20210820T010000Z
DTEND:20210820T014500Z
DTSTAMP:20260404T041448Z
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://stable.researchseminars.org/talk/BIRS-21w5151/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Thomas (The University of Sydney)
DTSTART:20210819T010000Z
DTEND:20210819T014500Z
DTSTAMP:20260404T041448Z
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://stable.researchseminars.org/talk/BIRS-21w5151/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Saul Freedman (University of St Andrews)
DTSTART:20210819T020000Z
DTEND:20210819T024500Z
DTSTAMP:20260404T041448Z
UID:BIRS-21w5151/35
DESCRIPTION:Title: Non-commuting\, non-generating graphs of groups\nby Saul
Freedman (University of St Andrews) as part of BIRS workshop: Totally Disc
onnected Locally Compact Groups via Group Actions\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5151/35/
END:VEVENT
END:VCALENDAR