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BEGIN:VEVENT
SUMMARY:Ilir Snopche
DTSTART:20210203T160000Z
DTEND:20210203T170000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/1
DESCRIPTION:Title: Test elements and retracts in free groups\nby Ilir Snopche
as part of Online Seminar on Probabilistic and Geometric Group Theory\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aner Shalev (Einstein Institute of Mathematics)
DTSTART:20210217T160000Z
DTEND:20210217T170000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/2
DESCRIPTION:Title: Random Generation: from Groups to Algebras\nby Aner Shalev
(Einstein Institute of Mathematics) as part of Online Seminar on Probabili
stic and Geometric Group Theory\n\n\nAbstract\nThere has been considerable
interest in recent decades in questions of random generation of finite an
d profinite groups\, with emphasis on finite simple groups. In this talk\,
based on a recent joint work with Damian Sercombe\, we study similar noti
ons \nfor finite and profinite associative algebras.\n\nLet $A$ be a finit
e associative\, unital algebra over a (finite) field $k$. Let $P(A)$ be th
e probability that two random elements of $A$ \nwill generate $A$ as a uni
tal $k$-algebra. It is known that\, if $A$ is simple\, then $P(A) \\to 1$
as $|A| \\to \\infty$. We extend this result \nfor larger classes of finit
e associative algebras. For $A$ simple\, we estimate the growth rate of $P
(A)$ and find the best possible lower \nbound for it. We also study the r
andom generation of $A$ by two special elements. \n\nFinally\, we let $A$
be a profinite algebra over $k$. We show that $A$ is positively finitely g
enerated if and only if $A$ has polynomial \nmaximal subalgebra growth. Re
lated quantitative results are also obtained.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Raum (Stockholm University)
DTSTART:20210224T160000Z
DTEND:20210224T170000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/3
DESCRIPTION:Title: Why group theorists could care about operator algebras\nby
Sven Raum (Stockholm University) as part of Online Seminar on Probabilisti
c and Geometric Group Theory\n\n\nAbstract\nOne of the foundational reason
s to introduce operator algebras in the 1930's was the study of unitary re
presentation theory\, that is of a certain aspect of group theory. Ever si
nce\, group theory has provided important input and inspiration to operato
r algebraists. But what about group theorists? Why could they be intereste
d in developments and questions from the field of operator algebras?\n\nIn
this talk\, I will illustrate my personal perspective on what the answer
to this question could be. I will start by discussing selected historical
examples of successful interaction between the fields\, taking a birds per
spective. Only then\, I will rigorously introduce basic notations from ope
rator algebras. A sample question on the relation between discrete groups
and Polish groups comes forth from this discussion naturally. The final pa
rt of the talk will focus on recent development in C*-simplicity of discre
te groups\, which reveals new structure of groups and motivates questions
in purely group theoretical terms.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gábor Pete
DTSTART:20210310T160000Z
DTEND:20210310T170000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/4
DESCRIPTION:Title: Kazhdan groups have cost 1\nby Gábor Pete as part of Onlin
e Seminar on Probabilistic and Geometric Group Theory\n\n\nAbstract\nA pro
babilistic definition of groups with Kazhdan's property\n(T)\, due to Glas
ner & Weiss (1997)\, is that on any Cayley graph G of\nthe group\, for an
y ergodic group-invariant random black-and-white\ncolouring of the vertice
s\, with the density of each colour bounded\naway from 0\, the density of
edges connecting black to white vertices\nremains bounded away from zero.
Amenable groups and free groups do not\nhave property (T)\, while $SL_d(\\
mathbb{Z})$ with $d\\geq 3$ do.\n\nThe cost of a transitive graph is one h
alf of the infimum of the\nexpected degree of invariant connected spanning
subgraphs. Amenable\ntransitive graphs and Cayley graphs of $SL_d(\\mathb
b{Z})$ with $d\\geq 3$ have cost\n1\, while any Cayley graph of the free g
roup on d generators has cost\nd\, by Gaboriau (2000).\n\nA question of Ga
boriau aims to connect cost with the first $L^2$-Betti\nnumber of groups.
For Kazhdan groups\, the latter has been known to be\n0 since Bekka & Vale
tte (1997)\, and Gaboriau's question then suggests\nthat the cost of any i
nfinite Kazhdan Cayley graph should be 1. This\nis what we prove\, in join
t work with Tom Hutchcroft (Cambridge).\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Wilkes (University of Cambridge)
DTSTART:20210331T150000Z
DTEND:20210331T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/5
DESCRIPTION:Title: Coherence of random groups\nby Gareth Wilkes (University of
Cambridge) as part of Online Seminar on Probabilistic and Geometric Group
Theory\n\n\nAbstract\nAmong the many properties one would wish a group to
have is coherence: the property that every finitely generated subgroup is
finitely presented. Among the 2-dimensional hyperbolic groups\, which in
some senses are 'generic' groups\, coherence has been observed to have an
empirical connection with Euler characteristic: those groups which are kno
wn to be coherent have nonpositive Euler characteristic. In this talk I wi
ll discuss joint work with Kielak & R. Kropholler which makes this connect
ion probabilistic: a random group of negative Euler characteristic is cohe
rent with high probability.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandra Garrido
DTSTART:20210407T150000Z
DTEND:20210407T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/6
DESCRIPTION:Title: Locally compact topological full groups\nby Alejandra Garri
do as part of Online Seminar on Probabilistic and Geometric Group Theory\n
\n\nAbstract\nTopological (a.k.a piecewise) full groups of homeomorphisms
of the Cantor set are a source of interesting examples of infinite simple
groups. In the developing theory of totally disconnected locally compact (
t.d.l.c.) groups\, there is reason to look for examples that are simple an
d compactly generated. Piecewise full groups therefore seem an ideal place
to look. Indeed\, some well-known examples of compactly generated\, simpl
e\, t.d.l.c. groups belong to this class\, namely\, Neretin's group of alm
ost-automorphisms of a regular tree. I will report on joint work with Coli
n Reid and David Robertson on when and how piecewise full groups yield new
examples of compactly generated\, simple\, t.d.l.c. groups.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oren Becker (University of Cambridge)
DTSTART:20210414T150000Z
DTEND:20210414T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/7
DESCRIPTION:Title: Stability of approximate group actions\nby Oren Becker (Uni
versity of Cambridge) as part of Online Seminar on Probabilistic and Geome
tric Group Theory\n\n\nAbstract\nAn approximate unitary representation of
a group $G$ is a function $f$ from $G$ to $U(n)$ such that $f(gh)$ is clos
e to $f(g)f(h)$ for all g\,h. Is every approximate unitary representation
just a slight deformation of a unitary representation? The answer depends
on $G$ and on the norm on $U(n)$. If G is amenable\, the answer is positiv
e for the operator norm on $U(n)$ (Kazhdan '82). The answer remains positi
ve if we use the normalized Hilbert-Schmidt norm and allow a slight change
in the dimension $n$ (Gowers-Hatami '15\, De Chiffre-Ozawa-Thom '17). For
both norms\, the answer is negative if $G$ is a nonabelian free group (or
a nonelementary word-hyperbolic group). In this talk we shall discuss a s
imilar notion where $U(n)$ is replaced by $Sym(n)$ with the normalized Ham
ming metric. We study the cases where G is either free\, amenable or equal
to $SL_r(\\mathbb{Z})$\, $r>=3$. When $G$ is finite\, a slight variation
of our main theorem provides an efficient probabilistic algorithm to deter
mine whether a function $f$ from $G$ to $Sym(n)$ is close to a homomorphis
m when $|G|$ and n are both large. Based on a joint work with Michael Chap
man.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ndeye Coumba Sarr (University of Caen)
DTSTART:20210519T150000Z
DTEND:20210519T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/8
DESCRIPTION:Title: Almost amalgamated profinite groups\nby Ndeye Coumba Sarr (
University of Caen) as part of Online Seminar on Probabilistic and Geometr
ic Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Elek (Lancaster University)
DTSTART:20210602T150000Z
DTEND:20210602T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/9
DESCRIPTION:Title: Uniform amenability\nby Gabor Elek (Lancaster University) a
s part of Online Seminar on Probabilistic and Geometric Group Theory\n\n\n
Abstract\nAccording to the classical result\nof Connes\, Feldman and Weiss
\, measured\nhyperfiniteness of a group action is equivalent to measured
amenability.\nIn the Borel category it is known that hyperfiniteness\nim
plies amenability and it is conjectured that\nthe converse is true.\nBased
on the work of Anantharaman-Delaroche and Renault\,\none can introduce th
e notion of uniform amenability\, a strengthening\nof measured amenability
(it is a sort of exactness in the category\nof measurable actions\, so th
e famous Gromov-Osajda groups have\nno free uniformly amenable actions).
One can also introduce the\nnotion of uniform hyperfiniteness in a rather
natural way. \nWe prove that the two notions are equivalent provided that
the measurable action\nsatisfies a boundedness condition for the Radon-Ni
kodym derivative (e.g. in the case of Poisson boundaries).\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Berlai (University of Vienna)
DTSTART:20210609T150000Z
DTEND:20210609T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/10
DESCRIPTION:Title: Automorphism groups of Cayley graphs of Coxeter groups\nby
Federico Berlai (University of Vienna) as part of Online Seminar on Proba
bilistic and Geometric Group Theory\n\n\nAbstract\nIt is known that automo
rphism groups of locally finite graphs admit a totally disconnected locall
y compact (tdlc) topology. In this talk I will present some recent results
concerning automorphism groups of a particular class of locally finite gr
aphs\, that is of Cayley graphs of Coxeter groups. Particular attention wi
ll be given to the right-angled case.\nJoint work with Michal Ferov.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Moritz Petschick (HHU Düsseldorf)
DTSTART:20210616T150000Z
DTEND:20210616T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/11
DESCRIPTION:Title: The Basilica Operation\nby Jan Moritz Petschick (HHU Düss
eldorf) as part of Online Seminar on Probabilistic and Geometric Group The
ory\n\n\nAbstract\nThe Basilica group is a well-studied example of a group
of automorphisms of the dyadic rooted tree. We will explore the connectio
n between it and the binary odometer\, and derive a construction that allo
ws us to associate a family of Basilica groups to every group of automorph
isms of a rooted regular tree. We consider the inheritance properties of t
his construction\, and apply this to calculate the Hausdorff dimension of
some spinal groups. This is joint work with Karthika Rajeev.\n\n(Zoom info
rmation can be found on the seminar website)\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giles Gardam (WWU Münster)
DTSTART:20210623T150000Z
DTEND:20210623T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/12
DESCRIPTION:Title: Kaplansky's conjectures\nby Giles Gardam (WWU Münster) as
part of Online Seminar on Probabilistic and Geometric Group Theory\n\n\nA
bstract\nThree conjectures on group rings of torsion-free groups are commo
nly attributed to Kaplansky\, namely the unit\, zero divisor and idempoten
t conjectures. For example\, the zero divisor 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 each other and to other conjectures and
group properties\, and present my recent counterexample to the unit conje
cture.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ged Corob Cook
DTSTART:20210630T150000Z
DTEND:20210630T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/13
DESCRIPTION:Title: Counting irreducible modules for profinite groups\nby Ged
Corob Cook as part of Online Seminar on Probabilistic and Geometric Group
Theory\n\n\nAbstract\nWe say a profinite group G has UBERG if the number o
f irreducible G-modules of order k grows polynomially in k. This is equiva
lent to the completed group ring $\\hat{\\mathbb{Z}}[[G]]$ being generated
with positive probability by n random elements\, for some n (with respect
to the Haar measure). I will talk about recent work\, joint with S. Kionk
e and M. Vannacci\, where we give algebraic conditions for G to have UBERG
in terms of the sizes of the crown-based powers of monolithic primitive g
roups appearing as a quotient of G. As an application\, we show that UBERG
is not closed under extensions\, unlike G being positively finitely gener
ated (PFG). I will also discuss our work on a probabilistic version of the
type FP1 condition\, and some examples showing how these conditions relat
e to each other and to the PFG condition.\n\n(Zoom access information can
be found on the seminar website)\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominik Francoeur (ICMAT\, Madird)
DTSTART:20220303T160000Z
DTEND:20220303T170000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/14
DESCRIPTION:Title: The quasi-transitivity degree of branch groups\nby Dominik
Francoeur (ICMAT\, Madird) as part of Online Seminar on Probabilistic and
Geometric Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Spriano (University of Oxford)
DTSTART:20220325T150000Z
DTEND:20220325T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/18
DESCRIPTION:Title: Hyperbolic spaces for CAT(0) groups\nby Davide Spriano (Un
iversity of Oxford) as part of Online Seminar on Probabilistic and Geometr
ic Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Moraschini (University of Bologna)
DTSTART:20220506T140000Z
DTEND:20220506T150000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/20
DESCRIPTION:Title: New computations in bounded cohomology\nby Marco Moraschin
i (University of Bologna) as part of Online Seminar on Probabilistic and G
eometric Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balint Virag (University of Toronto)
DTSTART:20220617T140000Z
DTEND:20220617T150000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/21
DESCRIPTION:Title: Amenability of quadratic automata groups\nby Balint Virag
(University of Toronto) as part of Online Seminar on Probabilistic and Geo
metric Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Girodano Bruno (University of Udine)
DTSTART:20220610T140000Z
DTEND:20220610T150000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/22
DESCRIPTION:Title: Growth and entropy for group endomorphisms\nby Anna Giroda
no Bruno (University of Udine) as part of Online Seminar on Probabilistic
and Geometric Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ángel del Río (University of Murcia)
DTSTART:20220708T140000Z
DTEND:20220708T150000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/24
DESCRIPTION:Title: The Isomorphism Problem for group rings\nby Ángel del Rí
o (University of Murcia) as part of Online Seminar on Probabilistic and Ge
ometric Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andoni Zozaya (University of the Basque country\, Bilbao)
DTSTART:20221115T150000Z
DTEND:20221115T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/25
DESCRIPTION:Title: Degree of commutativity and wreath products\nby Andoni Zoz
aya (University of the Basque country\, Bilbao) as part of Online Seminar
on Probabilistic and Geometric Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Tointon (University of Bristol)
DTSTART:20221206T150000Z
DTEND:20221206T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/26
DESCRIPTION:Title: Transience of random walks on vertex-transitive graphs via gro
wth and isoperimetry in groups\nby Matthew Tointon (University of Bris
tol) as part of Online Seminar on Probabilistic and Geometric Group Theory
\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Witzel (University of Gießen)
DTSTART:20221220T150000Z
DTEND:20221220T160000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/27
DESCRIPTION:Title: Strong property (T) for Ã_2-lattices\nby Stefan Witzel (U
niversity of Gießen) as part of Online Seminar on Probabilistic and Geome
tric Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Ueki (Ochanomizu University\, Tokyo)
DTSTART:20240214T140000Z
DTEND:20240214T150000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/28
DESCRIPTION:Title: The p-adic limits of torsions in the Z-covers of knots\nby
Jun Ueki (Ochanomizu University\, Tokyo) as part of Online Seminar on Pro
babilistic and Geometric Group Theory\n\n\nAbstract\nWe investigate the p-
adic limit values of the torsion sizes of the 1st homology groups in the Z
-covers of knots. \nWe compare the results with the cases of elliptic curv
es and give a remark on an analogue of the Lang--Trotter conjecture (Elkie
s's theorem) for an infinite set of knots from the viewpoint of arithmetic
topology.\nThis talk is based on joint works with Hyuga Yoshizaki and Soh
ei Tateno.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Cumplido Cabello (University of Seville)
DTSTART:20240306T130000Z
DTEND:20240306T140000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/29
DESCRIPTION:Title: Genericity properties in braid groups\nby María Cumplido
Cabello (University of Seville) as part of Online Seminar on Probabilistic
and Geometric Group Theory\n\n\nAbstract\nRoughly speaking\, a property i
n a group is said to be generic if "almost every" element in the group has
this property. This concept has at least two different technical definiti
ons and finds several applications. We will focus on the generic propertie
s that have been studied in braid groups\, namely being pseudo-Anosov and
computational properties. Additionally\, we will explore how these propert
ies can impact the security of some braid-based cryptosystems.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Eberhard (Queen's University Belfast)
DTSTART:20240320T130000Z
DTEND:20240320T140000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/30
DESCRIPTION:by Sean Eberhard (Queen's University Belfast) as part of Onlin
e Seminar on Probabilistic and Geometric Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Bishop (University of Geneva)
DTSTART:20240417T120000Z
DTEND:20240417T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/31
DESCRIPTION:Title: On the subgroup membership problem in bounded automata groups<
/a>\nby Alex Bishop (University of Geneva) as part of Online Seminar on Pr
obabilistic and Geometric Group Theory\n\n\nAbstract\nThe class of bounded
automata groups includes many important examples of tree automorphism gro
ups such as the Grigorchuk group and the Gupta-Sidki groups. Given a finit
e generating set X for a group G\, the subgroup membership problem is then
stated as follows: given a description of some subgroups H of G\, compute
a description of all the words over X which evaluate to elements of the s
ubgroup H. Notice that the word problem is an instance of the subgroup mem
bership problem. In the literature\, subgroup membership problems have bee
n considered for finitely generated subgroups.\n\nWe extend what is known
by instead considering the infinitely generated subgroups of bounded autom
ata groups which can be specified as the stabiliser of quasi-periodic rays
. We show that for such subgroups\, the subgroup membership problem (and i
ts set complement) is an ET0L language\, that this ET0L language is effect
ively constructible\, and that membership to such subgroups is decidable.\
n\nThe techniques used in this work have applications to the study of the
word and coword problem of bounded automata groups.\n\nThis is joint work
with Daniele D'Angeli\, Francesco Matucci\, Tatiana Nagnibeda\, Davide Per
ego and Emanuele Rodaro.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guy Blachar (Bar-Ilan University)
DTSTART:20240522T120000Z
DTEND:20240522T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/32
DESCRIPTION:Title: Probabilistic laws on groups\nby Guy Blachar (Bar-Ilan Uni
versity) as part of Online Seminar on Probabilistic and Geometric Group Th
eory\n\n\nAbstract\nSuppose a finite group satisfies the following propert
y: If you take two random elements\, then with probability bigger than 5/8
they commute. Then this group is commutative.\nStarting from this well-kn
own result\, it is natural to ask: Do similar results hold for other laws
(p-groups\, nilpotent groups...)? Are there analogous results for infinite
groups? Are there phenomena specific to the infinite setup?\nWe will surv
ey known and new results in this area. New results are joint with Gideon A
mir\, Maria Gerasimova and Gady Kozma.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Eberhard (Belfast)
DTSTART:20240327T130000Z
DTEND:20240327T140000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/33
DESCRIPTION:Title: Diameter bounds for finite classical groups generated by speci
al elements\nby Sean Eberhard (Belfast) as part of Online Seminar on P
robabilistic and Geometric Group Theory\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Lucchini (University of Padova)
DTSTART:20240529T120000Z
DTEND:20240529T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/34
DESCRIPTION:Title: Solubilizers\, nilpotentizers and p-elements in profinite grou
ps\nby Andrea Lucchini (University of Padova) as part of Online Semina
r on Probabilistic and Geometric Group Theory\n\n\nAbstract\nLet C be a cl
ass of finite groups which is closed for subgroups\, quotients and direct
products. Given a profinite group G and an element x in G\, we are interes
ted in the probability that a randomly chosen element of G generates a pro
-C subgroup together with x.\n\nFor different choices of C\, we will discu
ss the following questions: is there a characterization of the elements of
G with the property that this probability is positive? what can be deduce
d about the structure of G if we know that this probability is positive fo
r all the elements of G?\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mireille Soergel (MPI Leipzig)
DTSTART:20240703T120000Z
DTEND:20240703T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/35
DESCRIPTION:Title: Dyer groups: Coxeter groups\, right-angled Artin groups and mo
re...\nby Mireille Soergel (MPI Leipzig) as part of Online Seminar on
Probabilistic and Geometric Group Theory\n\n\nAbstract\nDyer groups are a
family encompassing both Coxeter groups and right-\nangled Artin groups. I
ndeed these two classes of groups share many\nproperties: they have the sa
me solution to the word problem\,\nintersections of parabolic subgroups ar
e parabolic\, they are CAT(0)...\nSo which of those generalize to Dyer gro
ups? In this talk I will\nintroduce Dyer groups and give some of their pro
perties.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Toti (University of Milano Bicocca and University of the B
asque Country)
DTSTART:20250416T120000Z
DTEND:20250416T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/36
DESCRIPTION:Title: Measuring torsion in virtually free pro-p groups\nby Tomma
so Toti (University of Milano Bicocca and University of the Basque Country
) as part of Online Seminar on Probabilistic and Geometric Group Theory\n\
n\nAbstract\nGiven a profinite group G and a non-trivial word w on k-lette
rs\, we denote by P(G\,w) the probability that G satisfies w\, i.e. the no
rmalized Haar measure of the k-tuples of elements that satisfy the word. W
e say that w is a probabilistic identity on G if the associated probabilit
y is positive. In 2016\, M. Larsen and A. Shalev conjectured that a finite
ly generated residually finite group that satisfies a probabilistic identi
ty must satisfy some (in general different) identity.\n\nIn this talk\, we
will give a sufficient condition to have a conjugacy class of measure zer
o in a profinite group. Moreover\, we will discuss how to apply it to give
a positive answer to the aforementioned conjecture for torsion words in t
he class of virtually free pro-p groups. This is a joint work with Matteo
Vannacci and Thomas Weigel.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pooja Singla (IIT Kanpur)
DTSTART:20250430T120000Z
DTEND:20250430T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/37
DESCRIPTION:Title: On decomposition of the Gelfand-Graev modules of $GL_n(O)$
\nby Pooja Singla (IIT Kanpur) as part of Online Seminar on Probabilistic
and Geometric Group Theory\n\n\nAbstract\nLet F be a non-Archimedean local
field with the ring of integers $O$ and the residue field k\, where k is
finite of odd characteristic. \nWhile the representation of the finite gro
ups of Lie type $GL_n(k)$ and the p-adic groups $GL_n(F)$ are well explore
d\, the continuous representations \nof $GL_n(O)$ remain comparatively les
s understood. It is known that any finite-dimensional continuous represent
ation of $GL_n(O)$ arises from \nrepresentations of $GL_n(R)$\, where $R$
is a principal ideal local ring of finite length.\n\nIn this talk\, we wil
l examine the challenges involved in constructing irreducible representati
ons of $GL_n(R)$\, emphasizing the key differences from the \n$GL_n(k)$ ca
se. We will then turn our attention to the decomposition of the Gelfand–
Graev (GG) module for $GL_n(R)$. While the decomposition of the \nnon-dege
nerate GG modules is well understood and known to be multiplicity-free\, t
he structure of the degenerate GG modules remains largely \nunexplored. We
will discuss some recent results in this direction. This talk is based on
a joint work with Archita Gupta.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anitha Thillaisundaram (Lund University)
DTSTART:20250507T120000Z
DTEND:20250507T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/38
DESCRIPTION:Title: The Amit-Ashurst conjecture for finite metacyclic p-groups
\nby Anitha Thillaisundaram (Lund University) as part of Online Seminar on
Probabilistic and Geometric Group Theory\n\n\nAbstract\nThe Amit conjectu
re about word maps on finite nilpotent groups has been shown to hold for c
ertain classes of groups. The generalised Amit conjecture says that the pr
obability of an element occurring in the image of a word map on a finite n
ilpotent group G is either 0\, or at least 1/|G|. Noting the work of Ashur
st\, we name the generalised Amit conjecture the Amit-Ashurst conjecture a
nd show that the Amit-Ashurst conjecture holds for finite p-groups with a
cyclic maximal subgroup. This is joint work with Rachel Camina and William
Cocke.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Fariña Asategui (Lund University / University of the Basque
Country)
DTSTART:20250521T120000Z
DTEND:20250521T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/39
DESCRIPTION:Title: Torsion elements in branch pro-p groups\nby Jorge Fariña
Asategui (Lund University / University of the Basque Country) as part of O
nline Seminar on Probabilistic and Geometric Group Theory\n\n\nAbstract\nT
he class of branch groups was introduced by Grigorchuk in 1997 and it prov
ides easy to construct examples of Burnside groups\, i.e. finitely generat
ed infinite torsion groups. However\, by a deep result of Zelmanov\, torsi
on pro-p groups are locally finite. Therefore\, the closure of finitely ge
nerated branch p-groups\, such as the first Grigorchuk group\, must contai
n elements of infinite order even if the discrete group is torsion. We sha
ll see that\, in fact\, the set of torsion elements in a branch pro-p grou
p has Haar measure zero. This contrasts with the case of p-adic analytic p
ro-p groups\, where one can construct examples whose set of torsion elemen
ts have positive Haar measure.\n\nIn this talk\, we shall discuss the set
of torsion elements of branch pro-p groups and other subsets of measure ze
ro. This is joint work with Santiago Radi.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Sabatini (University of Warwick)
DTSTART:20250604T120000Z
DTEND:20250604T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/40
DESCRIPTION:Title: Probabilistic construction of wild p-groups\nby Luca Sabat
ini (University of Warwick) as part of Online Seminar on Probabilistic and
Geometric Group Theory\n\n\nAbstract\nIn the early 1960s\, Higman and Sim
s proved that for any fixed prime $p$ and large $m$\, there are roughly $p
^{\\frac{2}{27} m^3}$ nonisomorphic groups of order $p^m$. The lower bound
was obtained by counting the bilinear maps between two vector spaces. In
1978\, Ol'shanskii showed the existence of a bilinear map such that the co
rresponding group of order $p^m$ has no abelian subgroup of order greater
than $p^{\\sqrt{8m}}$. In this seminar we see that picking a random biline
ar map provides other wild $p$-groups\, namely $d$-maximal groups and $ab$
-maximal groups with large derived subgroups. This is joint work with S. E
berhard.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Uschold (University of Regensburg)
DTSTART:20250618T120000Z
DTEND:20250618T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/41
DESCRIPTION:Title: A dynamical upper bound on logarithmic torsion homology growth
\nby Matthias Uschold (University of Regensburg) as part of Online Sem
inar on Probabilistic and Geometric Group Theory\n\n\nAbstract\nWe introdu
ce an invariant of dynamical systems (i.e. a group acting on a probability
measure space). When considering the dynamical system given by the profin
ite completion\, this invariant is an upper bound to logarithmic torsion h
omology growth. I will explain why this dynamical viewpoint can be benefic
ial and explain the main ideas of a result that this invariant behaves ind
eed in a "dynamical" way. This is based on ongoing joint work with K. Li\,
C. Löh\, M. Moraschini and R. Sauer.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Loisel (Université de Poitiers)
DTSTART:20250917T120000Z
DTEND:20250917T130000Z
DTSTAMP:20260404T111409Z
UID:PGGTseminar/42
DESCRIPTION:Title: On maximal unipotent subgroups of some arithmetic subgroups th
rought action on a Bruhat-Tits building\nby Benoit Loisel (Université
de Poitiers) as part of Online Seminar on Probabilistic and Geometric Gro
up Theory\n\n\nAbstract\nLet $\\mathcal{C}$ be a smooth\, projective\, geo
metrically integral curve defined over a perfect field $\\mathbb{F}$ and l
et $k=\\mathbb{F}(\\mathcal{C})$ be its function field. If $\\mathbb{G}$ i
s a split simply connected semisimple $\\mathbb{Z}$-group scheme and $S$ i
s a non-empty finite set of places of $\\mathcal{C}$\, we can consider an
$S$-arithmetic subgroup $H\\subset \\mathbb{G}(k)$ (i.e. commensurable to
$\\mathbb{G}(\\mathcal{O}_S)$. In this talk\, by considering the natural a
ction of $H$ on the Borel $k$-subgroups of $\\mathbb{G}$\, we will see tha
t it is possible to describe the $H$-conjugacy classes of Borel $k$-subgro
ups in terms of the semi-simple $k$-rank of $\\mathbb{G}$ and of the Picar
d group of $\\mathcal{O}_S$. Such a conjugacy class precisely corresponds
to a conjugacy class of a maximal unipotent subgroup of $H$. In order to p
rovide a better understanding of $S$-arithmetic subgroups\, we will provid
e some elements of the action of such a group on its associated Bruhat-Tit
s. Then\, those maximal unipotent subgroups can be interpreted inside cert
ain stabilizer of germs at infinity.\n
LOCATION:https://stable.researchseminars.org/talk/PGGTseminar/42/
END:VEVENT
END:VCALENDAR