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BEGIN:VEVENT
SUMMARY:Ilir Snopche
DTSTART:20210203T160000Z
DTEND:20210203T170000Z
DTSTAMP:20260422T225923Z
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\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aner Shalev (Einstein Institute of Mathematics)
DTSTART:20210217T160000Z
DTEND:20210217T170000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/2
DESCRIPTION:Title: Random Generation: from Groups to Algebras\nby Aner Shalev (Einste
in Institute of Mathematics) as part of Online Seminar on Probabilistic an
d Geometric Group Theory\n\n\nAbstract\nThere has been considerable intere
st in recent decades in questions of random generation of finite and profi
nite groups\, with emphasis on finite simple groups. In this talk\, based
on a recent joint work with Damian Sercombe\, we study similar notions \nf
or finite and profinite associative algebras.\n\nLet $A$ be a finite assoc
iative\, unital algebra over a (finite) field $k$. Let $P(A)$ be the proba
bility that two random elements of $A$ \nwill generate $A$ as a unital $k$
-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 finite assoc
iative algebras. For $A$ simple\, we estimate the growth rate of $P(A)$ an
d find the best possible lower \nbound for it. We also study the random g
eneration of $A$ by two special elements. \n\nFinally\, we let $A$ be a pr
ofinite algebra over $k$. We show that $A$ is positively finitely generate
d if and only if $A$ has polynomial \nmaximal subalgebra growth. Related q
uantitative results are also obtained.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Raum (Stockholm University)
DTSTART:20210224T160000Z
DTEND:20210224T170000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/3
DESCRIPTION:Title: Why group theorists could care about operator algebras\nby Sven Ra
um (Stockholm University) as part of Online Seminar on Probabilistic and G
eometric Group Theory\n\n\nAbstract\nOne of the foundational reasons to in
troduce operator algebras in the 1930's was the study of unitary represent
ation theory\, that is of a certain aspect of group theory. Ever since\, g
roup theory has provided important input and inspiration to operator algeb
raists. But what about group theorists? Why could they be interested in de
velopments and questions from the field of operator algebras?\n\nIn this t
alk\, I will illustrate my personal perspective on what the answer to this
question could be. I will start by discussing selected historical example
s of successful interaction between the fields\, taking a birds perspectiv
e. Only then\, I will rigorously introduce basic notations from operator a
lgebras. A sample question on the relation between discrete groups and Pol
ish groups comes forth from this discussion naturally. The final part of t
he talk will focus on recent development in C*-simplicity of discrete grou
ps\, which reveals new structure of groups and motivates questions in pure
ly group theoretical terms.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gábor Pete
DTSTART:20210310T160000Z
DTEND:20210310T170000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/4
DESCRIPTION:Title: Kazhdan groups have cost 1\nby Gábor Pete as part of Online Semin
ar on Probabilistic and Geometric Group Theory\n\n\nAbstract\nA probabilis
tic definition of groups with Kazhdan's property\n(T)\, due to Glasner &
Weiss (1997)\, is that on any Cayley graph G of\nthe group\, for any ergod
ic group-invariant random black-and-white\ncolouring of the vertices\, wit
h the density of each colour bounded\naway from 0\, the density of edges c
onnecting black to white vertices\nremains bounded away from zero. Amenabl
e 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 half of
the infimum of the\nexpected degree of invariant connected spanning subgra
phs. Amenable\ntransitive graphs and Cayley graphs of $SL_d(\\mathbb{Z})$
with $d\\geq 3$ have cost\n1\, while any Cayley graph of the free group on
d generators has cost\nd\, by Gaboriau (2000).\n\nA question of Gaboriau
aims to connect cost with the first $L^2$-Betti\nnumber of groups. For Kaz
hdan groups\, the latter has been known to be\n0 since Bekka & Valette (19
97)\, and Gaboriau's question then suggests\nthat the cost of any infinite
Kazhdan Cayley graph should be 1. This\nis what we prove\, in joint work
with Tom Hutchcroft (Cambridge).\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Wilkes (University of Cambridge)
DTSTART:20210331T150000Z
DTEND:20210331T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/5
DESCRIPTION:Title: Coherence of random groups\nby Gareth Wilkes (University of Cambri
dge) 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 i
s coherence: the property that every finitely generated subgroup is finite
ly presented. Among the 2-dimensional hyperbolic groups\, which in some se
nses are 'generic' groups\, coherence has been observed to have an empiric
al connection with Euler characteristic: those groups which are known to b
e coherent have nonpositive Euler characteristic. In this talk I will disc
uss joint work with Kielak & R. Kropholler which makes this connection pro
babilistic: a random group of negative Euler characteristic is coherent wi
th high probability.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandra Garrido
DTSTART:20210407T150000Z
DTEND:20210407T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/6
DESCRIPTION:Title: Locally compact topological full groups\nby Alejandra Garrido as p
art of Online Seminar on Probabilistic and Geometric Group Theory\n\n\nAbs
tract\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 and compa
ctly generated. Piecewise full groups therefore seem an ideal place to loo
k. Indeed\, some well-known examples of compactly generated\, simple\, t.d
.l.c. groups belong to this class\, namely\, Neretin's group of almost-aut
omorphisms of a regular tree. I will report on joint work with Colin Reid
and David Robertson on when and how piecewise full groups yield new exampl
es of compactly generated\, simple\, t.d.l.c. groups.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oren Becker (University of Cambridge)
DTSTART:20210414T150000Z
DTEND:20210414T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/7
DESCRIPTION:Title: Stability of approximate group actions\nby Oren Becker (University
of Cambridge) as part of Online Seminar on Probabilistic and Geometric Gr
oup 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 close 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 positive for t
he operator norm on $U(n)$ (Kazhdan '82). The answer remains positive if w
e 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 n
orms\, the answer is negative if $G$ is a nonabelian free group (or a none
lementary word-hyperbolic group). In this talk we shall discuss a similar
notion where $U(n)$ is replaced by $Sym(n)$ with the normalized Hamming me
tric. 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 determine wh
ether a function $f$ from $G$ to $Sym(n)$ is close to a homomorphism when
$|G|$ and n are both large. Based on a joint work with Michael Chapman.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ndeye Coumba Sarr (University of Caen)
DTSTART:20210519T150000Z
DTEND:20210519T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/8
DESCRIPTION:Title: Almost amalgamated profinite groups\nby Ndeye Coumba Sarr (Univers
ity of Caen) as part of Online Seminar on Probabilistic and Geometric Grou
p Theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Elek (Lancaster University)
DTSTART:20210602T150000Z
DTEND:20210602T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/9
DESCRIPTION:Title: Uniform amenability\nby Gabor Elek (Lancaster University) as part
of Online Seminar on Probabilistic and Geometric Group Theory\n\n\nAbstrac
t\nAccording to the classical result\nof Connes\, Feldman and Weiss\, meas
ured\nhyperfiniteness of a group action is equivalent to measured amenab
ility.\nIn the Borel category it is known that hyperfiniteness\nimplies a
menability and it is conjectured that\nthe converse is true.\nBased on the
work of Anantharaman-Delaroche and Renault\,\none can introduce the notio
n of uniform amenability\, a strengthening\nof measured amenability (it is
a sort of exactness in the category\nof measurable actions\, so the famou
s 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 me
asurable action\nsatisfies a boundedness condition for the Radon-Nikodym d
erivative (e.g. in the case of Poisson boundaries).\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Berlai (University of Vienna)
DTSTART:20210609T150000Z
DTEND:20210609T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/10
DESCRIPTION:Title: Automorphism groups of Cayley graphs of Coxeter groups\nby Federi
co Berlai (University of Vienna) as part of Online Seminar on Probabilisti
c and Geometric Group Theory\n\n\nAbstract\nIt is known that automorphism
groups of locally finite graphs admit a totally disconnected locally compa
ct (tdlc) topology. In this talk I will present some recent results concer
ning automorphism groups of a particular class of locally finite graphs\,
that is of Cayley graphs of Coxeter groups. Particular attention will be g
iven to the right-angled case.\nJoint work with Michal Ferov.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Moritz Petschick (HHU Düsseldorf)
DTSTART:20210616T150000Z
DTEND:20210616T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/11
DESCRIPTION:Title: The Basilica Operation\nby Jan Moritz Petschick (HHU Düsseldorf)
as part of Online Seminar on Probabilistic and Geometric Group Theory\n\n
\nAbstract\nThe Basilica group is a well-studied example of a group of aut
omorphisms of the dyadic rooted tree. We will explore the connection betwe
en it and the binary odometer\, and derive a construction that allows us t
o associate a family of Basilica groups to every group of automorphisms of
a rooted regular tree. We consider the inheritance properties of this con
struction\, and apply this to calculate the Hausdorff dimension of some sp
inal groups. This is joint work with Karthika Rajeev.\n\n(Zoom information
can be found on the seminar website)\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giles Gardam (WWU Münster)
DTSTART:20210623T150000Z
DTEND:20210623T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/12
DESCRIPTION:Title: Kaplansky's conjectures\nby Giles Gardam (WWU Münster) as part o
f Online Seminar on Probabilistic and Geometric Group Theory\n\n\nAbstract
\nThree conjectures on group rings of torsion-free groups are commonly att
ributed to Kaplansky\, namely the unit\, zero divisor and idempotent conje
ctures. 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 n
o zero divisors. I will survey what is known about the conjectures\, inclu
ding their relationships to each other and to other conjectures and group
properties\, and present my recent counterexample to the unit conjecture.\
n
LOCATION:https://researchseminars.org/talk/PGGTseminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ged Corob Cook
DTSTART:20210630T150000Z
DTEND:20210630T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/13
DESCRIPTION:Title: Counting irreducible modules for profinite groups\nby Ged Corob C
ook 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 of irred
ucible G-modules of order k grows polynomially in k. This is equivalent to
the completed group ring $\\hat{\\mathbb{Z}}[[G]]$ being generated with p
ositive probability by n random elements\, for some n (with respect to the
Haar measure). I will talk about recent work\, joint with S. Kionke and M
. Vannacci\, where we give algebraic conditions for G to have UBERG in ter
ms of the sizes of the crown-based powers of monolithic primitive groups a
ppearing as a quotient of G. As an application\, we show that UBERG is not
closed under extensions\, unlike G being positively finitely generated (P
FG). I will also discuss our work on a probabilistic version of the type F
P1 condition\, and some examples showing how these conditions relate to ea
ch other and to the PFG condition.\n\n(Zoom access information can be foun
d on the seminar website)\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominik Francoeur (ICMAT\, Madird)
DTSTART:20220303T160000Z
DTEND:20220303T170000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/14
DESCRIPTION:Title: The quasi-transitivity degree of branch groups\nby Dominik Franco
eur (ICMAT\, Madird) as part of Online Seminar on Probabilistic and Geomet
ric Group Theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Spriano (University of Oxford)
DTSTART:20220325T150000Z
DTEND:20220325T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/18
DESCRIPTION:Title: Hyperbolic spaces for CAT(0) groups\nby Davide Spriano (Universit
y of Oxford) as part of Online Seminar on Probabilistic and Geometric Grou
p Theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Moraschini (University of Bologna)
DTSTART:20220506T140000Z
DTEND:20220506T150000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/20
DESCRIPTION:Title: New computations in bounded cohomology\nby Marco Moraschini (Univ
ersity of Bologna) as part of Online Seminar on Probabilistic and Geometri
c Group Theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balint Virag (University of Toronto)
DTSTART:20220617T140000Z
DTEND:20220617T150000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/21
DESCRIPTION:Title: Amenability of quadratic automata groups\nby Balint Virag (Univer
sity of Toronto) as part of Online Seminar on Probabilistic and Geometric
Group Theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Girodano Bruno (University of Udine)
DTSTART:20220610T140000Z
DTEND:20220610T150000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/22
DESCRIPTION:Title: Growth and entropy for group endomorphisms\nby Anna Girodano Brun
o (University of Udine) as part of Online Seminar on Probabilistic and Geo
metric Group Theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ángel del Río (University of Murcia)
DTSTART:20220708T140000Z
DTEND:20220708T150000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/24
DESCRIPTION:Title: The Isomorphism Problem for group rings\nby Ángel del Río (Univ
ersity of Murcia) as part of Online Seminar on Probabilistic and Geometric
Group Theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andoni Zozaya (University of the Basque country\, Bilbao)
DTSTART:20221115T150000Z
DTEND:20221115T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/25
DESCRIPTION:Title: Degree of commutativity and wreath products\nby Andoni Zozaya (Un
iversity of the Basque country\, Bilbao) as part of Online Seminar on Prob
abilistic and Geometric Group Theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Tointon (University of Bristol)
DTSTART:20221206T150000Z
DTEND:20221206T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/26
DESCRIPTION:Title: Transience of random walks on vertex-transitive graphs via growth and
isoperimetry in groups\nby Matthew Tointon (University of Bristol) as
part of Online Seminar on Probabilistic and Geometric Group Theory\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Witzel (University of Gießen)
DTSTART:20221220T150000Z
DTEND:20221220T160000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/27
DESCRIPTION:Title: Strong property (T) for Ã_2-lattices\nby Stefan Witzel (Universi
ty of Gießen) as part of Online Seminar on Probabilistic and Geometric Gr
oup Theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Ueki (Ochanomizu University\, Tokyo)
DTSTART:20240214T140000Z
DTEND:20240214T150000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/28
DESCRIPTION:Title: The p-adic limits of torsions in the Z-covers of knots\nby Jun Ue
ki (Ochanomizu University\, Tokyo) as part of Online Seminar on Probabilis
tic and Geometric Group Theory\n\n\nAbstract\nWe investigate the p-adic li
mit 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 curves and
give a remark on an analogue of the Lang--Trotter conjecture (Elkies's the
orem) for an infinite set of knots from the viewpoint of arithmetic topolo
gy.\nThis talk is based on joint works with Hyuga Yoshizaki and Sohei Tate
no.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Cumplido Cabello (University of Seville)
DTSTART:20240306T130000Z
DTEND:20240306T140000Z
DTSTAMP:20260422T225923Z
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 Ge
ometric Group Theory\n\n\nAbstract\nRoughly speaking\, a property in a gro
up is said to be generic if "almost every" element in the group has this p
roperty. This concept has at least two different technical definitions and
finds several applications. We will focus on the generic properties that
have been studied in braid groups\, namely being pseudo-Anosov and computa
tional properties. Additionally\, we will explore how these properties can
impact the security of some braid-based cryptosystems.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Eberhard (Queen's University Belfast)
DTSTART:20240320T130000Z
DTEND:20240320T140000Z
DTSTAMP:20260422T225923Z
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://researchseminars.org/talk/PGGTseminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Bishop (University of Geneva)
DTSTART:20240417T120000Z
DTEND:20240417T130000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/31
DESCRIPTION:Title: On the subgroup membership problem in bounded automata groups\nby
Alex Bishop (University of Geneva) as part of Online Seminar on Probabili
stic and Geometric Group Theory\n\n\nAbstract\nThe class of bounded automa
ta groups includes many important examples of tree automorphism groups suc
h as the Grigorchuk group and the Gupta-Sidki groups. Given a finite gener
ating 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 desc
ription of all the words over X which evaluate to elements of the subgroup
H. Notice that the word problem is an instance of the subgroup membership
problem. In the literature\, subgroup membership problems have been consi
dered for finitely generated subgroups.\n\nWe extend what is known by inst
ead considering the infinitely generated subgroups of bounded automata gro
ups which can be specified as the stabiliser of quasi-periodic rays. We sh
ow that for such subgroups\, the subgroup membership problem (and its set
complement) is an ET0L language\, that this ET0L language is effectively c
onstructible\, and that membership to such subgroups is decidable.\n\nThe
techniques used in this work have applications to the study of the word an
d coword problem of bounded automata groups.\n\nThis is joint work with Da
niele D'Angeli\, Francesco Matucci\, Tatiana Nagnibeda\, Davide Perego and
Emanuele Rodaro.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guy Blachar (Bar-Ilan University)
DTSTART:20240522T120000Z
DTEND:20240522T130000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/32
DESCRIPTION:Title: Probabilistic laws on groups\nby Guy Blachar (Bar-Ilan University
) as part of Online Seminar on Probabilistic and Geometric Group Theory\n\
n\nAbstract\nSuppose a finite group satisfies the following property: If y
ou take two random elements\, then with probability bigger than 5/8 they c
ommute. Then this group is commutative.\nStarting from this well-known res
ult\, it is natural to ask: Do similar results hold for other laws (p-grou
ps\, nilpotent groups...)? Are there analogous results for infinite groups
? Are there phenomena specific to the infinite setup?\nWe will survey know
n and new results in this area. New results are joint with Gideon Amir\, M
aria Gerasimova and Gady Kozma.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Eberhard (Belfast)
DTSTART:20240327T130000Z
DTEND:20240327T140000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/33
DESCRIPTION:Title: Diameter bounds for finite classical groups generated by special elem
ents\nby Sean Eberhard (Belfast) as part of Online Seminar on Probabil
istic and Geometric Group Theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Lucchini (University of Padova)
DTSTART:20240529T120000Z
DTEND:20240529T130000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/34
DESCRIPTION:Title: Solubilizers\, nilpotentizers and p-elements in profinite groups\
nby Andrea Lucchini (University of Padova) as part of Online Seminar on Pr
obabilistic and Geometric Group Theory\n\n\nAbstract\nLet C be a class of
finite groups which is closed for subgroups\, quotients and direct product
s. Given a profinite group G and an element x in G\, we are interested in
the probability that a randomly chosen element of G generates a pro-C subg
roup together with x.\n\nFor different choices of C\, we will discuss the
following questions: is there a characterization of the elements of G with
the property that this probability is positive? what can be deduced about
the structure of G if we know that this probability is positive for all t
he elements of G?\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mireille Soergel (MPI Leipzig)
DTSTART:20240703T120000Z
DTEND:20240703T130000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/35
DESCRIPTION:Title: Dyer groups: Coxeter groups\, right-angled Artin groups and more...\nby Mireille Soergel (MPI Leipzig) as part of Online Seminar on Probabi
listic and Geometric Group Theory\n\n\nAbstract\nDyer groups are a family
encompassing both Coxeter groups and right-\nangled Artin groups. Indeed t
hese two classes of groups share many\nproperties: they have the same solu
tion to the word problem\,\nintersections of parabolic subgroups are parab
olic\, they are CAT(0)...\nSo which of those generalize to Dyer groups? In
this talk I will\nintroduce Dyer groups and give some of their properties
.\n
LOCATION:https://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:20260422T225923Z
UID:PGGTseminar/36
DESCRIPTION:Title: Measuring torsion in virtually free pro-p groups\nby Tommaso Toti
(University of Milano Bicocca and University of the Basque Country) as pa
rt of Online Seminar on Probabilistic and Geometric Group Theory\n\n\nAbst
ract\nGiven a profinite group G and a non-trivial word w on k-letters\, we
denote by P(G\,w) the probability that G satisfies w\, i.e. the normalize
d Haar measure of the k-tuples of elements that satisfy the word. We say t
hat w is a probabilistic identity on G if the associated probability is po
sitive. In 2016\, M. Larsen and A. Shalev conjectured that a finitely gene
rated residually finite group that satisfies a probabilistic identity must
satisfy some (in general different) identity.\n\nIn this talk\, we will g
ive a sufficient condition to have a conjugacy class of measure zero in a
profinite group. Moreover\, we will discuss how to apply it to give a posi
tive answer to the aforementioned conjecture for torsion words in the clas
s of virtually free pro-p groups. This is a joint work with Matteo Vannacc
i and Thomas Weigel.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pooja Singla (IIT Kanpur)
DTSTART:20250430T120000Z
DTEND:20250430T130000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/37
DESCRIPTION:Title: On decomposition of the Gelfand-Graev modules of $GL_n(O)$\nby Po
oja Singla (IIT Kanpur) as part of Online Seminar on Probabilistic and Geo
metric 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 groups of
Lie type $GL_n(k)$ and the p-adic groups $GL_n(F)$ are well explored\, the
continuous representations \nof $GL_n(O)$ remain comparatively less under
stood. It is known that any finite-dimensional continuous representation o
f $GL_n(O)$ arises from \nrepresentations of $GL_n(R)$\, where $R$ is a pr
incipal ideal local ring of finite length.\n\nIn this talk\, we will exami
ne the challenges involved in constructing irreducible representations of
$GL_n(R)$\, emphasizing the key differences from the \n$GL_n(k)$ case. 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-degenerate
GG modules is well understood and known to be multiplicity-free\, the stru
cture of the degenerate GG modules remains largely \nunexplored. We will d
iscuss some recent results in this direction. This talk is based on a join
t work with Archita Gupta.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anitha Thillaisundaram (Lund University)
DTSTART:20250507T120000Z
DTEND:20250507T130000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/38
DESCRIPTION:Title: The Amit-Ashurst conjecture for finite metacyclic p-groups\nby An
itha Thillaisundaram (Lund University) as part of Online Seminar on Probab
ilistic and Geometric Group Theory\n\n\nAbstract\nThe Amit conjecture abou
t word maps on finite nilpotent groups has been shown to hold for certain
classes of groups. The generalised Amit conjecture says that the probabili
ty of an element occurring in the image of a word map on a finite nilpoten
t group G is either 0\, or at least 1/|G|. Noting the work of Ashurst\, we
name the generalised Amit conjecture the Amit-Ashurst conjecture and 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://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:20260422T225923Z
UID:PGGTseminar/39
DESCRIPTION:Title: Torsion elements in branch pro-p groups\nby Jorge Fariña Asategu
i (Lund University / University of the Basque Country) as part of Online S
eminar on Probabilistic and Geometric Group Theory\n\n\nAbstract\nThe clas
s of branch groups was introduced by Grigorchuk in 1997 and it provides ea
sy to construct examples of Burnside groups\, i.e. finitely generated infi
nite torsion groups. However\, by a deep result of Zelmanov\, torsion pro-
p groups are locally finite. Therefore\, the closure of finitely generated
branch p-groups\, such as the first Grigorchuk group\, must contain eleme
nts of infinite order even if the discrete group is torsion. We shall see
that\, in fact\, the set of torsion elements in a branch pro-p group has H
aar measure zero. This contrasts with the case of p-adic analytic pro-p gr
oups\, where one can construct examples whose set of torsion elements have
positive Haar measure.\n\nIn this talk\, we shall discuss the set of tors
ion elements of branch pro-p groups and other subsets of measure zero. Thi
s is joint work with Santiago Radi.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Sabatini (University of Warwick)
DTSTART:20250604T120000Z
DTEND:20250604T130000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/40
DESCRIPTION:Title: Probabilistic construction of wild p-groups\nby Luca Sabatini (Un
iversity of Warwick) as part of Online Seminar on Probabilistic and Geomet
ric Group Theory\n\n\nAbstract\nIn the early 1960s\, Higman and Sims prove
d that for any fixed prime $p$ and large $m$\, there are roughly $p^{\\fra
c{2}{27} m^3}$ nonisomorphic groups of order $p^m$. The lower bound was ob
tained by counting the bilinear maps between two vector spaces. In 1978\,
Ol'shanskii showed the existence of a bilinear map such that the correspon
ding 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 bilinear map
provides other wild $p$-groups\, namely $d$-maximal groups and $ab$-maxima
l groups with large derived subgroups. This is joint work with S. Eberhard
.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Uschold (University of Regensburg)
DTSTART:20250618T120000Z
DTEND:20250618T130000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/41
DESCRIPTION:Title: A dynamical upper bound on logarithmic torsion homology growth\nb
y Matthias Uschold (University of Regensburg) as part of Online Seminar on
Probabilistic and Geometric Group Theory\n\n\nAbstract\nWe introduce an i
nvariant of dynamical systems (i.e. a group acting on a probability measur
e space). When considering the dynamical system given by the profinite com
pletion\, this invariant is an upper bound to logarithmic torsion homology
growth. I will explain why this dynamical viewpoint can be beneficial and
explain the main ideas of a result that this invariant behaves indeed in
a "dynamical" way. This is based on ongoing joint work with K. Li\, C. Lö
h\, M. Moraschini and R. Sauer.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Loisel (Université de Poitiers)
DTSTART:20250917T120000Z
DTEND:20250917T130000Z
DTSTAMP:20260422T225923Z
UID:PGGTseminar/42
DESCRIPTION:Title: On maximal unipotent subgroups of some arithmetic subgroups throught
action on a Bruhat-Tits building\nby Benoit Loisel (Université de Poi
tiers) as part of Online Seminar on Probabilistic and Geometric Group Theo
ry\n\n\nAbstract\nLet $\\mathcal{C}$ be a smooth\, projective\, geometrica
lly integral curve defined over a perfect field $\\mathbb{F}$ and let $k=\
\mathbb{F}(\\mathcal{C})$ be its function field. If $\\mathbb{G}$ is a spl
it simply connected semisimple $\\mathbb{Z}$-group scheme and $S$ is a non
-empty finite set of places of $\\mathcal{C}$\, we can consider an $S$-ari
thmetic subgroup $H\\subset \\mathbb{G}(k)$ (i.e. commensurable to $\\math
bb{G}(\\mathcal{O}_S)$. In this talk\, by considering the natural action o
f $H$ on the Borel $k$-subgroups of $\\mathbb{G}$\, we will see that it is
possible to describe the $H$-conjugacy classes of Borel $k$-subgroups in
terms of the semi-simple $k$-rank of $\\mathbb{G}$ and of the Picard group
of $\\mathcal{O}_S$. Such a conjugacy class precisely corresponds to a co
njugacy class of a maximal unipotent subgroup of $H$. In order to provide
a better understanding of $S$-arithmetic subgroups\, we will provide some
elements of the action of such a group on its associated Bruhat-Tits. Then
\, those maximal unipotent subgroups can be interpreted inside certain sta
bilizer of germs at infinity.\n
LOCATION:https://researchseminars.org/talk/PGGTseminar/42/
END:VEVENT
END:VCALENDAR