Cal
egary and Freedman showed that many homeomorphisms are distorted\, However
\, in general\, \\(C^1\\) diffeomorphisms are not\, for instance due to th
e existence of hyperbolic fixed points. Studying similar phenomena in high
er regularity turns out to be interesting in the context of elliptic dynam
ics. In particular\, we may address the following question: Given \\(r>\
;s>\;1\\)\, does there exist undistorted \\(C^r\\) diffeomorphisms that
are distorted inside the group of \\(C^s\\) diffeomorphisms? After a gener
al discussion\, we will focus on the 1–dimensional case of this question
for \\(r=2\\) and \\(s=1\\)\, for which we solve it in the affirmative vi
a the introduction of a new invariant\, namely the asymptotic variation.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florin Radulescu (IMAR and Rome)
DTSTART;VALUE=DATE-TIME:20220602T100000Z
DTEND;VALUE=DATE-TIME:20220602T104500Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/22
DESCRIPTION:Title: Dimension formulae of Gelfand-Graev\, Jones and their relation to automo
rphic forms and temperdness of quasiregular representations\nby Florin
Radulescu (IMAR and Rome) as part of Vienna Geometry and Analysis on Grou
ps Seminar\n\n\nAbstract\nVaughan Jones introduced a formula computing the
von Neumann dimension for the restriction to a lattice of the left regula
r representation of a semisimple Lie group.\n\nIt is a variant of a formul
a by Atiah Schmidt computing the formal dimension in the Haris Chandra t
race formula for discrete series. It is surprisingly similar (in the case
of PSL(2\,Z)) to the dimension of the space of automorphic forms and is si
milar to a formula proved by Gelfand\, Graev. We use an extension of this
formula to provide a method for computing the formal trace of representat
ions of PSL(2\,Q_p) (or more general situations)\, when analyzing the quas
i regular representation on PSL(2\,R)/PSL(2\,Z). It provides a method to o
btain estimates for eigenvalues of Hecke operators.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annette Karrer (McGill)
DTSTART;VALUE=DATE-TIME:20221004T130000Z
DTEND;VALUE=DATE-TIME:20221004T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/23
DESCRIPTION:Title: Contracting boundaries of right-angled Coxeter and Artin groups\nby
Annette Karrer (McGill) as part of Vienna Geometry and Analysis on Groups
Seminar\n\n\nAbstract\nA complete CAT(0) space has a topological space ass
ociated to it called the contracting or Morse boundary. This boundary capt
ures how similar the CAT(0) space is to a hyperbolic space. Charney--Sulta
n proved this boundary is a quasi-isometry invariant\, i.e. it can be defi
ned for CAT(0) groups. Interesting examples arise among contracting bounda
ries of right-anlged Artin and Coxeter groups. \n\nThe talk will consist o
f two parts. The first 45 minutes will be about the main result of my PhD
project. We will study the question of how the contracting boundary of a r
ight-connected Coxeter group changes when we glue certain graphs on its de
fining graph. We will focus on the question of when the resulting graph co
rresponds to a right-angled Coxeter group with totally disconnected contra
cting boundary. \n\nAfter a short break\, we will see a second result of
my PhD thesis concerning the question of what happens if we glue a path of
length at least two to a defining graph of a RACG. Afterwards\, we will u
se our insights to investigate contracting boundaries of certain RACGs t
hat contain surprising circles. These examples are joint work with Marius
Graeber\, Nir Lazarovich\, and Emily Stark. Finally\, we will transfer the
ideas we saw before to RAAGs. This will result in a proof that all right-
angled Artin groups have totally disconnected contracting boundaries\, rep
roving a result of Charney--Cordes--Sisto.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Emmanuel Caprace (UC Louvain)
DTSTART;VALUE=DATE-TIME:20221011T130000Z
DTEND;VALUE=DATE-TIME:20221011T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/24
DESCRIPTION:Title: New Kazhdan groups with infinitely many alternating quotients\nby Pi
erre-Emmanuel Caprace (UC Louvain) as part of Vienna Geometry and Analysis
on Groups Seminar\n\n\nAbstract\nIntroductory talk: "Generating the alter
nating groups"\n\nAbstract: The goal of this talk is to provide an overvie
w of results and methods allowing one to build generating sets for the fin
ite alternating groups. Some of those rely on the Classification of the Fi
nite Simple Groups\, others don't. This theme will be motivated by open pr
oblems concerning the construction of finite quotients of certain families
of finitely generated infinite groups. \n\nResearch talk: "New Kazhdan gr
oups with infinitely many alternating quotients"\n\nAbstract: I will intro
duce a new class of infinite groups enjoying Kazhdan's property (T) and ad
mitting alternating group quotients of arbitrarily large degree. Those gro
ups are constructed as automorphism groups of the ring of polynomials in n
indeterminates with coefficients in the finite field of order p\, generat
ed by a suitable finite set of polynomial transvections. As an application
\, we obtain the first examples of hyperbolic Kazdhan groups with infinite
ly many alternating group quotients. We also obtain expander Cayley graphs
of degree 4 for an infinite family of alternating groups. The talk is bas
ed on joint work with Martin Kassabov.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xabier Legaspi (ICMAT and IRMAR)
DTSTART;VALUE=DATE-TIME:20221018T130000Z
DTEND;VALUE=DATE-TIME:20221018T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/25
DESCRIPTION:Title: Constricting elements and the growth of quasi-convex subgroups\nby X
abier Legaspi (ICMAT and IRMAR) as part of Vienna Geometry and Analysis on
Groups Seminar\n\nLecture held in SR 10\, 2. OG.\, OMP 1.\n\nAbstract\nLe
t \\(G\\) be a group acting properly on a metric space \\(X\\) and conside
r a path system of \\(X\\). Assume that \\(G\\) contains a constricting el
ement with respect to this path system\, i.e. a very general condition of
non-positive curvature. This talk will be about the relative growth and th
e coset growth of the quasi-convex subgroups of \\(G\\) with respect to th
is path system. Through the triangle inequality\, we will see that we can
determine that the first kind of growth rates are strictly smaller than th
e growth rate of \\(G\\)\, while the second kind of growth rates coincide
with the growth rate of \\(G\\). Applications include actions of relativel
y hyperbolic groups\, CAT(0) groups with Morse elements and mapping class
groups. This generalises work of Antolín\, Dahmani-Futer-Wise and Gitik-R
ips.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tullio Ceccherini-Silberstein (U. Sannio)
DTSTART;VALUE=DATE-TIME:20221025T130000Z
DTEND;VALUE=DATE-TIME:20221025T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/26
DESCRIPTION:Title: Sofic entropy and surjunctive dynamical systems\nby Tullio Ceccherin
i-Silberstein (U. Sannio) as part of Vienna Geometry and Analysis on Group
s Seminar\n\nLecture held in SR 10\, 2. OG.\, OMP 1.\n\nAbstract\nA dynami
cal system is a pair \\((X\,G)\\)\, where \\(X\\) is a compact metrizable
space and \\(G\\) is a countable group acting by homeomorphisms of \\(X\\)
. An endomorphism of \\((X\,G)\\) is a continuous selfmap of \\(X\\) which
commutes with the action of \\(G\\). A dynamical system \\((X\, G)\\) is
said to be surjunctive if every injective endomorphism of \\((X\,G)\\) is
surjective. When the group \\(G\\) is sofic\, the combination of suitable
dynamical properties (such as expansivity\, nonnegative sofic topological
entropy\, weak specification\, and strong topological Markov property) gua
rantees that (X\,G) is surjunctive. I'll explain in detail all notions inv
olved\, the motivations\, and outline the main ideas of the proof of this
result obtained in collaboration with Michel Coornaert and Hanfeng Li.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Slofstra (Waterloo)
DTSTART;VALUE=DATE-TIME:20221108T140000Z
DTEND;VALUE=DATE-TIME:20221108T160000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/27
DESCRIPTION:Title: Group theory and nonlocal games\nby William Slofstra (Waterloo) as p
art of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nNonlo
cal games are simple games used in quantum information to explore the powe
r of entanglement. They are closely connected with Bell inequalities\, whi
ch have been in the news recently as the subject of this year's Nobel priz
e in physics. In this talk\, I'll give an overview of a class of nonlocal
games called linear system nonlocal games\, which are particularly interes
ting from the point of view of group theory\, in that every linear system
nonlocal games has an associated group which controls the perfect strategi
es for the game. The associated groups are finite colimits of finite abeli
an groups\, and exploring this class of groups from the perspective of non
local games gives rise to a number of interesting results and problems in
group theory. For the introductory talk\, I'll cover some of the backgroun
d concepts that come up: pictures of groups\, residual finiteness\, and hy
perlinearity (if time permits\, I may sketch the construction of a group w
ith superpolynomial hyperlinear profile).\n
LOCATION:https://researchseminars.org/talk/WienGAGT/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Motiejus Valiunas (Wrocław)
DTSTART;VALUE=DATE-TIME:20221213T140000Z
DTEND;VALUE=DATE-TIME:20221213T160000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/28
DESCRIPTION:Title: Biautomatic and hierarchically hyperbolic groups\nby Motiejus Valiun
as (Wrocław) as part of Vienna Geometry and Analysis on Groups Seminar\n\
n\nAbstract\nBiautomatic groups arose as groups explaining formal language
-theoretic aspects of geodesics in word-hyperbolic groups. Many classes o
f non-positively curved finitely generated groups\, such as hyperbolic\, v
irtually abelian\, cocompactly cubulated\, small cancellation and Coxeter
groups\, are known to be biautomatic. On the other hand\, there are some
other classes\, such as CAT(0) or hierarchically hyperbolic groups\, for w
hich the relationship to biautomaticity is more complicated.\n\nIn the fir
st half of the talk\, I will outline the notions of non-positive curvature
appearing in group theory and their connection to biautomaticity. In par
ticular\, I will overview recent results on the relationship between biaut
omaticity\, hierarchical hyperbolicity and being CAT(0)\, as well as some
constructions of non-biautomatic non-positively curved groups.\n\nThe goal
of the second half of the talk is to construct a non-biautomatic hierarch
ically hyperbolic group\, giving the first known example of such a group.
Our group acts geometrically on the cartesian product of a tree and the h
yperbolic plane\, and therefore satisfies many nice geometric properties.
The proof of non-biautomaticity will rely on the study of geodesic curren
ts on a closed hyperbolic surface. The talk is based on joint work with S
am Hughes.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Koberda (Virginia)
DTSTART;VALUE=DATE-TIME:20221115T140000Z
DTEND;VALUE=DATE-TIME:20221115T160000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/29
DESCRIPTION:Title: Model theory of the curve graph\nby Thomas Koberda (Virginia) as par
t of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nIntrodu
ctory talk: Automorphisms of the curve graph and related objects\n\nAbstra
ct: I will give a brief introduction to Ivanov's result on the automorphis
m group of the curve graph\, and survey some related results.\n\nResearch
talk: Model theory of the curve graph\n\nAbstract: I will describe some no
vel approaches to investigating the combinatorial topology of surfaces thr
ough model theoretic means. I will give a model theoretic explanation of h
ow a myriad of objects that are naturally associated to a surface are inte
rpretable inside of the curve graph\, and how this provides a new perspect
ive on a certain metaconjecture due to Ivanov. I will also discuss some of
the properties of the theory of the curve graph\, including stability and
quantifier elimination. This talk represents joint work with V. Disarlo a
nd J. de la Nuez Gonzalez.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pilar Páez Guillán (Vienna)
DTSTART;VALUE=DATE-TIME:20230110T140000Z
DTEND;VALUE=DATE-TIME:20230110T160000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/30
DESCRIPTION:Title: Counterexamples to the Zassenhaus conjecture on simple modular Lie algeb
ras\nby Pilar Páez Guillán (Vienna) as part of Vienna Geometry and A
nalysis on Groups Seminar\n\n\nAbstract\nHistorically\, the study of the (
outer) automorphism group of a given group (free\, simple...) has interest
ed group-theorists\, topologists and geometers\, and consequently it is al
so of great importance in the Lie algebra theory. In this talk\, we will b
riefly revise some of the connections between groups and Lie algebras befo
re giving a quick overview of the simple Lie algebras of classical and Car
tan type over fields of positive characteristic. After that\, we will comp
are the Schreier and Zassenhaus conjectures on the solvability of \\(\\mat
hrm{Out}(G)\\) (resp. \\(\\mathrm{Out}(L)\\))\, the group of outer automor
phisms (resp. the Lie algebra of outer derivations) of a finite simple gro
up \\(G\\) (resp. a finite-dimensional simple Lie algebra \\(L\\)). While
the former is known to be true as a consequence of the classification of f
inite simple groups\, the latter is false over fields of small characteris
tic \\(p=2\,3\\). We will finish the talk by presenting a new family of co
unterexamples to the Zassenhaus conjecture over fields of characteristic \
\(p=3\\)\, as well as commenting some advances for \\(p=2\\).\n
LOCATION:https://researchseminars.org/talk/WienGAGT/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Cashen (Vienna)
DTSTART;VALUE=DATE-TIME:20221122T140000Z
DTEND;VALUE=DATE-TIME:20221122T160000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/31
DESCRIPTION:Title: Snowflakes\, cones\, and shortcuts\nby Christopher Cashen (Vienna) a
s part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nA
graph is strongly shortcut if there exists \\(K>1\\) and a bound on the le
ngth of \\(K\\)-biLipschitz embedded cycles. A group is strongly shortcut
if it acts geometrically on a strongly shortcut graph. This is a kind of n
on-positive curvature condition enjoyed by hyperbolic and CAT(0) groups\,
for example. Strongly shortcut groups are finitely presented and have all
of their asymptotic cones simply connected (so have polynomial Dehn functi
on).\n\n We look at an infinite family of snowflake groups\, which are kno
wn to have polynomial Dehn function\, and show that all of their asymptoti
c cones are simply connected. The usual ways to show that a group has all
asymptotic cones simply connected are to show that it is either of polynom
ial growth or has quadratic Dehn function\, but our groups have neither of
these properties. We also show that the 'obvious' Cayley graph is not str
ongly shortcut. This implies that some of its asymptotic cones contain iso
metrically embedded circles\, so they have metrically nontrivial loops eve
n though there are no topologically nontrivial loops. Here are two questio
ns:\n\n 1. If a group has all of its asymptotic cones simply connected\, d
oes that imply that it is \nstrongly shortcut? \n\n2. Is it true that one
Cayley graph of a group is strongly shortcut if and only if every Cayley g
raph of that group is strongly shortcut? \n\nOur snowflake examples show t
hat the answer to one of these questions is 'no'. \n\nThis is joint work w
ith Nima Hoda and Daniel Woohouse.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hume (Bristol)
DTSTART;VALUE=DATE-TIME:20230124T140000Z
DTEND;VALUE=DATE-TIME:20230124T160000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/32
DESCRIPTION:Title: Thick embeddings of graphs into symmetric spaces\nby David Hume (Bri
stol) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstr
act\nInspired by the work of Kolmogorov-Barzdin in the 60’s and more rec
ently by Gromov-Guth on thick embeddings into Euclidean spaces\, we consid
er thick embeddings of graphs into more general symmetric spaces. Roughly\
, a thick embedding is a topological embedding of a graph where disjoint p
airs of edges and vertices are at least a uniformly controlled distance ap
art (consistent with applications where vertices and edges are considered
as having volume). The goal is to find thick embeddings with minimal “vo
lume”.\n\nWe prove a dichotomy depending upon the rank of the non-compac
t factor of the symmetric space. For rank at least 2\, there are thick emb
eddings of \\(N\\)-vertex graphs with volume \\(\\leq C N\\log(N)\\) where
\\(C\\) depends on the maximal degree of the graph. By contrast\, for ran
k at most 1\, thick embeddings of expander graphs have volume \\(\\geq c N
^{1+a}\\) for some \\(a\\geq 0\\).\n\nThe key tool required for these resu
lts is the notion of a coarse wiring\, which is a continuous embedding of
one graph inside another satisfying some additional properties. We prove t
hat the minimal “volume” of a coarse wiring into a symmetric space is
equivalent to the minimal volume of a thick embedding. We obtain lower bou
nds on the volume of coarse wirings by comparing the relative connectivity
(as measured by the separation profile) of the domain and target\, and up
per bounds by direct construction.\n\nThis is joint work with Benjamin Bar
rett.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alon Dogon (Weizmann Institute)
DTSTART;VALUE=DATE-TIME:20230117T140000Z
DTEND;VALUE=DATE-TIME:20230117T160000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/33
DESCRIPTION:Title: Hyperlinearity versus flexible Hilbert Schmidt stability for property (T
) groups\nby Alon Dogon (Weizmann Institute) as part of Vienna Geometr
y and Analysis on Groups Seminar\n\n\nAbstract\nIn these two talks\, we wi
ll present and illustrate a phenomenon\, commonly termed "stability vs. ap
proximation"\, that has been present in several works in recent years. \nO
n the one hand\, consider the following classical question: Given two almo
st commuting matrices/permutations\, are they necessarily close to a pair
of commuting matrices/permutations? This turns out to be a typical stabili
ty question for groups\, which was introduced by G.N. Arzhantseva and L. P
aunescu\, and since then considered in different scenarios for general gro
ups. \n\nOn the other hand\, the well known subject of approximation for g
roups is of central interest. Various metric approximation properties for
groups have been defined by different mathematicians (including M. Gromov\
, A. Connes\, F. Radulescu\, E. Kirchberg....)\, resulting in notions such
as sofic and hyperlinear groups\, which have gained importance since thei
r inception. Surprisingly\, no counterexamples for failing soficity or hyp
erlinearity are known. A somewhat simple observation shows that a group th
at is both stable and approximable is residually finite. This yielded a su
ccessful strategy for constructing certain non-approximable groups by givi
ng ones that are stable but not residually finite. \n\nIn the introductory
lecture we will discuss these notions precisely\, and in the research par
t we will present classical residually finite groups\, for which establish
ing (flexible Hilbert Schmidt) stability would still give non hyperlinear
groups.\nThe same phenomenon is also shown to be generic for random groups
in certain models.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Guillon (CNRS/Marseille)
DTSTART;VALUE=DATE-TIME:20230418T130000Z
DTEND;VALUE=DATE-TIME:20230418T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/34
DESCRIPTION:Title: Decidability and symbolic dynamics over groups\nby Pierre Guillon (C
NRS/Marseille) as part of Vienna Geometry and Analysis on Groups Seminar\n
\n\nAbstract\nShifts of finite type are sets of biinfinite words (sequence
s of colors from a finite alphabet indexed in \\(\\mathbb{Z}\\)) that avoi
d a finite collection of finite patterns. Their dynamical properties are v
ery well understood thanks to their representation by matrices or finite g
raphs. When changing \\(\\mathbb{Z}\\) into \\(\\mathbb{Z}^2\\)\, the defi
nition stays coherent\, but most classical dynamical properties or invaria
nts become intractable\; one way to understand this is to consider this ob
ject as a computational model\, capable of some algorithmic behavior.

Now\, when changing \\(\\mathbb{Z}^2\\) into any finitely generated gro
up\, it is not completely clear when the behavior is close to that of \\(\
\mathbb{Z}\\) or to that of \\(\\mathbb{Z}^2\\). I will try to give some i
ntuition on this open problem\, survey what is known\, and sketch some ide
as that could help approach a solution.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lvzhou Chen (Purdue)
DTSTART;VALUE=DATE-TIME:20230516T130000Z
DTEND;VALUE=DATE-TIME:20230516T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T073123Z
UID:WienGAGT/35
DESCRIPTION:Title: The Kervaire conjecture and the minimal complexity of surfaces\nby L
vzhou Chen (Purdue) as part of Vienna Geometry and Analysis on Groups Semi
nar\n\n\nAbstract\n

Talk 1

\nTitle: Weights of groups

\nAb stract: This is an introductory talk on weights of groups. The weight (als o called the normal rank) of a group \\(G\\) is the smallest number of ele ments that normally generate \\(G\\). We will discuss basic properties and examples in connection to topology. Although it is a simple notion\, seve ral basic problems remain open\, including the Kervaire conjecture and the Wiegold question. We will explain some well-known partial results and the ir proofs.

\n\;

\nTalk 2

\nTitle: The Kervaire con jecture and the minimal complexity of surfaces

\nAbstract: We use to pological methods to solve special cases of a fundamental problem in group theory\, the Kervaire conjecture\, which has connection to various proble ms in topology. The conjecture asserts that\, for any nontrivial group \\( G\\) and any element \\(w\\) in the free product \\(G*Z\\)\, the quotient \\((G*Z)/<\;<\;w>\;>\;\\) is still nontrivial\, i.e. the group \\( G*Z\\) has weight greater than 1. We interpret this as a problem of estima ting the minimal complexity (in terms of Euler characteristic) of surface maps to certain spaces. This gives a conceptually simple proof of Klyachko 's theorem that confirms the Kervaire conjecture for any \\(G\\) torsion-f ree. We also obtain injectivity of the map \\(G\\to(G*Z)/<\;<\;w>\;& gt\;\\) when \\(w\\) is a proper power for arbitrary \\(G\\). Both results generalize to certain HNN extensions.

\n\;

\n LOCATION:https://researchseminars.org/talk/WienGAGT/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Lysenok (Steklov Institute) DTSTART;VALUE=DATE-TIME:20230606T130000Z DTEND;VALUE=DATE-TIME:20230606T150000Z DTSTAMP;VALUE=DATE-TIME:20231130T073123Z UID:WienGAGT/36 DESCRIPTION:Title: A sample iterated small cancellation theory for groups of Burnside type< /a>\nby Igor Lysenok (Steklov Institute) as part of Vienna Geometry and An alysis on Groups Seminar\n\n\nAbstract\nThe free Burnside group \\(B(m\ ,n)\\) is the \\(m\\)-generated group defined by all relations of the form \\(x^n=1\\). Despite the simplicity of the definition\, obtaining a struc tural information about the free Burnside groups is known to be a difficul t problem. The primary question of this sort is whether \\(B(m\,n)\\) is f inite for given \\(m\, n \\ge 2\\). Starting from fundamental results of N ovikov and Adian\, it became known that \\(B(m\,n)\\) is infinite for all sufficiently large exponents \\(n\\). There are known several approaches t o prove this result and to establish other properties of groups \\(B(m\,n) \\) in the `infinite' case. However\, even simpler ones are quite technica l and require a large lower bound on the exponent \\(n\\) (as odd \\(n \\g t 10^{10}\\) in Ol'shanskii's approach).

\nThe aim of the talk is to present yet another approach to free Burnside groups of odd exponent \\(n \\) with \\(m\\ge2\\) generators based on a version of iterated small canc ellation theory. The approach works for a `moderate' bound \\(n \\gt 2000\ \). In the introductory part\, I make a brief survey of results around Bur nside groups and give an informal introduction to the small cancellation t heory.

\n LOCATION:https://researchseminars.org/talk/WienGAGT/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Monika Kudlinska (Oxford) DTSTART;VALUE=DATE-TIME:20230523T130000Z DTEND;VALUE=DATE-TIME:20230523T150000Z DTSTAMP;VALUE=DATE-TIME:20231130T073123Z UID:WienGAGT/37 DESCRIPTION:Title: Profinite rigidity and free-by-cyclic groups\nby Monika Kudlinska (O xford) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbst ract\nIt is a natural question to ask how much algebraic information is en coded in the set of finite quotient of a given group. More precisely\, one tries to establish which properties of infinite\, discrete\, residually f inite groups are preserved under isomorphisms of their profinite completio ns. A group is said to be (absolutely) profinitely rigid if its isomorphis m type is completely determined by its profinite completion. The first tal k will focus on the history of this problem\, covering some classical resu lts as well as more recent work and open problems in the area. We will int roduce all the necessary background\, so no prior knowledge of the topic w ill be assumed.\n\nA variation of this problem involves restricting to a c ertain family of groups and trying to decide whether a group is profinitel y rigid relative to this family. Much work has been done towards solving t his problem for fundamental groups of 3-manifolds. In the second talk\, we will focus our attention on a related family of groups known as free-by-c yclic groups\, which have natural connections with 3-manifolds. We will se e that many properties of free-by-cyclic groups are invariants of their pr ofinite completion. As a consequence\, we obtain various profinite rigidit y results\, including the almost profinite rigidity of generic free-by-cyc lic groups amongst the class of all free-by-cyclic groups. \n\nThis is joi nt work with Sam Hughes.\n LOCATION:https://researchseminars.org/talk/WienGAGT/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Pansu (Paris-Saclay) DTSTART;VALUE=DATE-TIME:20231114T140000Z DTEND;VALUE=DATE-TIME:20231114T160000Z DTSTAMP;VALUE=DATE-TIME:20231130T073123Z UID:WienGAGT/38 DESCRIPTION:Title: Computing homology robustly: from persistence to the geometry of normed chain complexes\nby Pierre Pansu (Paris-Saclay) as part of Vienna Geom etry and Analysis on Groups Seminar\n\n\nAbstract\nTopological Data Analys is uses homology as a feature for large data sets. It has successfully add ressed the issue of the robustness of computing homology. Nevertheless\, t he conditioning number suggests an alternative approach. When computing th e cohomology of a graph (or a simplicial complex)\, it has geometric signi ficance: it is known as Cheeger's constant or spectral gap. This indicates that (co-)chain complexes contain more information than their mere (co-)h omology. We turn the set of normed chain complexes into a metric space and study a compactness criterion.\n LOCATION:https://researchseminars.org/talk/WienGAGT/38/ END:VEVENT END:VCALENDAR