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BEGIN:VEVENT
SUMMARY:Koji Fujiwara (Kyoto)\, Macarena Arenas (Cambridge)\, Indira Chatt
erji (Nice)
DTSTART;VALUE=DATE-TIME:20201027T080000Z
DTEND;VALUE=DATE-TIME:20201027T110000Z
DTSTAMP;VALUE=DATE-TIME:20210419T090510Z
UID:GroupTheoryENS/1
DESCRIPTION:Title: A group theory morning\nby Koji Fujiwara (Kyoto)\, Macarena Are
nas (Cambridge)\, Indira Chatterji (Nice) as part of ENS group theory semi
nar\n\n\nAbstract\n09.00-09.45 Koji Fujiwara (Kyoto) "The rates of growth
in a hyperbolic group"\n\n10.00-10.45 Macarena Arenas (Cambridge) "Linear
isoperimetric functions for surfaces in hyperbolic groups"\n\nOne of the m
ain characterisations of word-hyperbolic groups is that they are the group
s with a linear isoperimetric function. That is\, for\na compact 2-complex
X\, the hyperbolicity of its fundamental group is equivalent to the exist
ence of a linear isoperimetric function for\ndisc diagrams D -->X. It is l
ikewise known that hyperbolic groups have a linear annular\nisoperimetric
function and a linear homological isoperimetric function. I will tell you
a bit about these isoperimetric functions\nand a generalisation to all hom
otopy types of surface diagrams. This is joint work with Dani Wise.\n\n\n1
1.15-12.00 Indira Chatterji (Nice) "Tangent bundles on hyperbolic spaces a
nd proper actions on Lp spaces".\n\nI will define a notion of a negatively
curved tangent bundle of a metric measured space\, and relate that notion
to proper actions on Lp spaces. I will discuss hyperbolic spaces as examp
les.\n
LOCATION:https://researchseminars.org/talk/GroupTheoryENS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Sisto (Heriot-Watt)\, Thomas Haettel (Montpellier)\, Ma
rk Hagen (Bristol)
DTSTART;VALUE=DATE-TIME:20201124T130000Z
DTEND;VALUE=DATE-TIME:20201124T160000Z
DTSTAMP;VALUE=DATE-TIME:20210419T090510Z
UID:GroupTheoryENS/2
DESCRIPTION:Title: A group theory afternoon\nby Alessandro Sisto (Heriot-Watt)\, T
homas Haettel (Montpellier)\, Mark Hagen (Bristol) as part of ENS group th
eory seminar\n\n\nAbstract\n14.00-14.45 Alessandro Sisto (Heriot-Watt)\n\n
15.00-15.45 Thomas Haettel ( Montpellier)\n\n16.15-17.00 Mark Hagen ( Bris
tol)\n\n\nAlessandro Sisto "Cubulation of hulls and bicombings"\n\nIt is w
ell-known that the quasi-convex hull of finitely many points in a\nhyperbo
lic space is quasi-isometric to a tree. I will discuss an\nanalogous fact
in the context of hierarchically hyperbolic spaces\, a\nlarge class of spa
ces and groups including mapping class groups\,\nTeichmueller space\, righ
t-angled Artin and Coxeter groups\, and many\nothers. In this context\, th
e approximating tree is replaced by a CAT(0)\ncube complex. I will also br
iefly discuss applications\, including how\nthis can be used to construct
bicombings.\nBased on joint works with Behrstock-Hagen and Durham-Minsky.\
n\nThomas Haettel "The coarse Helly property\, hierarchical hyperbolicity
and semihyperbolicity"\n\nFor any hierarchical hyperbolic group\, and in p
articular any mapping\nclass group\, we define a new metric that satisfies
a coarse Helly\nproperty. This enables us to deduce that the group is sem
ihyperbolic\,\ni.e. that it admits a bounded quasigeodesic bicombing\, and
also that\nit has finitely many conjugacy classes of finite subgroups. Th
is has\nseveral other consequences for the group. This is a joint work wit
h\nNima Hoda and Harry Petyt.\n\n\n\nMark Hagen "Wallspaces\, the Behrstoc
k inequality\, and l_1 metrics on\nasymptotic cones"\n\nFrom its hyperplan
es\, one can always characterise a CAT(0)\ncube complex as the subset of s
ome (often infinite) cube consisting of\nthe solutions to a system of "con
sistency" conditions. Analogously\, a\nhierarchically hyperbolic space (H
HS) can be coarsely characterised as a\nsubset of a product of Gromov-hype
rbolic spaces consisting of the\n"solutions" to a system of coarse consist
ency conditions.\nHHSes are a common generalisation of hyperbolic spaces\,
mapping class\ngroups\, Teichmuller space\, and right-angled Artin/Coxete
r groups. The\noriginal motivation for defining HHSes was to provide a un
ified\nframework for studying the large-scale properties of examples like
these.\nSo\, it is natural to ask about the structure of asymptotic cones
of\nhierarchically hyperbolic spaces.\nMotivated by the above characterisa
tion of a CAT(0) cube complex\, we\nintroduce the notion of an R-cubing.
This is a space that can be\nobtained from a product of R-trees\, with the
l_1 metric\, as a solution\nset of a similar set of consistency condition
s. R-cubings are therefore\na common generalisation of R-trees and (finite
-dimensional) CAT(0) cube\ncomplexes. R-cubings are median spaces with ex
tra structure\, in much\nthe same way that HHSes are coarse median spaces
with extra structure.\nThe main result in this talk says that every asympt
otic cone of a\nhierarchically hyperbolic space is bilipschitz equivalent
to an\nR-cubing. This strengthens a theorem of Behrstock-Drutu-Sapir abou
t\nasymptotic cones of mapping class groups. Time permitting\, I will tal
k\nabout an application of this result which is still in progress\, namely
\nuniqueness of asymptotic cones of various hierarchically hyperbolic\ngro
ups\, including mapping class groups and right-angled Artin groups.\nThis
is joint work with Montse Casals-Ruiz and Ilya Kazachkov.\n
LOCATION:https://researchseminars.org/talk/GroupTheoryENS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Young (NYY Courant and IAS Princeton)\, Matei Coiculescu (B
rown University)\, Richard Schwartz (Brown University and IAS Princeton)
DTSTART;VALUE=DATE-TIME:20201208T140000Z
DTEND;VALUE=DATE-TIME:20201208T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T090510Z
UID:GroupTheoryENS/3
DESCRIPTION:Title: A group theory afternoon\nby Robert Young (NYY Courant and IAS
Princeton)\, Matei Coiculescu (Brown University)\, Richard Schwartz (Brown
University and IAS Princeton) as part of ENS group theory seminar\n\n\nA
bstract\nRobert Young\, "Hölder maps to the Heisenberg group"\n\nIn this
talk\, we construct Hölder maps to the Heisenberg group H\, answering a
question of Gromov. Pansu and Gromov observed that any surface embedded in
H has Hausdorff dimension at least 3\, so there is no α-Hölder embeddin
g of a surface into H when α > 2/3. Züst improved this result to show th
at when α > 2/3\, any α-Hölder map from a simply-connected Riemannian m
anifold to H factors through a metric tree. We use new techniques for cons
tructing self-similar extensions to show that any continuous map to H can
be approximated by a (2/3 - ε)-Hölder map. This is joint work with Stefa
n Wenger.\n\n\nMatei Coiculescu\, "The Spheres of Sol"\n\nSol\, one of the
eight Thurston geometries\, is a solvable three-dimensional Lie group equ
ipped with a canonical left invariant metric. Sol has sectional curvature
of both signs and is not rotationally symmetric\, which complicates the st
udy of its Riemannian geometry.\nOur main result is a characterization of
the cut locus of Sol\, which implies as a corollary that the metric sphere
s in Sol are topological spheres. \nThis is joint work with Richard Schwar
tz".\n\n\nRichard Schwartz\, "The areas of metric spheres in Sol"\n\nThis
is a sequel talk\, following Matei Coiculescu's talk about our joint work
characterizing the cut locus of the identity in Sol.\nIn this talk\, I wi
ll explain my result that the area of a metric sphere of radius r in Sol i
s at most Ce^r for some uniform constant C. That is\,\nup to constants\,
the sphere of radius r in Sol has the same area as the hyperbolic disk of
radius r.\n
LOCATION:https://researchseminars.org/talk/GroupTheoryENS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Pak (UCLA)\, Behrang Forghani (the College of Charleston)\, M
ehrdad Kalantar (University of Houston)
DTSTART;VALUE=DATE-TIME:20210119T150000Z
DTEND;VALUE=DATE-TIME:20210119T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T090510Z
UID:GroupTheoryENS/4
DESCRIPTION:Title: A group theory afternoon\nby Igor Pak (UCLA)\, Behrang Forghani
(the College of Charleston)\, Mehrdad Kalantar (University of Houston) a
s part of ENS group theory seminar\n\n\nAbstract\nIgor Pak\, "Cogrowth seq
uences in groups and graphs"\n\nLet G be a finitely generated group with
generating set S. We study the cogrowth sequence {a_n(G\,S)}\, which cou
nts the number of words of length n over the alphabet S that are equal to
1 in G. I will survey recent asymptotic and analytic results on the cogro
wth sequence\, motivated by both combinatorial and algebraic applications.
I will then present our recent work with Kassabov on spectral radii of C
ayley graphs\, which are also governed by the asymptotics of cogrowth sequ
ences. \n\n\nBehrang Forghani\, "Boundary Preserving Transformations"\n\nT
his talk concerns the situations when the Poisson boundaries of different
random walks on the same group coincide. In some special cases\, Furstenbe
rg and Willis addressed this question. However\, the scopes of their const
ructions are limited. I will show how randomized stopping times can constr
uct measures that preserve Poisson boundaries and discuss their applicatio
ns regarding the Poisson boundary identification problem. This talk is bas
ed on joint work with Kaimanovich.\n\nMehrdad Kalantar\, "On weak containm
ent properties of quasi-regular representations of stabilizer subgroups of
boundary actions"\n\nA continuous action of a group G on a compact space
X is said to be a boundary action if the weak*-closure of the orbit of eve
ry Borel probability on X under G-action contains all point measures on X.
Given a boundary action of a discrete countable group\, we prove that at
any continuity point of the stabilizer map\, the quasi-regular representat
ion of the stabilizer subgroup is weakly equivalent to every representatio
n that it weakly contains. We also completely characterize when these quas
i-regular representations weakly contain the GNS representation of a chara
cter on the group.\nThis is joint work with Eduardo Scarparo.\n
LOCATION:https://researchseminars.org/talk/GroupTheoryENS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingyin Huang (Ohio State University)\, Jérémie Chalopin (Aix-Ma
rseille Université)\, Daniel Wise (McGill University)
DTSTART;VALUE=DATE-TIME:20210223T143000Z
DTEND;VALUE=DATE-TIME:20210223T173000Z
DTSTAMP;VALUE=DATE-TIME:20210419T090510Z
UID:GroupTheoryENS/5
DESCRIPTION:Title: A group theory and CAT(0) cubical afternoon\nby Jingyin Huang (
Ohio State University)\, Jérémie Chalopin (Aix-Marseille Université)\,
Daniel Wise (McGill University) as part of ENS group theory seminar\n\n\nA
bstract\nJingyin Huang "Morse quasiflats"\n\nWe are motivated by looking
for traces of hyperbolicity in a space or\ngroup which is not Gromov-hyper
bolic. One previous approach in this\ndirection is the notion of Morse qua
sigeodesics\, which describes\n``negatively-curved'' directions in the spa
ces\; another previous\napproach is ``higher rank hyperbolicity'' with one
example being that\nthough triangles in products of two hyperbolic planes
are not thin\,\ntetrahedrons made of minimal surfaces are ``thin''. We in
troduce the\nnotion of Morse quasiflats\, which unifies these two seemingl
y\ndifferent approaches and applies to a wider range of objects. In the\nt
alk\, we will provide motivations and examples for Morse quasiflats\,\nas
well as a number of equivalent definitions and quasi-isometric\ninvariance
(under mild assumptions). We will also show that Morse\nquasiflats are as
ymptotically conical\, and comment on potential\napplications. Based on jo
int work with B. Kleiner and S. Stadler.\n\nJérémie Chalopin (TBA)\n\nDa
niel Wise (TBA)\n
LOCATION:https://researchseminars.org/talk/GroupTheoryENS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanna Oppelmayer (TU Graz)\, Georgii Veprev (St-Petersburg)\, Paul
-Henry Leemann (University of Neuchâtel)
DTSTART;VALUE=DATE-TIME:20210330T120000Z
DTEND;VALUE=DATE-TIME:20210330T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T090510Z
UID:GroupTheoryENS/6
DESCRIPTION:Title: An afternoon on random walks and amenable groups\nby Hanna Oppe
lmayer (TU Graz)\, Georgii Veprev (St-Petersburg)\, Paul-Henry Leemann (Un
iversity of Neuchâtel) as part of ENS group theory seminar\n\n\nAbstract
\nHanna Oppelmayer\, "Random walks on dense subgroups of totally discon
nected locally compact groups"\n\nThere is a class of random walks on som
e countable discrete groups that capture the asymptotic behaviour of certa
in random walks\non totally disconnected locally compact second countable
(t.d.l.c.) groups which are completions of the discrete group. We will see
that\nthe Poisson boundary of the t.d.l.c. group is always a factor of th
e Poisson boundary of the discrete group\, when equipped with these\nrando
m walks. All this is done by means of a so-called Hecke subgroup.\nIn part
icular\, if the two Poisson boundaries are isomorphic then this Hecke subg
roup is forced to be amenable. The reverse direction holds\nwhenever there
is a uniquely stationary compact model for the Poisson boundary of the di
screte group. Furthermore\, we will deduce some\napplications to concrete
examples\, like the lamplighter group over Z and solvable Baumslag-Solitar
groups and show that they are prime\,\ni.e. there are random walks such t
hat the Poisson boundary and the one-point-space are the only boundaries.\
nThis is a joint work with Michael Björklund (Chalmers\, Sweden) and\nYai
r Hartman (Ben Gurion University\, Israel).\n\n\nGeorgi Veprev\, "Non-exi
stence of a universal zero entropy system for non-periodic amenable group
actions"\n\nLet G be a discrete amenable group. We study interrelations be
tween topological and measure-theoretic actions of G. For a given continuo
us representation of G on a compact metric space X we consider the set of
all ergodic invariant measures on X. For any such measure we associate the
corresponding measure-theoretic dynamical system. The general wild questi
on is what the family M of these systems could be up to measure-theoretic
isomorphisms.\nThe topological system for which M coincides with a given c
lass S of ergodic actions is called universal. B.Weiss's question regards
the existence of a universal system for the class of all zero-entropy acti
ons. For the case of Z\, the negative answer was given by J. Serafin.\nOur
main result establishes the non-existence of a universal zero-entropy sys
tem for any non-periodic amenable group. The condition of non-periodicity
is crucial in our arguments so the question is still open for general tors
ion amenable groups.\nOur proof bases on the slow entropy type invariant c
alled scaling entropy introduced by A. Vershik. This invariant characteriz
es the intermediate growth of the entropy in a sense on the verge of topol
ogical and measure-preserving dynamics. I will present a brief survey of s
caling entropy and show how this invariant applies to the non-existence th
eorem.\n\n\nPaul-Henry Leemann\, "De Bruijn graphs\, spider web graphs an
d Lamplighter groups"\n\nDe Bruijn graphs represent word overlaps in symbo
lic dynamical systems. They naturally occur in dynamical systems and combi
natorics\, as well as in computer science and bioinformatics. We will show
that de Bruijn graphs converge to a Cayley graph of the Lamplighter group
and and will also compute their spetra. We will then discuss some general
izations of them as for examples Spider web graphs or Rauzy graphs.\nBased
on a joint work with R. Grigorchuk and T. Nagnibeda.\n
LOCATION:https://researchseminars.org/talk/GroupTheoryENS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Panos Papazoglu (Oxford)\, Urs Lang (ETH Zurich)\, Karim Adiprasit
o (Hebrew University & University of Copenhagen)
DTSTART;VALUE=DATE-TIME:20210427T130000Z
DTEND;VALUE=DATE-TIME:20210427T160000Z
DTSTAMP;VALUE=DATE-TIME:20210419T090510Z
UID:GroupTheoryENS/7
DESCRIPTION:Title: An afternoon on asymptotic dimension\nby Panos Papazoglu (Oxfor
d)\, Urs Lang (ETH Zurich)\, Karim Adiprasito (Hebrew University & Univers
ity of Copenhagen) as part of ENS group theory seminar\n\nInteractive live
stream: https://us02web.zoom.us/j/87679868475\nPassword hint: Degree of st
andard Cayley graph of free group on 107 generators.\n\nAbstract\n15.00 -
15.45 Panos Papazoglu (Oxford)\n\n16.00 - 16.45 Urs Lang (ETH Zurich)\
n\n17.15 - 18.00 Karim Adiprasito (Hebrew University & University of Cop
enhagen)\n\n\nPanos Papazoglu\, "Asymptotic dimension of planes" (joint wi
th K. Fujiwara)\n\nIt is easy to see that there are Riemannian manifolds h
omeomorphic to $\\mathbb R ^3$\nwith infinite asymptotic dimension. In con
trast to this we showed with K. Fujiwara that\nthe asymptotic dimension of
Riemannian planes (and planar graphs) is bounded by 3. This was\nimproved
to 2 by Jorgensen-Lang and Bonamy-Bousquet-Esperet-Groenland-Pirot-Scott.
\n\n\n\nUrs Lang\, "Assouad-Nagata dimension and Lipschitz extensions "\n
\nIt follows from a recent result of Fujiwara-Papasoglu and a Hurewicz-typ
e theorem due to Brodskiy-Dydak-Levin-Mitra that every planar geodesic met
ric space has\n\n(Assouad-)Nagata dimension at most two and hence asymptot
ic dimension at most two. This can be used further to prove that every thr
ee-dimensional Hadamard manifold \n\nhas Nagata dimension three and is an
absolute Lipschitz retract (joint work with Martina Jørgensen). The role
of the Nagata dimension in Lipschitz extension problems\nwill be discussed
further.\n\n\nKarim Adiprasito\, TBA\n
LOCATION:https://researchseminars.org/talk/GroupTheoryENS/7/
URL:https://us02web.zoom.us/j/87679868475
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