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BEGIN:VEVENT
SUMMARY:Koji Fujiwara (Kyoto)\, Macarena Arenas (Cambridge)\, Indira Chatt
 erji (Nice)
DTSTART:20201027T080000Z
DTEND:20201027T110000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/1/">A group theory morning</a>\nby Koji Fujiwara (Kyoto)\, Macar
 ena Arenas (Cambridge)\, Indira Chatterji (Nice) as part of ENS group theo
 ry seminar\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 o
 f the main characterisations of word-hyperbolic groups is that they are th
 e groups with a linear isoperimetric function. That is\, for\na compact 2-
 complex X\, the hyperbolicity of its fundamental group is equivalent to th
 e existence of a linear isoperimetric function for\ndisc diagrams D -->X. 
 It is likewise known that hyperbolic groups have a linear annular\nisoperi
 metric function and a linear homological isoperimetric function. I will te
 ll you a bit about these isoperimetric functions\nand a generalisation to 
 all homotopy types of surface diagrams. This is joint work with Dani Wise.
 \n\n\n11.15-12.00 Indira Chatterji (Nice) "Tangent bundles on hyperbolic s
 paces and proper actions on Lp spaces".\n\nI will define a notion of a neg
 atively curved tangent bundle of a metric measured space\, and relate that
  notion to proper actions on Lp spaces. I will discuss hyperbolic spaces a
 s examples.\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Sisto (Heriot-Watt)\, Thomas Haettel (Montpellier)\, Ma
 rk Hagen (Bristol)
DTSTART:20201124T130000Z
DTEND:20201124T160000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/2/">A group theory afternoon</a>\nby Alessandro Sisto (Heriot-Wa
 tt)\, Thomas Haettel (Montpellier)\, Mark Hagen (Bristol) as part of ENS g
 roup theory seminar\n\n\nAbstract\n14.00-14.45 Alessandro Sisto (Heriot-Wa
 tt)\n\n15.00-15.45 Thomas Haettel ( Montpellier)\n\n16.15-17.00 Mark Hagen
  ( Bristol)\n\n\nAlessandro Sisto "Cubulation of hulls and bicombings"\n\n
 It is well-known that the quasi-convex hull of finitely many points in a\n
 hyperbolic space is quasi-isometric to a tree. I will discuss an\nanalogou
 s fact in the context of hierarchically hyperbolic spaces\, a\nlarge class
  of spaces and groups including mapping class groups\,\nTeichmueller space
 \, right-angled Artin and Coxeter groups\, and many\nothers. In this conte
 xt\, the approximating tree is replaced by a CAT(0)\ncube complex. I will 
 also briefly discuss applications\, including how\nthis can be used to con
 struct bicombings.\nBased on joint works with Behrstock-Hagen and Durham-M
 insky.\n\nThomas Haettel "The coarse Helly property\, hierarchical hyperbo
 licity and semihyperbolicity"\n\nFor any hierarchical hyperbolic group\, a
 nd in particular any mapping\nclass group\, we define a new metric that sa
 tisfies a coarse Helly\nproperty. This enables us to deduce that the group
  is semihyperbolic\,\ni.e. that it admits a bounded quasigeodesic bicombin
 g\, and also that\nit has finitely many conjugacy classes of finite subgro
 ups. This has\nseveral other consequences for the group. This is a joint w
 ork with\nNima Hoda and Harry Petyt.\n\n\n\nMark Hagen "Wallspaces\, the B
 ehrstock inequality\, and l_1 metrics on\nasymptotic cones"\n\nFrom its hy
 perplanes\, one can always characterise a CAT(0)\ncube complex as the subs
 et of some (often infinite) cube consisting of\nthe solutions to a system 
 of "consistency" conditions.  Analogously\, a\nhierarchically hyperbolic s
 pace (HHS) can be coarsely characterised as a\nsubset of a product of Grom
 ov-hyperbolic spaces consisting of the\n"solutions" to a system of coarse 
 consistency conditions.\nHHSes are a common generalisation of hyperbolic s
 paces\, mapping class\ngroups\, Teichmuller space\, and right-angled Artin
 /Coxeter groups.  The\noriginal motivation for defining HHSes was to provi
 de a unified\nframework for studying the large-scale properties of example
 s like these.\nSo\, it is natural to ask about the structure of asymptotic
  cones of\nhierarchically hyperbolic spaces.\nMotivated by the above chara
 cterisation of a CAT(0) cube complex\, we\nintroduce the notion of an R-cu
 bing.  This is a space that can be\nobtained from a product of R-trees\, w
 ith the l_1 metric\, as a solution\nset of a similar set of consistency co
 nditions. R-cubings are therefore\na common generalisation of R-trees and 
 (finite-dimensional) CAT(0) cube\ncomplexes.  R-cubings are median spaces 
 with extra structure\, in much\nthe same way that HHSes are coarse median 
 spaces with extra structure.\nThe main result in this talk says that every
  asymptotic cone of a\nhierarchically hyperbolic space is bilipschitz equi
 valent to an\nR-cubing.  This strengthens a theorem of Behrstock-Drutu-Sap
 ir about\nasymptotic cones of mapping class groups.  Time permitting\, I w
 ill talk\nabout an application of this result which is still in progress\,
  namely\nuniqueness of asymptotic cones of various hierarchically hyperbol
 ic\ngroups\, including mapping class groups and right-angled Artin groups.
 \nThis is joint work with Montse Casals-Ruiz and Ilya Kazachkov.\n
LOCATION:https://stable.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:20201208T140000Z
DTEND:20201208T170000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/3/">A group theory afternoon</a>\nby Robert Young (NYY Courant a
 nd IAS Princeton)\, Matei Coiculescu (Brown University)\, Richard Schwartz
  (Brown University  and IAS Princeton) as part of ENS group theory seminar
 \n\n\nAbstract\nRobert Young\,  "Hölder maps to the Heisenberg group"\n\n
 In this talk\, we construct Hölder maps to the Heisenberg group H\, answe
 ring a question of Gromov. Pansu and Gromov observed that any surface embe
 dded in H has Hausdorff dimension at least 3\, so there is no α-Hölder e
 mbedding of a surface into H when α > 2/3. Züst improved this result to 
 show that when α > 2/3\, any α-Hölder map from a simply-connected Riema
 nnian manifold to H factors through a metric tree. We use new techniques f
 or constructing 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 wit
 h Stefan Wenger.\n\n\nMatei Coiculescu\, "The Spheres of Sol"\n\nSol\, one
  of the eight Thurston geometries\, is a solvable three-dimensional Lie gr
 oup equipped with a canonical left invariant metric. Sol has sectional cur
 vature of both signs and is not rotationally symmetric\, which complicates
  the study of its Riemannian geometry.\nOur main result is a characterizat
 ion of the cut locus of Sol\, which implies as a corollary that the metric
  spheres in Sol are topological spheres. \nThis is joint work with Richard
  Schwartz".\n\n\nRichard Schwartz\,  "The areas of metric spheres in Sol"\
 n\nThis is a sequel talk\, following Matei Coiculescu's talk about our joi
 nt work characterizing the cut locus of the identity in Sol.\nIn this talk
 \, I will explain my result that the area of a metric sphere of radius r i
 n Sol is at most Ce^r for some uniform constant C.  That is\,\nup to const
 ants\, the sphere of radius r in Sol has the same area as the hyperbolic d
 isk of radius r.\n
LOCATION:https://stable.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:20210119T150000Z
DTEND:20210119T180000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/4/">A group theory afternoon</a>\nby Igor Pak (UCLA)\, Behrang F
 orghani (the College of Charleston)\, Mehrdad Kalantar  (University of Hou
 ston) as part of ENS group theory seminar\n\n\nAbstract\nIgor Pak\, "Cogro
 wth sequences in groups and graphs"\n\nLet G  be a finitely generated grou
 p with generating set S.  We study the cogrowth sequence  {a_n(G\,S)}\, wh
 ich counts the number of words of length n over the alphabet S that are eq
 ual to 1 in G.  I will survey recent asymptotic and analytic results on th
 e cogrowth sequence\, motivated by both combinatorial and algebraic applic
 ations.  I will then present our recent work with Kassabov on spectral rad
 ii of Cayley graphs\, which are also governed by the asymptotics of cogrow
 th sequences. \n\n\nBehrang Forghani\, "Boundary Preserving Transformation
 s"\n\nThis talk concerns the situations when the Poisson boundaries of dif
 ferent random walks on the same group coincide. In some special cases\, Fu
 rstenberg and Willis addressed this question. However\, the scopes of thei
 r constructions are limited. I will show how randomized stopping times can
  construct measures that preserve Poisson boundaries and discuss their app
 lications regarding the Poisson boundary identification problem. This talk
  is based on joint work with Kaimanovich.\n\nMehrdad Kalantar\, "On weak c
 ontainment properties of quasi-regular representations of stabilizer subgr
 oups 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 every Borel probability on X under G-action contains all point measure
 s on X. Given a boundary action of a discrete countable group\, we prove t
 hat at any continuity point of the stabilizer map\, the quasi-regular repr
 esentation of the stabilizer subgroup is weakly equivalent to every repres
 entation that it weakly contains. We also completely characterize when the
 se quasi-regular representations weakly contain the GNS representation of 
 a character on the group.\nThis is joint work with Eduardo Scarparo.\n
LOCATION:https://stable.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:20210223T143000Z
DTEND:20210223T173000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/5/">A group theory and CAT(0) cubical afternoon</a>\nby Jingyin 
 Huang (Ohio State University)\, Jérémie Chalopin (Aix-Marseille Universi
 té)\, Daniel Wise (McGill University) as part of ENS group theory seminar
 \n\n\nAbstract\nJingyin Huang  "Morse quasiflats"\n\nWe are motivated by l
 ooking for traces of hyperbolicity in a space or\ngroup which is not Gromo
 v-hyperbolic. One previous approach in this\ndirection is the notion of Mo
 rse quasigeodesics\, which describes\n``negatively-curved'' directions in 
 the spaces\; another previous\napproach is ``higher rank hyperbolicity'' w
 ith one example being that\nthough triangles in products of two hyperbolic
  planes are not thin\,\ntetrahedrons made of minimal surfaces are ``thin''
 . We introduce the\nnotion of Morse quasiflats\, which unifies these two s
 eemingly\ndifferent approaches and applies to a wider range of objects. In
  the\ntalk\, we will provide motivations and examples for Morse quasiflats
 \,\nas well as a number of equivalent definitions and quasi-isometric\ninv
 ariance (under mild assumptions). We will also show that Morse\nquasiflats
  are asymptotically conical\, and comment on potential\napplications. Base
 d on joint work with B. Kleiner and S. Stadler.\n\nJérémie Chalopin (TBA
 )\n\nDaniel Wise (TBA)\n
LOCATION:https://stable.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:20210330T120000Z
DTEND:20210330T150000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/6/">An afternoon on random walks and amenable groups</a>\nby Han
 na Oppelmayer (TU Graz)\, Georgii Veprev (St-Petersburg)\, Paul-Henry Leem
 ann (University of  Neuchâtel) as part of ENS group theory seminar\n\n\nA
 bstract\nHanna Oppelmayer\,   "Random walks on dense subgroups of  totally
  disconnected locally compact  groups"\n\nThere is a class of random walks
  on some countable discrete groups that capture the asymptotic behaviour o
 f certain random walks\non totally disconnected locally compact second cou
 ntable (t.d.l.c.) groups which are completions of the discrete group. We w
 ill see that\nthe Poisson boundary of the t.d.l.c. group is always a facto
 r of the Poisson boundary of the discrete group\, when equipped with these
 \nrandom walks. All this is done by means of a so-called Hecke subgroup.\n
 In particular\, if the two Poisson boundaries are isomorphic then this Hec
 ke subgroup is forced to be amenable. The reverse direction holds\nwheneve
 r there is a uniquely stationary compact model for the Poisson boundary of
  the discrete group. Furthermore\, we will deduce some\napplications to co
 ncrete 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 that the Poisson boundary and the one-point-space are the only bound
 aries.\nThis is a joint work with Michael Björklund (Chalmers\, Sweden) a
 nd\nYair Hartman (Ben Gurion University\, Israel).\n\n\nGeorgi Veprev\,  "
 Non-existence of a universal zero entropy system for non-periodic amenable
  group actions"\n\nLet G be a discrete amenable group. We study interrelat
 ions between topological and measure-theoretic actions of G. For a given c
 ontinuous 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 associ
 ate the corresponding measure-theoretic dynamical system. The general wild
  question is what the family M of these systems could be up to measure-the
 oretic isomorphisms.\nThe topological system for which M coincides with a 
 given class S of ergodic actions is called universal. B.Weiss's question r
 egards the existence of a universal system for the class of all zero-entro
 py actions. For the case of Z\, the negative answer was given by J. Serafi
 n.\nOur main result establishes the non-existence of a universal zero-entr
 opy system for any non-periodic amenable group. The condition of non-perio
 dicity is crucial in our arguments so the question is still open for gener
 al torsion amenable groups.\nOur proof bases on the slow entropy type inva
 riant called scaling entropy introduced by A. Vershik. This invariant char
 acterizes the intermediate growth of the entropy in a sense on the verge o
 f topological and measure-preserving dynamics. I will present a brief surv
 ey of scaling entropy and show how this invariant applies to the non-exist
 ence theorem.\n\n\nPaul-Henry Leemann\,  "De Bruijn graphs\, spider web gr
 aphs and Lamplighter groups"\n\nDe Bruijn graphs represent word overlaps i
 n symbolic dynamical systems. They naturally occur in dynamical systems an
 d combinatorics\, as well as in computer science and bioinformatics. We wi
 ll show that de Bruijn graphs converge to a Cayley graph of the Lamplighte
 r group and and will also compute their spetra. We will then discuss some 
 generalizations 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://stable.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:20210427T130000Z
DTEND:20210427T160000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/7/">An afternoon on asymptotic dimension</a>\nby Panos Papazoglu
  (Oxford)\, Urs Lang (ETH Zurich)\, Karim Adiprasito (Hebrew University & 
 University of Copenhagen) as part of ENS group theory seminar\n\n\nAbstrac
 t\n15.00 - 15.45   Panos Papazoglu (Oxford)\n\n16.00 - 16.45   Urs Lang (E
 TH Zurich)\n\n17.15 - 18.00   Karim Adiprasito (Hebrew University & Univer
 sity of Copenhagen)\n\n\nPanos Papazoglu\, "Asymptotic dimension of planes
 " (joint with K. Fujiwara)\n\nIt is easy to see that there are Riemannian 
 manifolds homeomorphic to $\\mathbb R ^3$\nwith infinite asymptotic dimens
 ion. In contrast to this we showed with K. Fujiwara that\nthe asymptotic d
 imension of Riemannian planes (and planar graphs) is bounded by 3. This wa
 s\nimproved to 2 by Jorgensen-Lang and Bonamy-Bousquet-Esperet-Groenland-P
 irot-Scott.\n\n\n\nUrs Lang\,  "Assouad-Nagata dimension and Lipschitz ext
 ensions "\n\nIt follows from a recent result of Fujiwara-Papasoglu and a H
 urewicz-type theorem due to Brodskiy-Dydak-Levin-Mitra that every planar g
 eodesic metric space has\n\n(Assouad-)Nagata dimension at most two and hen
 ce asymptotic dimension at most two. This can be used further to prove tha
 t every three-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 b
 e discussed further.\n\n\nKarim Adiprasito\, "l^2 cohomology and stable Le
 fschetz theory"\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Tiozzo (Toronto)\, Sébastien Gouëzel (Rennes)\, Andrei Al
 peev (St-Petersburg)
DTSTART:20210525T133000Z
DTEND:20210525T163000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/8/">An afternoon on random walks and groups</a>\nby Giulio Tiozz
 o (Toronto)\, Sébastien Gouëzel (Rennes)\, Andrei Alpeev (St-Petersburg)
  as part of ENS group theory seminar\n\n\nAbstract\n15.30 - 16.15   Giulio
  Tiozzo (Toronto)\n\n16.30 - 17.15  Sébastien Gouëzel (Rennes)\n\n17.45 
 - 18.30  Andrei Alpeev (St-Petersburg)\n\n\nGiulio Tiozzo\,  "The fundamen
 tal inequality for cocompact Fuchsian groups".\n\nA recurring question in 
 the theory of random walks on hyperbolic spaces asks whether the hitting (
 harmonic) measures can coincide with measures of geometric origin\, such a
 s the Lebesgue measure. This is also related to the inequality between ent
 ropy and drift.\nFor finitely-supported random walks on cocompact Fuchsian
  groups with symmetric fundamental domain\, we prove that the hitting meas
 ure is singular with respect to Lebesgue measure\; moreover\, its Hausdorf
 f dimension is strictly less than 1.\nAlong the way\, we prove a purely ge
 ometric inequality for geodesic lengths\, strongly reminiscent of the Ande
 rson-Canary-Culler-Shalen inequality for free Kleinian groups.\nJoint with
  P. Kosenko.\n\n\nSébastien Gouëzel\, "Exponential estimates for random 
 walks without moment conditions on\nhyperbolic spaces"\n\nConsider a rando
 m walk on a nonelementary hyperbolic space (proper or  not\, but one may j
 ust think of a free group for simplicity). It is known\nthat the walk is c
 onverging almost surely towards a point at a boundary\,  and that the rate
  of escape is positive. We will discuss quantitative\nversions of these st
 atements: when can one show that these facts hold with an exponentially sm
 all probability for exceptions? While there are\nseveral such results in t
 he literature\, the originality of our approach is that it does not requir
 e any moment condition on the random walk. We\nwill discuss the main techn
 ical new idea in the case of the free group.\n\nAndrei Alpeev\,  "Examples
  of different boundary behaviour of left and right random walks on groups"
 .\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Hruska (University of Wisconsin)\, Anthony Genevois (Montpel
 lier)\, Romain Tessera (Jussieu)
DTSTART:20210622T133000Z
DTEND:20210622T163000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/9/">An afternoon on quasi-isometries of groups</a>\nby Chris Hru
 ska (University of Wisconsin)\, Anthony Genevois (Montpellier)\, Romain Te
 ssera (Jussieu) as part of ENS group theory seminar\n\n\nAbstract\n15.30 -
  16.15  Chris Hruska (University of Wisconsin)\n\n16.30 - 17.15  Anthony G
 enevois (Montpellier)\n\n17.45 - 18.30  Romain Tessera (Jussieu)\n\nChris 
 Hruska\,  "Canonical splittings of relatively hyperbolic groups"\n\nA JSJ 
 decomposition is a graph of groups decomposition that allows one to classi
 fy all splittings of a group over certain subgroups.  I will discuss a JSJ
  decomposition for relatively hyperbolic groupssplitting over elementary s
 ubgroups that depends only on the topology of its boundary.  This decompos
 ition could potentially be of use forunderstanding groups that have homeom
 orphic boundaries\, but are not necessarily quasi-isometric. (Joint work w
 ith Matt Haulmark.)\n\nAnthony Genevois  "Asymptotic geometry of lamplight
 ers over one-ended groups".\n\nAfter a general introduction to lamplighter
  groups and their asymptotic geometry\, I will describe a complete quasi-i
 sometric classification of lamplighters over one-ended finitely presented 
 groups. The proof will be briefly overviewed\, and the rest of the talk wi
 ll be dedicated to the central tool of the argument: an embedding theorem 
 proved thanks to (quasi-)median geometry.\n\nRomain Tessera "Asymptotic ge
 ometry of lamplighters over one-ended groups II".\n\nThis second talk will
  be dedicated to the asymmetry between amenable and non-amenable groups in
  the quasi-isometric classification previously described. In particular\, 
 I will explain why lamplighters over non-amenable groups are more often qu
 asi-isometric than lamplighters over amenable groups. Also\, I will show h
 ow the distance from a quasi-isometry between amenable groups to a bijecti
 on can be quantified\, introducing quasi-k-to-one quasi-isometries for an 
 arbitrary real k>0\, and explain how this notion is fundamental in the und
 erstanding of the asymptotic geometry of lamplighters over amenable groups
 .\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:François Le Maître (Université Paris Diderot -Paris VII)\, Roma
 in Tessera (Université Paris Diderot -Paris VII)\, Pierre Fima (Universit
 é Paris Diderot -Paris VII)
DTSTART:20211011T120000Z
DTEND:20211011T150000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/10/">Group theory afternoon</a>\nby François Le Maître (Univer
 sité Paris Diderot -Paris VII)\, Romain Tessera (Université Paris Didero
 t -Paris VII)\, Pierre Fima (Université Paris Diderot -Paris VII) as part
  of ENS group theory seminar\n\nLecture held in ENS\, 45 rue d'Ulm\, room 
 "salle W"\, roof of the DMA.\n\nAbstract\n14.00 - 14.45    François Le Ma
 ître (Université Paris Diderot -Paris VII)\n\n15.00- 15.45  Romain Tesse
 ra (Université Paris Diderot -Paris VII)\n\n16.00- 16.45  Pierre Fima (Un
 iversité Paris Diderot -Paris VII)\n\n\nFrançois Le Maître  "Reconstruc
 tion for Boolean measure-preserving actions of full groups and application
 s"\n\nGiven a two measure-preserving ergodic action of  countable groups o
 n a standard probability space\, Dye's reconstruction theorem asserts that
  any isomorphism between the associated full groups must come from an isom
 orphism of the space which sends the first partition of the space into orb
 its to the second. It is thus natural to ask what happens more generally f
 or homomorphisms between full groups. I will present a joint work with Ale
 ssandro Carderi and Alice Giraud where we show that any such homomorphism 
  comes from a measure-preserving action of the equivalence relation or of 
 one of its symmetric powers. Such a result is very similar in spirit to Ma
 tte Bon's striking classification of actions by homeomorphisms of topologi
 cal full groups\, but we will see that the proof is much simpler modulo th
 e Thomas-Tucker-Drob classification of invariant random subgroups of the d
 yadic symmetric group. As an application\, we characterize Kazhdan's prope
 rty (T) of a measure-preserving equivalence relation in terms of its full 
 group: the equivalence relation has (T) if and only if all non-free ergodi
 c Boolean actions of its full group are strongly ergodic.\n\n\nRomain Tess
 era "Coarse geometry meets measured group theory" .\n\n We will present a 
 new induction technique based on ideas of Gromov and Shalom. Given two fin
 itely generated groups H and G and a Lipschitz injective map from H to G\,
  we construct a topological coupling space between them. If H is amenable\
 , then this enables us to view H as a ``measured subgroup" of G. Using thi
 s formalism\, we manage to prove that the Folner function of G grows faste
 r than the Folner function of H.\n\nAn application of this result is the f
 ollowing (new) theorem: an amenable group coarsely embeds into a hyperboli
 c group if and only it is virtually nilpotent.\n\n\nPierre Fima\, "Highly 
 transitive groups among groups acting on trees".\n\nAfter an introduction 
 to the topic of highly transitive groups\, I will present a joint work wit
 h F. Le Maître\, S. Moon and Y. Stalder in which we characterize groups a
 cting on trees which are highly transitive.\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Przytycki (McGill\; on sabbatical leave at Paris-Saclay)\, S
 ami Douba (McGill\; visiting Paris-Saclay)\, Jean Lecureux (Paris-Saclay)
DTSTART:20211115T130000Z
DTEND:20211115T160000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/11/">An afternoon of CAT(0) spaces and group theory</a>\nby Piot
 r Przytycki (McGill\; on sabbatical leave at Paris-Saclay)\, Sami Douba (M
 cGill\; visiting Paris-Saclay)\, Jean Lecureux (Paris-Saclay) as part of E
 NS group theory seminar\n\n\nAbstract\n14.00 - 14.45 Piotr Przytycki (McGi
 ll University\; on sabbatical leave at Paris-Saclay)\n\n15.00- 15.45 Sami 
 Douba (McGill University\; visiting Paris-Saclay)\n\n16.00- 16.45 Jean Lec
 ureux (Paris-Saclay) \n\n\nPiotr Przytycki\, "Groups acting almost freely 
 on 2-dimensional CAT(0) complexes satisfy the Tits Alternative"\n\nLet X b
 e a 2-dimensional complex with piecewise smooth Riemannian metric\, finite
 ly many isometry types of cells\, that is CAT(0). Let G be a group acting 
 on X with a bound on cell stabilisers. We will sketch the proof of the Tit
 s Alternative saying that G is virtually cyclic\, virtually Z^2 or contain
 s a nonabelian free group. This generalises our earlier work for X a 2-dim
 ensional systolic complex or a 2-dimensional Euclidean building. This is j
 oint work with Damian Osajda.\n\n\nSami Douba "Proper CAT(0) actions of un
 ipotent-free linear groups".\n\nButton observed that finitely generated ma
 trix groups containing no nontrivial unipotent matrices behave much like g
 roups admitting proper actions by semisimple isometries on complete CAT(0)
  spaces. It turns out that any finitely generated matrix group possesses a
 n action on such a space whose restrictions to unipotent-free subgroups ar
 e in some sense tame. We discuss this phenomenon and some of its implicati
 ons for the representation theory of certain 3-manifold groups.\n\n\nJean 
 Lecureux\,  "Rigidity properties of Ã_2 lattices".\n\nBuildings of type 
 Ã_2 are commonly associated to groups such as G=SL_3(k)\, where k is a no
 n-archimedean local field. Lattices in such a group G have strong rigidity
  properties (for example\, they satisfy Margulis' superrgidity). But there
  are also buildings for which the automorphism group is smaller\, and much
  less understood - but in some cases still cocompact. In this talk I will 
 explain how these other "exotic" lattices are still very rigid\, and raise
  some open questions.\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:MurphyKate Montee (Carleton College)\, Tsung-Hsuan Tsai (IRMA\, CN
 RS\, Université de Strasbourg)\, Damian Orlef (IMPAN\, Warsaw)
DTSTART:20211214T140000Z
DTEND:20211214T170000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/12/">An afternoon on random groups</a>\nby MurphyKate Montee (Ca
 rleton College)\, Tsung-Hsuan Tsai (IRMA\, CNRS\, Université de Strasbour
 g)\, Damian Orlef (IMPAN\, Warsaw) as part of ENS group theory seminar\n\n
 \nAbstract\n15.00 - 15.45  MurphyKate Montee (Carleton College)\n\n16.00 -
 16.45  Tsung-Hsuan Tsai (IRMA\, CNRS\, Université de Strasbourg)\n\n17.15
  - 18.00  Damian Orlef (IMPAN)\n\nMurphyKate Montee\, "Cubulating Random G
 roups at Densities d<3/14"\n\nRandom groups are one way to study "typical"
  behavior of groups. In the Gromov density model\, we often find a thresho
 ld density above which a property is satisfied with probability 1\, and be
 low which it is satisfied with probability 0. Two properties of random gro
 ups that have studied are cubulation and Property (T). In this setting the
 se are mutually exclusive\, but the threshold densities are not known. In 
 this talk I'll present a method to demonstrate cubulation on groups with d
 ensity less than 3/14\, and discuss how this might be extended to demonstr
 ate cubulation for densities up to 1/4. In particular\, I will describe a 
 construction of walls in the Cayley complex X which give rise to a non-tri
 vial action by isometries on a CAT(0) cube complex. This extends results o
 f Ollivier-Wise and Mackay-Przytycki at\ndensities less than 1/5 and 5/24\
 , respectively.\n\n\nTsung-Hsuan Tsai\, "Freiheitssatz for the density mod
 el of random groups"\n\nMagnus' Freiheitssatz states that if a group is de
 fined by a presentation with m generators and a single cyclically reduced 
 relator\, and this relator contains the last generating letter\, then the 
 first m-1 letters freely generate a free subgroup. We study an analogue of
  this theorem in the Gromov density model of random groups\, showing a pha
 se transition phenomenon at density d_r = min{1/2\, 1-log_{2m-1}(2r-1)} wi
 th 0<r<m: we prove that for a random group with m generators at density d\
 , if d<d_r then the first r letters freely generate a free subgroup\; wher
 eas if d>d_r then the first r letters generate the whole group.\n\n\nDamia
 n Orlef\, "Non-orderability of random triangular groups by using random 3C
 NF formulas"\n\nA random group in the triangular binomial model $\\Gamma(n
 \,p)$ is given by the presentation $\\langle S|R \\rangle$\, where $S$ is 
 a set of $n$ generators and $R$ is a random set of cyclically reduced rela
 tors of length 3 over $S$\, with each relator included in $R$ independentl
 y with probability $p$. When $n\\rightarrow\\infty$\, the asymptotic prope
 rties of groups in $\\Gamma(n\,p)$ vary widely with the choice of $p=p(n)$
 . By Antoniuk-Łuczak-Świątkowski and Żuk\, there exist constants $C\, 
 C'$\, such that a random triangular group is asymptotically almost surely 
 (a.a.s.) free if $p<Cn^{-2}$ and a.a.s. infinite\, hyperbolic\, but not fr
 ee\, if $p\\in (C'n^{-2}\, n^{-3/2-\\varepsilon})$. We generalize the seco
 nd statement by finding a constant $c$ such that if $p\\in(cn^{-2}\, n^{-3
 /2-\\varepsilon})$\, then a random triangular group is a.a.s. not left-ord
 erable. We prove this by linking left-orderability of $\\Gamma \\in \\Gamm
 a(n\,p)$ to the satisfiability of the random propositional formula\, const
 ructed from the presentation of $\\Gamma$. The left-orderability of quotie
 nts will\nbe also discussed.\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Friedrich Martin Schneider (Freiberg)\, Eduardo Scarparo (Federal 
 University of Santa Catarina)\, Gidi Amir (Bar Ilan)
DTSTART:20220111T140000Z
DTEND:20220111T170000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/13/">An afternoon on amenable groups</a>\nby Friedrich Martin Sc
 hneider (Freiberg)\, Eduardo Scarparo (Federal University of Santa Catarin
 a)\, Gidi Amir (Bar Ilan) as part of ENS group theory seminar\n\n\nAbstrac
 t\n15.00 - 15.45 	Friedrich Martin Schneider (Freiberg)\n\n16.00 -16.45   
    Eduardo Scarparo (Federal University of Santa Catarina)\n\n17.15 - 18.0
 0    Gidi Amir (Bar Ilan) \n\n\nFriedrich Martin Schneider\,  "Concentrati
 on of invariant means"\n\nIn the context of large (non-locally compact) to
 pological groups\, one frequently witnesses an extreme form  of amenabilit
 y: extreme amenability. A topological group G is called extremely amenable
  if everycontinuous action of G on a non-void compact Hausdorff space admi
 ts afixed point. Most of the currently known manifestations of this phenom
 enon have been exhibited using either structural Ramsey theory\, or concen
 tration of measure. The talk will be focused on the latter method. Among o
 ther things\, I will discuss a new concentration result for convolution pr
 oducts of invariant means\, based on a suitable adaptation of Azuma's ineq
 uality. Furthermore\, I will show how this result can beused to prove extr
 eme amenability of certain topological groups arising from von Neumann's c
 ontinuous geometries.\n\n\nEduardo Scarparo "Amenability and unitary repre
 sentations of groups of dynamical origin.\n\n In the first half\, we repor
 t on joint work with Mehrdad Kalantar in which we completely characterize 
 C*-simplicity of quasi-regular representations associated to stabilizers o
 f boundary actions in terms of amenability of the isotropy groups of the g
 roupoid of germs of the action. For quasi-regular representations associat
 ed to "open" stabilizers\, a complete characterization of C*-simplicity is
  still missing\, and we illustrate this fact with an ad hoc proof that\, f
 or Thompson's group F < T\, the quasi-regular representation of T associat
 ed to [F\,F] properly weakly contains the one associated to F (a year ago 
 Kalantar spoke at this seminar  and I will emphasize the new results and e
 xamples obtained since then).In the second half\, we show that the topolog
 ical full group of a minimal action on the Cantor set is C*-simple if and 
 only if the alternating full group is non-amenable. We use this to conclud
 e that\, e.g.\, for free actions of groups of subexponential growth\, non-
 amenability of the topological full group is equivalent to C*-simplicity\,
  but in general this equivalence is an open problem.\n\n\nGidi Amir  "Amen
 ability of quadratic activity automata groups".\n\n  Automata groups are a
  family of groups acting on rooted trees that have a simple definition yet
  exhibit a very rich behavior. Automaton groups include many interesting e
 xamples such as Grigorchuk groups\, the Basilica group\, Hanoi tower group
 s and lamplighter groups. \n\nThe activity of an automaton group\, introdu
 ced by Sidki\, can be viewed as  a measure of complexity that can  grow ei
 ther polynomially (with some degree)  or exponentially. Sidki proved that 
 polynomial activity automata groups do not contain free subgroups\, which 
 prompted him to ask “Are all polynomial activity automata groups amenabl
 e?”\n\nThis was answered positively  for degree 0 (“bounded”) by Bar
 tholdi-Kaimanovich-Nekrashevych and for degree 1 (“linear”) by Amir-An
 gel-Virag.\n\nJuschenko\, Nekrashevych and de la Salle gave a general appr
 oach allowing to deduce the amenability of  groups from recurrence of the 
 orbital Schreier graphs of group actions satisfying  some conditions. This
  allowed\, among other things\, to reprove the amenability of automata gro
 ups of degree 0 and 1\, and to prove the conditional result that if the "n
 atural" action of a quadratic activity (d=2) automata group is recurrent t
 hen it is amenable.\n\nIn recent work with Omer Angel and Balint Virag\, w
 e prove that the natural Schreier graphs of the quadratic activity mother 
 groups\, a special family into which all quadratic activity automata group
 s can be embedded\, is recurrent. This allows us to conclude the amenabili
 ty of all quadratic activity automata groups.The proof relies on bounding 
 the electrical resistance between vertices in the Schreier graphs\, which 
 in turn relies on a "combinatorial" analysis of the graph structure togeth
 er with  new Nash-Williams type lower bound on resistances.\n\nAfter surve
 ying some background on automata groups\, mother groups and  electrical re
 sistance\, and some previous amenability results on automata groups\, we w
 ill focus on the new analysis giving the resistance lower bounds. No previ
 ous knowledge on random walks\, automata groups or electrical resistance w
 ill be assumed. This talk is based on joint work with O. Angel and B. Vira
 g.\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsachik Gelander (Weizmann Institute)\, Matthieu Joseph (ENS Lyon)
 \, Yair Hartman (Ben Gurion University)
DTSTART:20220208T140000Z
DTEND:20220208T170000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/14/">An afternoon on invariant and stationary random subgroups</
 a>\nby Tsachik Gelander (Weizmann Institute)\, Matthieu Joseph (ENS Lyon)\
 , Yair Hartman (Ben Gurion University) as part of ENS group theory seminar
 \n\n\nAbstract\n15.00 - 15.45    Tsachik Gelander (Weizmann Institute)\, "
 Stationary\nrandom discrete subgroups of semisimple Lie groups"\n\n16.00 -
  16.45    Matthieu Joseph (ENS Lyon)\, "Allosteric actions of\nsurface gro
 ups"\n\n17.15 - 18.00     Yair Hartman (Ben Gurion University)\,\n"Interse
 ctional Invariant Random Subgroups"\n\nPlease see details for talks at the
  following link:\nhttps://sites.google.com/site/annaerschler/grseminar\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcin Sabok (McGill University)\, Juan Paucar (Jussieu)\, Josh Fr
 isch (l'ENS\, Paris)
DTSTART:20200315T130000Z
DTEND:20200315T160000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/15/">A group theory afternoon</a>\nby Marcin Sabok (McGill Unive
 rsity)\, Juan Paucar (Jussieu)\, Josh Frisch (l'ENS\, Paris) as part of EN
 S group theory seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcin Sabok (McGill University)\, Juan Paucar (Jussieu)\, Josh Fr
 isch (l'ENS\, Paris)
DTSTART:20220315T130000Z
DTEND:20220315T160000Z
DTSTAMP:20260404T100115Z
UID:GroupTheoryENS/16
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Group
 TheoryENS/16/">A group theory afternoon</a>\nby Marcin Sabok (McGill Unive
 rsity)\, Juan Paucar (Jussieu)\, Josh Frisch (l'ENS\, Paris) as part of EN
 S group theory seminar\n\nLecture held in Room W\, ENS\, Paris.\n\nAbstrac
 t\n14.00-14.45  Marcin Sabok (McGill University)\n\n15.00 -15.45     Juan 
 Paucar (Jussieu)\n\n16.00 - 16.45    Josh Frisch (l'ENS\, Paris)\n\n\nMarc
 in Sabok\, "Hyperfiniteness at hyperbolic boundaries".  I will discuss rec
 ent results establishing hyperfiniteness of the equivalence relations indu
 ced by actions on the Gromov boundaries of various hyperbolic spaces. This
  includes boundary actions of hyperbolic groups (joint work with T. Marqui
 s) and actions of the mapping class group on the boundaries of the arc gra
 ph and the curve graph (joint work with P. Przytycki).\n\n\n\n\n\nJuan Pau
 car\, "Coarse embeddings between locally compact groups and quantitative m
 easured equivalence". I will discuss about quantitative versions of Measur
 e Equivalence for locally compact compactly generated groups\, a notion in
 troduced by Tessera\, Le Maître\, Delabie and Koivisto on the finitely ge
 nerated case. Moreover\, they introduced as well quantitative asymmetric v
 ersions of it\, called $L^p$-measured subgroups\, and in particular they p
 roved that coarse embeddings between amenable groups imply the existence o
 f a $L^\\infty$-measured coupling. In this talk\, I will prove the same st
 atement on the locally compact case\, which will gives us an obstruction t
 o coarse embeddings for locally compact compactly generated groups.\n\nJos
 h Frisch\,   "Characteristic Measures and Minimal Subdynamics"\n
LOCATION:https://stable.researchseminars.org/talk/GroupTheoryENS/16/
END:VEVENT
END:VCALENDAR