BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Elia Fioravanti (MPIM-Bonn) DTSTART:20211019T130000Z DTEND:20211019T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/1 DESCRIPTION:Title: Automorphisms and splittings of special groups\nby Elia Fiorav anti (MPIM-Bonn) as part of Vienna Geometry and Analysis on Groups Seminar \n\n\nAbstract\nThe automorphism group of a discrete group \\(G\\) can oft en be described quite explicitly in terms of the amalgamated-product and H NN splittings of \\(G\\) over a family of subgroups. In the introductory t alk\, I will discuss the classical case when \\(G\\) is a Gromov-hyperboli c group (originally due to Rips and Sela)\, highlighting some of the techn iques involved. The research talk will then focus on automorphisms of 'spe cial groups'\, a broad family of subgroups of right-angled Artin groups in troduced by Haglund and Wise. The main result is that\, when \\(G\\) is sp ecial\, the outer automorphism group \\(\\mathrm{Out}(G)\\) is infinite if and only if \\(G\\) splits over a centraliser or closely related subgroup s. A similar result holds for automorphisms that preserve a coarse median structure on \\(G\\).\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Greg Bell (UNC Greensboro) DTSTART:20211109T140000Z DTEND:20211109T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/2 DESCRIPTION:Title: Property A and duality in linear programming\nby Greg Bell (UN C Greensboro) as part of Vienna Geometry and Analysis on Groups Seminar\n\ n\nAbstract\nYu introduced property A in 2000 in his work on the Novikov c onjecture as a means to guarantee a uniform embedding into Hilbert space. The class of groups and metric spaces with property A is vast and includes spaces with finite asymptotic dimension or finite decomposition complexit y\, among others. We reduce property A to a sequence of linear programming optimization problems on finite graphs. We explore the dual problem\, whi ch provides a means to show that a graph fails to have property A. As cons equences\, we examine the difference between graphs with expanders and gra phs without property A\, we recover theorems of Willett and Nowak concerni ng graphs without property A\, and arrive at a natural notion of mean prop erty A. This is joint work with Andrzej Nagórko\, University of Warsaw.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Sahana Balasubramanya (Münster) DTSTART:20211116T140000Z DTEND:20211116T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/3 DESCRIPTION:Title: Actions of solvable groups on hyperbolic spaces\nby Sahana Bal asubramanya (Münster) as part of Vienna Geometry and Analysis on Groups S eminar\n\n\nAbstract\nRecent papers of Balasubramanya and Abbott-Rasmussen have classified the hyperbolic actions of several families of classically studied solvable groups. A key tool for these investigations is the machi nery of confining subsets of Caprace-Cornulier-Monod-Tessera. This machine ry applies in particular to solvable groups with virtually cyclic abeliani zations.\n\nIn this talk\, my goal is to explain how to extend this machin ery to classify the hyperbolic actions of certain solvable groups with hig her rank abelianizations. We apply this extension to classify the hyperbol ic actions of a family of groups related to Baumslag-Solitar groups.\n\nTh e first half of the talk will cover the required preliminary information a nd some of the known results concerning the hyperbolic actions of certain solvable groups. In the second half\, I shall explain the techniques used to prove the aforementioned results. Lastly\, I shall talk about the new results that we prove in our paper that generalize these techniques. \n\n (joint work with A.Rasmussen and C.Abbott)\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Pierre Mutanguha (IAS) DTSTART:20211123T140000Z DTEND:20211123T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/4 DESCRIPTION:Title: Limit pretrees for free group automorphisms\nby Jean Pierre Mu tanguha (IAS) as part of Vienna Geometry and Analysis on Groups Seminar\n\ n\nAbstract\nFree group automorphisms seem to share a lot with surface hom eomorphisms. While tools for studying mapping class groups do not always h ave counterparts in the free group setting\, it has nevertheless been extr emely fruitful to mimic these tools as much as we can. This talk will desc ribe our attempt to develop one important missing analogue. Nielsen--Thurs ton theory gives a canonical representation of a surface homeomorphism's i sotopy class. Currently\, no such canonical representation of free group o uter automorphisms exists. \n\nIn the introductory talk\, I will describe the Nielsen--Thurston theory in some detail and outline the proof of this canonical representation. For the research talk\, I will discuss the main obstacles to carrying out the same argument with free group automorphisms. Fortunately\, it appears these obstacles are surmountable and I will disc uss some partial results in this direction.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Zaremsky (SUNY Albany) DTSTART:20211130T140000Z DTEND:20211130T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/5 DESCRIPTION:Title: Higher virtual algebraic fibering of certain right-angled Coxeter groups\nby Matt Zaremsky (SUNY Albany) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nA group is said to "virtually al gebraically fiber" if it has a finite index subgroup admitting a map onto Z with finitely generated kernel. Stronger than finite generation\, if the kernel is even of type F_n for some n then we say the group "virtually al gebraically F_n-fibers". Right-angled Coxeter groups (RACGs) are a class o f groups for which the question of virtual algebraic F_n-fibering is of gr eat interest. In joint work with Eduard Schesler\, we introduce a new prob abilistic criterion for the defining flag complex that ensures a RACG virt ually algebraically F_n-fibers. This expands on work of Jankiewicz--Norin- -Wise\, who developed a way of applying Bestvina--Brady Morse theory to th e Davis complex of a RACG to deduce virtual algebraic fibering. We apply o ur criterion to the special case where the defining flag complex comes fro m a certain family of finite buildings\, and establish virtual algebraic F _n-fibering for such RACGs. The bulk of the work involves proving that a " random" (in some sense) subcomplex of such a building is highly connected\ , which is interesting in its own right.\n\nIn the first half of the talk I will focus just on what Jankiewicz--Norin--Wise did\, so in particular a lways n=1\, and then in the second half I will get into the n>1 case and t he specific examples.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Cordes (ETH Zürich) DTSTART:20211207T140000Z DTEND:20211207T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/6 DESCRIPTION:Title: Coxeter groups with connected Morse boundary\nby Matt Cordes ( ETH Zürich) as part of Vienna Geometry and Analysis on Groups Seminar\n\n \nAbstract\nThe Morse boundary is a quasi-isometry invariant that encodes the possible "hyperbolic" directions of a group. The topology of the Morse boundary can be challenging to understand\, even for simple examples. In this talk\, I will focus on a basic topological property: connectivity and on a well-studied class of CAT(0) groups: Coxeter groups. I will discuss a criteria that guarantees that the Morse boundary of a Coxeter group is c onnected. In particular\, when we restrict to the right-angled case\, we g et a full characterization of right-angled Coxeter groups with connected M orse boundary. This is joint work with Ivan Levcovitz.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:David Kerr (Münster) DTSTART:20220111T140000Z DTEND:20220111T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/7 DESCRIPTION:Title: Entropy\, orbit equivalence\, and sparse connectivity\nby Davi d Kerr (Münster) as part of Vienna Geometry and Analysis on Groups Semina r\n\n\nAbstract\nIt was shown a few years ago by Tim Austin that if an orb it equivalence between probability-measure-preserving actions of finitely generated amenable groups is integrable then it preserves entropy. I will discuss some joint work with Hanfeng Li in which we show that the same con clusion holds for the maximal sofic entropy when the acting groups are cou ntable and sofic and contain an amenable w-normal subgroup which is not lo cally virtually cyclic\, and that it is moreover enough to assume that the Shannon entropy of the cocycle partitions is finite (what we call Shannon orbit equivalence). One consequence is that two Bernoulli actions of a gr oup in the above class are Shannon orbit equivalent if and only if they ar e conjugate.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Steinberg (CUNY) DTSTART:20220118T140000Z DTEND:20220118T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/8 DESCRIPTION:Title: Simplicity of Nekrashevych algebras of contracting self-similar gr oups\nby Benjamin Steinberg (CUNY) as part of Vienna Geometry and Anal ysis on Groups Seminar\n\n\nAbstract\nA self-similar group is a group $G$ acting on the Cayley graph of a finitely generated free monoid $X^*$ (i.e. \, regular rooted tree) by automorphisms in such a way that the self-simil arity of the tree is reflected in the group. The most common examples are generated by the states of a finite automaton. Many famous groups\, like G rigorchuk's 2-group of intermediate growth are of this form. Nekrashevych associated $C^*$-algebras and algebras with coefficients in a field to sel f-similar groups. In the case $G$ is trivial\, the algebra is the classica l Leavitt algebra\, a famous finitely presented simple algebra. Nekrashevy ch showed that the algebra associated to the Grigorchuk group is not simpl e in characteristic 2\, but Clark\, Exel\, Pardo\, Sims and Starling showe d its Nekrashevych algebra is simple over all other fields. Nekrashevych t hen showed that the algebra associated to the Grigorchuk-Erschler group is not simple over any field (the first such example). The Grigorchuk and Gr igorchuk-Erschler groups are contracting self-similar groups. This importa nt class of self-similar groups includes Gupta-Sidki p-groups and many ite rated monodromy groups like the Basilica group. Nekrashevych proved algebr as associated to contacting groups are finitely presented.\n\nIn this talk we discuss a recent result of the speaker and N. Szakacs (Manchester) cha racterizing simplicity of Nekrashevych algebras of contracting groups. In particular\, we give an algorithm for deciding simplicity given an automat on generating the group. We apply our results to several families of contr acting groups like Gupta-Sidki groups\, GGS groups and Sunic's generalizat ions of Grigorchuk's group associated to polynomials over finite fields.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Triestino (Dijon) DTSTART:20220308T140000Z DTEND:20220308T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/9 DESCRIPTION:Title: Describing spaces of harmonic actions on the line\nby Michele Triestino (Dijon) as part of Vienna Geometry and Analysis on Groups Semina r\n\n\nAbstract\nConsidering actions of a given group on a manifold can be seen as a nonlinear version of classical representation theory. In this c ontext\, there is a well-developed theory for actions on one-manifolds\, i n contrast to the situation for higher-dimensional manifolds\, where the s ituation is still at the level of exploration. This is mainly due to the t ight relation to the theory of orderable groups\, which has no analogue in higher dimension.\n\nHow to describe all possible actions on the line of a given group? For finitely generated groups\, one can consider the space of harmonic actions\, whose existence is based on a result of Deroin-Klept syn-Navas-Parwani. This turns out to be a compact space endowed with a tra nslation flow\, whose space of orbits gives exactly the space of all semi- conjugacy classes of actions on the line without global fixed points.\n\nW e are able to understand the space of harmonic actions for solvable groups and many locally moving groups (including Thompson's F and generalization s): the actions of these groups which are not the obvious ones\, are all o btained from actions on planar real trees fixing a point at infinity. This talk is based on a joint project with J Brum\, N Matte Bon and C Rivas.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Ioana (UCSD) DTSTART:20220315T140000Z DTEND:20220315T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/10 DESCRIPTION:Title: Almost commuting matrices and stability for product groups\nb y Adrian Ioana (UCSD) as part of Vienna Geometry and Analysis on Groups Se minar\n\n\nAbstract\nI will present a result showing that the direct produ ct group \\(G=\\mathbb F_2\\times\\mathbb F_2\\)\, where \\(\\mathbb F_2\\ ) is the free group on two generators\, is not Hilbert-Schmidt stable. Thi s means that \\(G\\) admits a sequence of asymptotic homomorphisms (with r espect to the normalized Hilbert-Schmidt norm) which are not perturbations of genuine homomorphisms. While this result concerns unitary matrices\, its proof relies on techniques and ideas from the theory of von Neumann al gebras. I will also explain how this result can be used to settle in the n egative a natural version of an old question of Rosenthal concerning almos t commuting matrices. More precisely\, we derive the existence of contract ion matrices \\(A\,B\\) such that \\(A\\) almost commutes with \\(B\\) and \\(B^*\\) (in the normalized Hilbert-Schmidt norm)\, but there are no mat rices \\(A’\,B’\\) close to \\(A\,B\\) such that \\(A’\\) commutes w ith \\(B’\\) and \\(B’*\\).\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Cameron Cinel (UCSD) DTSTART:20220322T140000Z DTEND:20220322T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/11 DESCRIPTION:Title: Sofic Lie Algebras\nby Cameron Cinel (UCSD) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nWe introduce a not ion of soficity for Lie algebras\, similar to linear soficity for groups a nd associative algebras. Sofic Lie algebras can be thought of as Lie algeb ras that locally are almost embeddable in \\(\\mathfrak{gl}_n(F)\\) for so me \\(n\\). We provide equivalent characterizations for soficity via metri c ultraproducts and local \\(\\varepsilon\\)-almost representations. We sh ow that Lie algebras of subexponential growth are sofic and give explicit families of almost representations for specific Lie algebras. Finally we s how that\, over fields of characteristic 0\, a Lie algebra is sofic if and only if its universal enveloping algebra is linearly sofic.\n\n \n\n \n\n Join Zoom meeting ID 641 2123 2568 or via the link below. Passcode: A grou p is called an ________ group if it admits an invariant mean. (8 letters\, lowercase)\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Edletzberger (Vienna) DTSTART:20220329T130000Z DTEND:20220329T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/12 DESCRIPTION:Title: Quasi-Isometries for certain Right-Angled Coxeter Groups\nby Alexandra Edletzberger (Vienna) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nWe will introduce a construction of a speci fic graph of groups\, the so-called JSJ tree of cylinders\, for certain ri ght-angled Coxeter groups (RACGs) in terms of the defining graph.\nWe will use this as a tool in the hunt for a solution to the Quasi-Isometry Probl em of certain RACGs\, because if there is a quasi-isometry between two RAC Gs\, there is an induced tree isomorphism between the respective JSJ trees of cylinders. In particular\, this tree isomorphism preserves some additi onal structure of the JSJ tree of cylinders. With this fact at hand we can distinguish RACGs up to quasi-isometry.\nAdditionally\, we explain that i n certain cases this structure preserving tree isomorphism even provides a complete quasi-isometry invariant.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Linton (Warwick) DTSTART:20220405T130000Z DTEND:20220405T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/13 DESCRIPTION:Title: Primitivity rank\, one-relator groups and hyperbolicity\nby M arco Linton (Warwick) as part of Vienna Geometry and Analysis on Groups Se minar\n\n\nAbstract\nThe primitivity rank of an element \\(w\\) of a free group \\(F\\) is defined as the minimal rank of a subgroup containing \\(w \\) as an imprimitive element. Recent work of Louder and Wilton has shown that there is a striking connection between this quantity and the subgroup structure of the one-relator group \\(F/\\langle\\langle w\\rangle\\rangl e\\). In this talk\, I will start by motivating the study of one-relator g roups and survey some recent advancements. Then\, I will show that one-rel ator groups whose defining relation has primitivity rank at least 3 are hy perbolic\, confirming a conjecture of Louder and Wilton. Finally\, I will discuss the ingredients that go into proving this result.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Emmanuel Breuillard (Oxford) DTSTART:20220426T130000Z DTEND:20220426T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/14 DESCRIPTION:Title: Random character varieties\nby Emmanuel Breuillard (Oxford) a s part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nCo nsider a random group \\(\\Gamma\\) with \\(k\\) generators and \\(r\\) ra ndom relators of large length \\(N\\). We ask about the geometry of the ch aracter variety of \\(\\Gamma\\) with values in \\(\\mathrm{SL}(2\,\\mathb b{C})\\) or any semisimple Lie group \\(G\\). \nThis is the moduli space o f group homomorphisms from \\(\\Gamma\\) to \\(G\\) up to conjugation. \nW e show that with an exponentially small proportion of exceptions the chara cter variety is empty\, \\(k\\lt r+1\\)\, finite and large\, \\(k=r+1\\)\, or irreducible of dimension \\((k-r-1) \\mathrm{dim}\\thinspace G\\)\, \\ (k\\gt r+1\\). The proofs use new results on expander graphs for finite si mple groups of Lie type and are conditional of the Riemann hypothesis.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Joseph Maher (CSI CUNY) DTSTART:20220503T130000Z DTEND:20220503T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/15 DESCRIPTION:Title: Random walks on WPD groups\nby Joseph Maher (CSI CUNY) as par t of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nWe'll i ntroduce the WPD property for groups\, which can be thought of as a discre teness property for the action of a group on a space which need not be loc ally compact. More precisely\, the action of a group on a Gromov hyperboli c space X is WPD if the action is coarsely discrete along the quasi-axis o f a loxodromic isometry. We'll give some examples of WPD groups\, which in clude the mapping class group of a surface and Out(F_n)\, and consider whe n the action of a group on a quotient of X might still satisfy the WPD pro perty. We'll also show that WPD elements are generic for random walks on WPD groups. This includes joint work with Hidetoshi Masai\, Saul Schleimer and Giulio Tiozzo.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessandro Sisto (Heriot-Watt) DTSTART:20220510T130000Z DTEND:20220510T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/16 DESCRIPTION:Title: Morse boundaries are sometimes not that wild\nby Alessandro S isto (Heriot-Watt) as part of Vienna Geometry and Analysis on Groups Semin ar\n\n\nAbstract\nThe Morse boundary of a metric space X is a topological space that encodes the "hyperbolic directions" of X. When X is not hyperbo lic\, its Morse boundary is not even metrisable\, which makes it sound lik e it should be impossible to understand. As it turns out\, however\, there are various results that describe the Morse boundaries of various interes ting groups\, some even giving complete descriptions of the homeomorphism type. The talk will be an overview of these results.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Yves de Cornulier (Lyon) DTSTART:20220517T130000Z DTEND:20220517T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/17 DESCRIPTION:Title: Near group actions\nby Yves de Cornulier (Lyon) as part of Vi enna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nFor a group ac tion\, every group element acts on a set as a permutation. We consider a s imilar setting where each group element acts a permutation "modulo indeter minacy on finite subsets". We will indicate various natural occurrences of near actions. We will discuss realizability notions: is a given near acti on induced by a genuine action?\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Evetts (Manchester) DTSTART:20220524T130000Z DTEND:20220524T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/18 DESCRIPTION:Title: Equations\, rational sets and formal languages\nby Alex Evett s (Manchester) as part of Vienna Geometry and Analysis on Groups Seminar\n \n\nAbstract\nThe set of solutions to a system of equations over a group i s known as an algebraic set. The study of such sets goes back to the 1970s and 1980s and work of Makanin and Razborov. More recently\, there has bee n a significant amount of effort to describe algebraic sets in various cla sses of groups using formal languages\, and in particular the class of EDT 0L languages. I will explain what an EDT0L language is and describe some r ecent results on virtually abelian groups. Namely that their algebraic set s can be represented by EDT0L languages (joint work with A. Levine)\, and that the same is true for their rational sets\, those sets described by fi nite state automata (joint work with L. Ciobanu).\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Pallavi Dani (LSU) DTSTART:20220531T130000Z DTEND:20220531T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/19 DESCRIPTION:Title: Divergence\, thickness\, and hypergraph index for Coxeter groups< /a>\nby Pallavi Dani (LSU) as part of Vienna Geometry and Analysis on Grou ps Seminar\n\n\nAbstract\nDivergence and thickness are well studied quasi- isometry invariants for finitely generated groups. In general\, they can be quite difficult to compute. In the case of right-angled Coxeter groups \, Levcovitz introduced the notion of hypergraph index\, which can be algo rithmically computed from the defining graph\, and proved that it determin es the thickness and divergence of the group. I will talk about joint wor k with Yusra Naqvi\, Ignat Soroko\, and Anne Thomas\, in which we propose a definition of hypergraph index for general Coxeter groups. We show that it determines the divergence and thickness in an infinite family of non-r ight-angled Coxeter groups.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Sang-hyun Kim (KIAS) DTSTART:20220614T130000Z DTEND:20220614T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/20 DESCRIPTION:Title: Critical regularity of one-manifold actions by right-angled Artin groups and mapping class groups\nby Sang-hyun Kim (KIAS) as part of V ienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nFor each fini te index subgroup \\(H\\) of the mapping class group of a closed hyperboli c surface\, and for each real number \\(r>1\\) we prove that there does no t exist a faithful \\(C^r\\)-action (in Hölder's sense) of \\(H\\) on a c ircle. For this\, we determine the allowed regularities of faithful action s by many right-angled Artin groups on a circle. (Joint with Thomas Koberd a and Cristobal Rivas)\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrés Navas (Santiago de Chile) DTSTART:20220628T130000Z DTEND:20220628T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/21 DESCRIPTION:Title: Distorted diffeomorphisms\nby Andrés Navas (Santiago de Chil e) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract \nAn element of a finitely-generated group is said to be distorted if the word-length of its powers grows sublinearly. An element of a general group is said to be distorted if it is distorted inside a finitely-generated su bgroup. This notion was introduced by Gromov and is worth studying in many frameworks. In this talk I will be interested in diffeomorphisms groups.\ n

Calegary and Freedman showed that many homeomorphisms are distorted\, However\, in general\, \\(C^1\\) diffeomorphisms are not\, for instance du e to the existence of hyperbolic fixed points. Studying similar phenomena in higher regularity turns out to be interesting in the context of ellipti c dynamics. In particular\, we may address the following question: Given \ \(r>\;s>\;1\\)\, does there exist undistorted \\(C^r\\) diffeomorphism s that are distorted inside the group of \\(C^s\\) diffeomorphisms? After a general discussion\, we will focus on the 1–dimensional case of this q uestion for \\(r=2\\) and \\(s=1\\)\, for which we solve it in the affirma tive via the introduction of a new invariant\, namely the asymptotic varia tion.

\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Florin Radulescu (IMAR and Rome) DTSTART:20220602T100000Z DTEND:20220602T104500Z DTSTAMP:20260404T111412Z UID:WienGAGT/22 DESCRIPTION:Title: Dimension formulae of Gelfand-Graev\, Jones and their relation to automorphic forms and temperdness of quasiregular representations\nby Florin Radulescu (IMAR and Rome) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nVaughan Jones introduced a formula comput ing the von Neumann dimension for the restriction to a lattice of the left regular representation of a semisimple Lie group.\n\nIt is a variant of a formula by Atiah Schmidt computing the formal dimension in the Haris Ch andra trace formula for discrete series. It is surprisingly similar (in th e case of PSL(2\,Z)) to the dimension of the space of automorphic forms an d is similar to a formula proved by Gelfand\, Graev. We use an extension of this formula to provide a method for computing the formal trace of repr esentations of PSL(2\,Q_p) (or more general situations)\, when analyzing t he quasi regular representation on PSL(2\,R)/PSL(2\,Z). It provides a meth od to obtain estimates for eigenvalues of Hecke operators.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Annette Karrer (McGill) DTSTART:20221004T130000Z DTEND:20221004T150000Z DTSTAMP:20260404T111412Z 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 sp ace associated to it called the contracting or Morse boundary. This bounda ry captures how similar the CAT(0) space is to a hyperbolic space. Charney --Sultan proved this boundary is a quasi-isometry invariant\, i.e. it can be defined for CAT(0) groups. Interesting examples arise among contracting boundaries of right-anlged Artin and Coxeter groups. \n\nThe talk will co nsist of 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 right-connected Coxeter group changes when we glue certain graphs on its defining graph. We will focus on the question of when the resulting g raph corresponds to a right-angled Coxeter group with totally disconnected contracting boundary. \n\nAfter a short break\, we will see a second res ult 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 use our insights to investigate contracting boundaries of certain R ACGs that contain surprising circles. These examples are joint work with Marius Graeber\, Nir Lazarovich\, and Emily Stark. Finally\, we will trans fer the ideas we saw before to RAAGs. This will result in a proof that all right-angled Artin groups have totally disconnected contracting boundarie s\, reproving a result of Charney--Cordes--Sisto.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Emmanuel Caprace (UC Louvain) DTSTART:20221011T130000Z DTEND:20221011T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/24 DESCRIPTION:Title: New Kazhdan groups with infinitely many alternating quotients \nby Pierre-Emmanuel Caprace (UC Louvain) as part of Vienna Geometry and A nalysis on Groups Seminar\n\n\nAbstract\nIntroductory talk: "Generating th e alternating groups"\n\nAbstract: The goal of this talk is to provide an overview of results and methods allowing one to build generating sets for the finite alternating groups. Some of those rely on the Classification of the Finite Simple Groups\, others don't. This theme will be motivated by open problems concerning the construction of finite quotients of certain f amilies of finitely generated infinite groups. \n\nResearch talk: "New Kaz hdan groups with infinitely many alternating quotients"\n\nAbstract: I wil l introduce a new class of infinite groups enjoying Kazhdan's property (T) and admitting alternating group quotients of arbitrarily large degree. Th ose groups are constructed as automorphism groups of the ring of polynomia ls in n indeterminates with coefficients in the finite field of order p\, generated by a suitable finite set of polynomial transvections. As an appl ication\, we obtain the first examples of hyperbolic Kazdhan groups with i nfinitely many alternating group quotients. We also obtain expander Cayley graphs of degree 4 for an infinite family of alternating groups. The talk is based on joint work with Martin Kassabov.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Xabier Legaspi (ICMAT and IRMAR) DTSTART:20221018T130000Z DTEND:20221018T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/25 DESCRIPTION:Title: Constricting elements and the growth of quasi-convex subgroups\nby Xabier Legaspi (ICMAT and IRMAR) as part of Vienna Geometry and Anal ysis on Groups Seminar\n\nLecture held in SR 10\, 2. OG.\, OMP 1.\n\nAbstr act\nLet \\(G\\) be a group acting properly on a metric space \\(X\\) and consider a path system of \\(X\\). Assume that \\(G\\) contains a constric ting element with respect to this path system\, i.e. a very general condit ion of non-positive curvature. This talk will be about the relative growth and the coset growth of the quasi-convex subgroups of \\(G\\) with respec t to this path system. Through the triangle inequality\, we will see that we can determine that the first kind of growth rates are strictly smaller than the growth rate of \\(G\\)\, while the second kind of growth rates co incide with the growth rate of \\(G\\). Applications include actions of re latively hyperbolic groups\, CAT(0) groups with Morse elements and mapping class groups. This generalises work of Antolín\, Dahmani-Futer-Wise and Gitik-Rips.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Tullio Ceccherini-Silberstein (U. Sannio) DTSTART:20221025T130000Z DTEND:20221025T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/26 DESCRIPTION:Title: Sofic entropy and surjunctive dynamical systems\nby Tullio Ce ccherini-Silberstein (U. Sannio) as part of Vienna Geometry and Analysis o n Groups Seminar\n\nLecture held in SR 10\, 2. OG.\, OMP 1.\n\nAbstract\nA dynamical system is a pair \\((X\,G)\\)\, where \\(X\\) is a compact metr izable 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 su itable dynamical properties (such as expansivity\, nonnegative sofic topol ogical entropy\, weak specification\, and strong topological Markov proper ty) guarantees that (X\,G) is surjunctive. I'll explain in detail all noti ons involved\, the motivations\, and outline the main ideas of the proof o f this result obtained in collaboration with Michel Coornaert and Hanfeng Li.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/26/ END:VEVENT BEGIN:VEVENT SUMMARY:William Slofstra (Waterloo) DTSTART:20221108T140000Z DTEND:20221108T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/27 DESCRIPTION:Title: Group theory and nonlocal games\nby William Slofstra (Waterlo o) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract \nNonlocal games are simple games used in quantum information to explore t he power of entanglement. They are closely connected with Bell inequalitie s\, which have been in the news recently as the subject of this year's Nob el prize in physics. In this talk\, I'll give an overview of a class of no nlocal games called linear system nonlocal games\, which are particularly interesting from the point of view of group theory\, in that every linear system nonlocal games has an associated group which controls the perfect s trategies for the game. The associated groups are finite colimits of finit e abelian groups\, and exploring this class of groups from the perspective of nonlocal games gives rise to a number of interesting results and probl ems in group theory. For the introductory talk\, I'll cover some of the ba ckground concepts that come up: pictures of groups\, residual finiteness\, and hyperlinearity (if time permits\, I may sketch the construction of a group with superpolynomial hyperlinear profile).\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Motiejus Valiunas (Wrocław) DTSTART:20221213T140000Z DTEND:20221213T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/28 DESCRIPTION:Title: Biautomatic and hierarchically hyperbolic groups\nby Motiejus Valiunas (Wrocław) as part of Vienna Geometry and Analysis on Groups Sem inar\n\n\nAbstract\nBiautomatic groups arose as groups explaining formal l anguage-theoretic aspects of geodesics in word-hyperbolic groups. Many cl asses of non-positively curved finitely generated groups\, such as hyperbo lic\, virtually abelian\, cocompactly cubulated\, small cancellation and C oxeter groups\, are known to be biautomatic. On the other hand\, there ar e some other classes\, such as CAT(0) or hierarchically hyperbolic groups\ , for which the relationship to biautomaticity is more complicated.\n\nIn the first half of the talk\, I will outline the notions of non-positive cu rvature appearing in group theory and their connection to biautomaticity. In particular\, I will overview recent results on the relationship betwee n biautomaticity\, hierarchical hyperbolicity and being CAT(0)\, as well a s some constructions of non-biautomatic non-positively curved groups.\n\nT he goal of the second half of the talk is to construct a non-biautomatic h ierarchically hyperbolic group\, giving the first known example of such a group. Our group acts geometrically on the cartesian product of a tree an d the hyperbolic plane\, and therefore satisfies many nice geometric prope rties. The proof of non-biautomaticity will rely on the study of geodesic currents on a closed hyperbolic surface. The talk is based on joint work with Sam Hughes.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Koberda (Virginia) DTSTART:20221115T140000Z DTEND:20221115T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/29 DESCRIPTION:Title: Model theory of the curve graph\nby Thomas Koberda (Virginia) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\n Introductory talk: Automorphisms of the curve graph and related objects\n\ nAbstract: I will give a brief introduction to Ivanov's result on the auto morphism group of the curve graph\, and survey some related results.\n\nRe search talk: Model theory of the curve graph\n\nAbstract: I will describe some novel approaches to investigating the combinatorial topology of surfa ces through model theoretic means. I will give a model theoretic explanati on of how a myriad of objects that are naturally associated to a surface a re interpretable inside of the curve graph\, and how this provides a new p erspective on a certain metaconjecture due to Ivanov. I will also discuss some of the properties of the theory of the curve graph\, including stabil ity and quantifier elimination. This talk represents joint work with V. Di sarlo and J. de la Nuez Gonzalez.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Pilar Páez Guillán (Vienna) DTSTART:20230110T140000Z DTEND:20230110T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/30 DESCRIPTION:Title: Counterexamples to the Zassenhaus conjecture on simple modular Li e algebras\nby Pilar Páez Guillán (Vienna) as part of Vienna Geometr y and Analysis on Groups Seminar\n\n\nAbstract\nHistorically\, the study o f the (outer) automorphism group of a given group (free\, simple...) has i nterested group-theorists\, topologists and geometers\, and consequently i t is also of great importance in the Lie algebra theory. In this talk\, we will briefly revise some of the connections between groups and Lie algebr as before giving a quick overview of the simple Lie algebras of classical and Cartan type over fields of positive characteristic. After that\, we wi ll compare the Schreier and Zassenhaus conjectures on the solvability of \ \(\\mathrm{Out}(G)\\) (resp. \\(\\mathrm{Out}(L)\\))\, the group of outer automorphisms (resp. the Lie algebra of outer derivations) of a finite sim ple group \\(G\\) (resp. a finite-dimensional simple Lie algebra \\(L\\)). While the former is known to be true as a consequence of the classificati on of finite simple groups\, the latter is false over fields of small char acteristic \\(p=2\,3\\). We will finish the talk by presenting a new famil y of counterexamples to the Zassenhaus conjecture over fields of character istic \\(p=3\\)\, as well as commenting some advances for \\(p=2\\).\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Christopher Cashen (Vienna) DTSTART:20221122T140000Z DTEND:20221122T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/31 DESCRIPTION:Title: Snowflakes\, cones\, and shortcuts\nby Christopher Cashen (Vi enna) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstr act\nA graph is strongly shortcut if there exists \\(K>1\\) and a bound on the length of \\(K\\)-biLipschitz embedded cycles. A group is strongly sh ortcut if it acts geometrically on a strongly shortcut graph. This is a ki nd of non-positive curvature condition enjoyed by hyperbolic and CAT(0) gr oups\, for example. Strongly shortcut groups are finitely presented and ha ve all of their asymptotic cones simply connected (so have polynomial Dehn function).\n\n We look at an infinite family of snowflake groups\, which are known to have polynomial Dehn function\, and show that all of their as ymptotic cones are simply connected. The usual ways to show that a group h as all asymptotic cones simply connected are to show that it is either of polynomial growth or has quadratic Dehn function\, but our groups have nei ther of these properties. We also show that the 'obvious' Cayley graph is not strongly shortcut. This implies that some of its asymptotic cones cont ain isometrically embedded circles\, so they have metrically nontrivial lo ops even though there are no topologically nontrivial loops. Here are two questions:\n\n 1. If a group has all of its asymptotic cones simply connec ted\, does that imply that it is \nstrongly shortcut? \n\n2. Is it true th at one Cayley graph of a group is strongly shortcut if and only if every C ayley graph of that group is strongly shortcut? \n\nOur snowflake examples show that the answer to one of these questions is 'no'. \n\nThis is joint work with Nima Hoda and Daniel Woohouse.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/31/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hume (Bristol) DTSTART:20230124T140000Z DTEND:20230124T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/32 DESCRIPTION:Title: Thick embeddings of graphs into symmetric spaces\nby David Hu me (Bristol) as part of Vienna Geometry and Analysis on Groups Seminar\n\n \nAbstract\nInspired by the work of Kolmogorov-Barzdin in the 60’s and m ore recently by Gromov-Guth on thick embeddings into Euclidean spaces\, we consider thick embeddings of graphs into more general symmetric spaces. R oughly\, a thick embedding is a topological embedding of a graph where dis joint pairs of edges and vertices are at least a uniformly controlled dist ance apart (consistent with applications where vertices and edges are cons idered as having volume). The goal is to find thick embeddings with minima l “volume”.\n\nWe prove a dichotomy depending upon the rank of the non -compact factor of the symmetric space. For rank at least 2\, there are th ick embeddings of \\(N\\)-vertex graphs with volume \\(\\leq C N\\log(N)\\ ) where \\(C\\) depends on the maximal degree of the graph. By contrast\, for rank 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 the se results is the notion of a coarse wiring\, which is a continuous embedd ing of one graph inside another satisfying some additional properties. We prove that the minimal “volume” of a coarse wiring into a symmetric sp ace is equivalent to the minimal volume of a thick embedding. We obtain lo wer bounds on the volume of coarse wirings by comparing the relative conne ctivity (as measured by the separation profile) of the domain and target\, and upper bounds by direct construction.\n\nThis is joint work with Benja min Barrett.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Alon Dogon (Weizmann Institute) DTSTART:20230117T140000Z DTEND:20230117T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/33 DESCRIPTION:Title: Hyperlinearity versus flexible Hilbert Schmidt stability for prop erty (T) groups\nby Alon Dogon (Weizmann Institute) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nIn these two talks\ , we will present and illustrate a phenomenon\, commonly termed "stability vs. approximation"\, that has been present in several works in recent yea rs. \nOn the one hand\, consider the following classical question: Given t wo almost commuting matrices/permutations\, are they necessarily close to a pair of commuting matrices/permutations? This turns out to be a typical stability question for groups\, which was introduced by G.N. Arzhantseva a nd L. Paunescu\, and since then considered in different scenarios for gene ral groups. \n\nOn the other hand\, the well known subject of approximatio n for groups is of central interest. Various metric approximation properti es for groups have been defined by different mathematicians (including M. Gromov\, A. Connes\, F. Radulescu\, E. Kirchberg....)\, resulting in notio ns such as sofic and hyperlinear groups\, which have gained importance sin ce their inception. Surprisingly\, no counterexamples for failing soficity or hyperlinearity are known. A somewhat simple observation shows that a g roup that is both stable and approximable is residually finite. This yield ed a successful strategy for constructing certain non-approximable groups by giving ones that are stable but not residually finite. \n\nIn the intro ductory lecture we will discuss these notions precisely\, and in the resea rch part we will present classical residually finite groups\, for which es tablishing (flexible Hilbert Schmidt) stability would still give non hyper linear groups.\nThe same phenomenon is also shown to be generic for random groups in certain models.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Guillon (CNRS/Marseille) DTSTART:20230418T130000Z DTEND:20230418T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/34 DESCRIPTION:Title: Decidability and symbolic dynamics over groups\nby Pierre Gui llon (CNRS/Marseille) as part of Vienna Geometry and Analysis on Groups Se minar\n\n\nAbstract\nShifts of finite type are sets of biinfinite words (s equences of colors from a finite alphabet indexed in \\(\\mathbb{Z}\\)) th at avoid a finite collection of finite patterns. Their dynamical propertie s are very well understood thanks to their representation by matrices or f inite graphs. When changing \\(\\mathbb{Z}\\) into \\(\\mathbb{Z}^2\\)\, t he definition stays coherent\, but most classical dynamical properties or invariants become intractable\; one way to understand this is to consider this object as a computational model\, capable of some algorithmic behavio r.
Now\, when changing \\(\\mathbb{Z}^2\\) into any finitely genera ted group\, 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 intuition on this open problem\, survey what is known\, and sketch s ome ideas that could help approach a solution.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Lvzhou Chen (Purdue) DTSTART:20230516T130000Z DTEND:20230516T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/35 DESCRIPTION:Title: The Kervaire conjecture and the minimal complexity of surfaces\nby Lvzhou Chen (Purdue) as part of Vienna Geometry and Analysis on Grou ps Seminar\n\n\nAbstract\n

Talk 1

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Title: Weights of groups

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Abstract: This is an introductory talk on weights of groups. The weig ht (also called the normal rank) of a group \\(G\\) is the smallest number of elements that normally generate \\(G\\). We will discuss basic propert ies and examples in connection to topology. Although it is a simple notion \, several basic problems remain open\, including the Kervaire conjecture and the Wiegold question. We will explain some well-known partial results and their proofs.

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Talk 2

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Title: The Kerva ire conjecture and the minimal complexity of surfaces

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Abstract: We use topological methods to solve special cases of a fundamental problem i n group theory\, the Kervaire conjecture\, which has connection to various problems in topology. The conjecture asserts that\, for any nontrivial gr oup \\(G\\) and any element \\(w\\) in the free product \\(G*Z\\)\, the qu otient \\((G*Z)/<\;<\;w>\;>\;\\) is still nontrivial\, i.e. the gr oup \\(G*Z\\) has weight greater than 1. We interpret this as a problem of estimating the minimal complexity (in terms of Euler characteristic) of s urface maps to certain spaces. This gives a conceptually simple proof of K lyachko's theorem that confirms the Kervaire conjecture for any \\(G\\) to rsion-free. We also obtain injectivity of the map \\(G\\to(G*Z)/<\;<\; w>\;>\;\\) when \\(w\\) is a proper power for arbitrary \\(G\\). Both results generalize to certain HNN extensions.

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\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Lysenok (Steklov Institute) DTSTART:20230606T130000Z DTEND:20230606T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/36 DESCRIPTION:Title: A sample iterated small cancellation theory for groups of Burnsid e type\nby Igor Lysenok (Steklov Institute) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\n

The free Burnside group \\(B(m\,n)\\) is the \\(m\\)-generated group defined by all relations of t he form \\(x^n=1\\). Despite the simplicity of the definition\, obtaining a structural information about the free Burnside groups is known to be a d ifficult problem. The primary question of this sort is whether \\(B(m\,n)\ \) is finite for given \\(m\, n \\ge 2\\). Starting from fundamental resul ts of Novikov and Adian\, it became known that \\(B(m\,n)\\) is infinite f or all sufficiently large exponents \\(n\\). There are known several appro aches to prove this result and to establish other properties of groups \\( B(m\,n)\\) in the `infinite' case. However\, even simpler ones are quite t echnical and require a large lower bound on the exponent \\(n\\) (as odd \ \(n \\gt 10^{10}\\) in Ol'shanskii's approach).

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The aim of the tal k is to present yet another approach to free Burnside groups of odd expone nt \\(n\\) with \\(m\\ge2\\) generators based on a version of iterated sma ll cancellation theory. The approach works for a `moderate' bound \\(n \\g t 2000\\). In the introductory part\, I make a brief survey of results aro und Burnside groups and give an informal introduction to the small cancell ation theory.

\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Monika Kudlinska (Oxford) DTSTART:20230523T130000Z DTEND:20230523T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/37 DESCRIPTION:Title: Profinite rigidity and free-by-cyclic groups\nby Monika Kudli nska (Oxford) as part of Vienna Geometry and Analysis on Groups Seminar\n\ n\nAbstract\nIt is a natural question to ask how much algebraic informatio n is encoded in the set of finite quotient of a given group. More precisel y\, one tries to establish which properties of infinite\, discrete\, resid ually finite groups are preserved under isomorphisms of their profinite co mpletions. A group is said to be (absolutely) profinitely rigid if its iso morphism type is completely determined by its profinite completion. The fi rst talk will focus on the history of this problem\, covering some classic al results as well as more recent work and open problems in the area. We w ill introduce all the necessary background\, so no prior knowledge of the topic will be assumed.\n\nA variation of this problem involves restricting to a certain family of groups and trying to decide whether a group is pro finitely rigid relative to this family. Much work has been done towards so lving this problem for fundamental groups of 3-manifolds. In the second ta lk\, we will focus our attention on a related family of groups known as fr ee-by-cyclic groups\, which have natural connections with 3-manifolds. We will see that many properties of free-by-cyclic groups are invariants of t heir profinite completion. As a consequence\, we obtain various profinite rigidity results\, including the almost profinite rigidity of generic free -by-cyclic groups amongst the class of all free-by-cyclic groups. \n\nThis is joint work with Sam Hughes.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Pansu (Paris-Saclay) DTSTART:20231114T140000Z DTEND:20231114T160000Z DTSTAMP:20260404T111412Z 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 Vien na Geometry and Analysis on Groups Seminar\n\n\nAbstract\nTopological Data Analysis uses homology as a feature for large data sets. It has successfu lly addressed the issue of the robustness of computing homology. Neverthel ess\, the conditioning number suggests an alternative approach. When compu ting the cohomology of a graph (or a simplicial complex)\, it has geometri c significance: it is known as Cheeger's constant or spectral gap. This in dicates that (co-)chain complexes contain more information than their mere (co-)homology. We turn the set of normed chain complexes into a metric sp ace and study a compactness criterion.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Cantrell (Warwick) DTSTART:20240116T140000Z DTEND:20240116T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/39 DESCRIPTION:Title: Sparse spectrally rigid sets for negatively curved manifolds\ nby Stephen Cantrell (Warwick) as part of Vienna Geometry and Analysis on Groups Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Bogdan Nica (IUPUI) DTSTART:20240604T130000Z DTEND:20240604T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/40 DESCRIPTION:Title: Norms of averaging operators on hyperbolic groups\nby Bogdan Nica (IUPUI) as part of Vienna Geometry and Analysis on Groups Seminar\n\n \nAbstract\nConsider an infinite\, finitely generated group. A natural ope rator\, acting on complex-valued functions on the group\, is the averaging operator defined by a finite subset. What can be said about its norm(s)? I will discuss some results that\, in particular\, address the case of sph erical averaging operators on Gromov hyperbolic groups. In order to provid e some context\, the introductory part of the talk will be devoted to the property of Rapid Decay.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandros Eskenazis (Sorbonne) DTSTART:20241203T140000Z DTEND:20241203T153000Z DTSTAMP:20260404T111412Z UID:WienGAGT/41 DESCRIPTION:Title: Metric rigidity of nonpositive curvature\nby Alexandros Esken azis (Sorbonne) as part of Vienna Geometry and Analysis on Groups Seminar\ n\n\nAbstract\nWe shall present a novel rigidity theorem for metric transf orms of nonpositively curved Alexandrov spaces. We will then use this resu lt to construct counterexamples to previously conjectured metric formulati ons of Kwapień's theorem from Banach space theory. Time permitting\, furt her geometric and algorithmic applications will also be discussed. The tal ks will be based on joint work with M. Mendel (Open University of Israel) and A. Naor (Princeton).\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Ewan Cassidy (Durham) DTSTART:20250114T140000Z DTEND:20250114T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/42 DESCRIPTION:Title: Random permutations\, word maps and Schreier graph expansion\ nby Ewan Cassidy (Durham) as part of Vienna Geometry and Analysis on Group s Seminar\n\n\nAbstract\nGiven a word \\(w\\) in the free group on \\(r\\) generators\, one can obtain a word map for any finite group\, \\(w \\colo n\\thinspace G^r\\to G\\)\, by substitutions. By uniformly randomly sampli ng \\(r\\) random permutations in \\(S_n\\) and evaluating their image und er this word map\, we obtain a '\\(w\\)-random permutation'. Recent studie s of these random permutations have exposed some deep connections with var ious other areas of mathematics. I will discuss the current asymptotic bou nds we have for the expected irreducible characters of \\(w\\)-random perm utations\, and an application towards showing that a large family of rando m Schreier graphs have a near-optimal spectral gap with high probability.\ n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Ignacio Vergara (University of Santiago de Chile) DTSTART:20250325T140000Z DTEND:20250325T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/43 DESCRIPTION:Title: Property (T) and actions on the real line\nby Ignacio Vergara (University of Santiago de Chile) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nThis talk will focus on the class of cou ntable groups admitting a faithful action on \\(\\mathbb{R}\\) by orientat ion-preserving homeomorphisms. Equivalently\, these are the groups that ad mit a left-invariant order. The main question that we will address is how Property (T) -an analytic property defined in terms of unitary representat ions- imposes restrictions on the kinds of action that a group can have on \\(\\mathbb{R}\\).\n\nThe first part of the talk will be devoted to basic definitions and examples. In the second part\, I will present a result th at links the Lipschitz and Kazhdan constants associated to finite generati ng subsets.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Agelos Georgakopoulos (Warwick) DTSTART:20250506T130000Z DTEND:20250506T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/44 DESCRIPTION:Title: A Notion of Dimension based on Probability on Groups\nby Agel os Georgakopoulos (Warwick) as part of Vienna Geometry and Analysis on Gro ups Seminar\n\n\nAbstract\nProbability on Groups studies how properties of a group \\(G\\)\, such as amenability or growth rate\, influence the outc ome of random experiments\, such as random walk or percolation\, carried o ut on (a Cayley graph of) \\(G\\). Can we learn something new about \\(G\\ ) by studying such experiments? I will survey some results in the area and introduce a notion of “dimension” of a group that arose from the hope to answer this question positively.
https://arxiv.org/abs/2404.17278

\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Jintao Deng (SUNY at Buffalo) DTSTART:20250513T130000Z DTEND:20250513T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/45 DESCRIPTION:Title: Higher index theory and the large-scale geometry\nby Jintao D eng (SUNY at Buffalo) as part of Vienna Geometry and Analysis on Groups Se minar\n\n\nAbstract\nThe Novikov conjecture is an important problem in geo metry and topology\, asserting the higher signatures of compact oriented s mooth manifolds are invariant under orientation-preserving homotopy equiva lences. It has inspired a lot of beautiful mathematics\, including the dev elopment of Kasparov’s KK-theory\, Connes’ cyclic cohomology theory\, Gromov-Connes-Moscovici theory of almost flat bundles\, Connes-Higson’s E-theory\, and quantitative operator K-theory. Recent breakthroughs\, such as the works of Connes\, Kasparov\, Higson\, Yu and others\, have extende d its validity to a large class of groups using techniques from geometric group theory\, operator algebras\, and index theory. \n\nTo date\, the Nov ikov conjecture has been verified for a wide range of cases of groups with "good" large scale geometry including amenability\, Yu's Property A\, and coarsely embeddability into Hilbert space. In the first part of the talk\ , I will introduce key concepts in the large-scale geometry. In the second part\, I will discuss the definition of the Novikov conjecture\, and the latest progress in this area.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Cordes (Heriot-Watt) DTSTART:20250520T130000Z DTEND:20250520T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/46 DESCRIPTION:Title: Cannon-Thurston maps for the Morse boundary\nby Matthew Corde s (Heriot-Watt) as part of Vienna Geometry and Analysis on Groups Seminar\ n\n\nAbstract\nFundamental to the study of hyperbolic groups is their Grom ov boundaries. The classical Cannon--Thurston map for a closed fibered hyp erbolic 3-manifolds relates two such boundaries: it gives a continuous sur jection from the boundary of the surface group (a circle) to the boundary of the 3-manifold group (a 2-sphere). Mj (Mitra) generalized this to all h yperbolic groups with hyperbolic normal subgroups. A generalization of the Gromov boundary to all finitely generated groups is called the Morse boun dary. It collects all the "hyperbolic-like" rays in a group. In this talk we will discuss Cannon--Thurston maps for Morse boundaries. This is joint work with Ruth Charney\, Antoine Goldsborough\, Alessandro Sisto and Stefa nie Zbinden.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Hoang Thanh Nguyen (FPT University\, DaNang) DTSTART:20250603T130000Z DTEND:20250603T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/47 DESCRIPTION:Title: Quasi-redirecting boundaries of groups\nby Hoang Thanh Nguyen (FPT University\, DaNang) as part of Vienna Geometry and Analysis on Grou ps Seminar\n\n\nAbstract\nQing and Rafi recently introduced a new boundary for metric spaces\, called the quasi-redirecting (QR) boundary. This boun dary is quasi-isometry invariant\, often compact\, and contains the sublin early Morse boundary as a topological subspace. While the existence of the QR boundary for all finitely generated groups remains an open question\, we establish well-defined QR boundaries for several well-studied classes o f groups\, including relatively hyperbolic groups and all finitely generat ed 3-manifold groups.\n\nWe also demonstrate a connection between the QR b oundary and the divergence of groups: groups with linear divergence have s ingle-point QR boundaries\, whereas certain groups with quadratic divergen ce\, such as graph manifolds and CAT(0) admissible groups\, have QR posets of height 2. Some open questions will be discussed if time permits.\n\nTh is talk is based on joint work with Yulan Qing.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/47/ END:VEVENT BEGIN:VEVENT SUMMARY:John Mackay (Bristol) DTSTART:20251021T130000Z DTEND:20251021T150000Z DTSTAMP:20260404T111412Z UID:WienGAGT/48 DESCRIPTION:Title: Critical exponents for Poincaré profiles and conformal dimension \nby John Mackay (Bristol) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nBenjamini\, Schramm and Timár quantified ho w well-connected an infinite \ngraph is in terms of its "separation profil e"\, where one considers the \ncut size of finite subgraphs. There is an "L^p" version of this that \nuses Poincaré inequalities to measure the co nnectivity of finite \nsubgraphs. These "p-Poincaré profiles" were used in previous work with \nHume and Tessera to show a variety of non-embeddin g results between \ngroups. I'll mainly talk about current work with Hume where we further \nstudy the connection between these profiles and the co nformal dimension \nof the boundary at infinity of certain Gromov hyperbol ic groups.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Eberhard (Warwick) DTSTART:20251104T140000Z DTEND:20251104T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/49 DESCRIPTION:Title: Growth gap of residually soluble groups\nby Sean Eberhard (Wa rwick) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbst ract\nIf \\(G = \\langle X\\rangle\\) is a finitely generated group\, the growth function \\(\\gamma_G(n)\\) is the number of elements of \\(G\\) wo rd length at most \\(n\\). We ignore the fine-scale detail of this functio n and focus on how fast it tends to infinity. The growth of a group is a f undamental quasi-isometric invariant\, but there are still many mysteries. It can be as slow as polynomial (e.g.\, for nilpotent groups)\, or as fas t as exponential (e.g.\, for free groups)\, and nothing else was known unt il the 80's when Grigorchuk gave his famous example of a group of intermed iate growth\, i.e.\, neither polynomial nor exponential\, and it is now kn own (Erschler--Zheng\, 2020) that this group has growth roughly \\(\\exp(n ^{0.767})\\). Grigorchuk's "gap conjecture" predicts that there is some co nstant \\(c > 0\\) such if the growth is slower than \\(\\exp(n^c)\\) then it should be polynomial (which is equivalent to virtual nilpotence\, by a theorem of a Gromov). This is known for residually nilpotent groups with \\(c = 1/2\\)\, and Wilson (2011) showed that it holds for residually solu ble groups with \\(c = 1/6\\). Elena Maini and I have now improved this to \\(c = 1/4\\) in the residually soluble case. To be precise\, if \\(G\\) is residually soluble and its growth is \\(< \\exp(\\frac{n^{1/4}}{100})\\ ) for large \\(n\\) then \\(G\\) is in fact virtually nilpotent. In this t alk I will give an overview of this landsacpe\, including a basic introduc tion to the theory of growth\, and by the end of the talk I will give the whole proof of a slightly weaker bound with exponent \\(\\frac{1}{4.16}\\) .\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne Lonjou (Paris-Saclay) DTSTART:20260113T140000Z DTEND:20260113T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/50 DESCRIPTION:Title: Cremona group and CAT(0) cube complexes\nby Anne Lonjou (Pari s-Saclay) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nA bstract\nThe Cremona group is the group of birational transformations of t he projective plane\, namely isomorphisms between two dense open subsets. This group acts on a CAT(0) cube complex that we constructed with Urech. A fter an introduction on Cremona group and CAT(0) cube complexes\, I will f ocus on fixed-point property for actions on CAT(0) cube complexes and expl ain how it is related to an open question for the Cremona group.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Sablik (Toulouse) DTSTART:20260127T140000Z DTEND:20260127T160000Z DTSTAMP:20260404T111412Z UID:WienGAGT/51 DESCRIPTION:Title: Self-simulable groups\nby Mathieu Sablik (Toulouse) as part o f Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nA configur ation is a colouring of a finitely generated group by a finite alphabet. A subshift of finite type is a set of configurations defined by a finite co llection of forbidden patterns. Subshifts of finite type naturally arise i n the study of tilings and play are of great interest from a computational point of view and symbolic dynamics.\n\nIn the first part of the talk\, w e will address several questions that are classical in the case Z^2\, but which lead to new and largely unexplored phenomena for general finitely ge nerated groups. These include:\n- existence of a subshift of finite type c ontaining at most one element of the alphabet.\n- existence of a subshift of finite type containing only aperiodic configurations (local rules force global behaviour).\n- decidability of the emptiness problem for subshift of finite type\, given the set of forbidden patterns as input.\n\nIn the s econd part of the talk\, we introduce a new class of groups. A finitely ge nerated group is said to be self-simulable if every computable action of t he group on an effectively closed zero-dimensional space is a topological factor of a subshift of finite type over that group. In other words\, any “reasonable” group action can be encoded by local rules. We will show that such groups do exist\, and that the class of self-simulable groups is stable under commensurability and under quasi-isometries among finitely p resented groups. Finally\, we will present several examples of self-simula ble groups\, including Thompson’s group V and higher-dimensional general linear groups.\n\nThis is a joint work with Sebastian Barbieri and Ville Salo.\n LOCATION:https://stable.researchseminars.org/talk/WienGAGT/51/ END:VEVENT END:VCALENDAR