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:20260422T225924Z UID:WienGAGT/1 DESCRIPTION:Title: Automorphisms and splittings of special groups\nby Elia Fioravanti (M PIM-Bonn) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nA bstract\nThe automorphism group of a discrete group \\(G\\) can often be d escribed quite explicitly in terms of the amalgamated-product and HNN spli ttings of \\(G\\) over a family of subgroups. In the introductory talk\, I will discuss the classical case when \\(G\\) is a Gromov-hyperbolic group (originally due to Rips and Sela)\, highlighting some of the techniques i nvolved. The research talk will then focus on automorphisms of 'special gr oups'\, a broad family of subgroups of right-angled Artin groups introduce d by Haglund and Wise. The main result is that\, when \\(G\\) is special\, the outer automorphism group \\(\\mathrm{Out}(G)\\) is infinite if and on ly if \\(G\\) splits over a centraliser or closely related subgroups. A si milar result holds for automorphisms that preserve a coarse median structu re on \\(G\\).\n LOCATION:https://researchseminars.org/talk/WienGAGT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Greg Bell (UNC Greensboro) DTSTART:20211109T140000Z DTEND:20211109T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/2 DESCRIPTION:Title: Property A and duality in linear programming\nby Greg Bell (UNC Green sboro) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbst ract\nYu introduced property A in 2000 in his work on the Novikov conjectu re as a means to guarantee a uniform embedding into Hilbert space. The cla ss of groups and metric spaces with property A is vast and includes spaces with finite asymptotic dimension or finite decomposition complexity\, amo ng others. We reduce property A to a sequence of linear programming optimi zation problems on finite graphs. We explore the dual problem\, which prov ides a means to show that a graph fails to have property A. As consequence s\, we examine the difference between graphs with expanders and graphs wit hout property A\, we recover theorems of Willett and Nowak concerning grap hs without property A\, and arrive at a natural notion of mean property A. This is joint work with Andrzej Nagórko\, University of Warsaw.\n LOCATION:https://researchseminars.org/talk/WienGAGT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Sahana Balasubramanya (Münster) DTSTART:20211116T140000Z DTEND:20211116T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/3 DESCRIPTION:Title: Actions of solvable groups on hyperbolic spaces\nby Sahana Balasubram anya (Münster) as part of Vienna Geometry and Analysis on Groups Seminar\ n\n\nAbstract\nRecent papers of Balasubramanya and Abbott-Rasmussen have c lassified the hyperbolic actions of several families of classically studie d solvable groups. A key tool for these investigations is the machinery of confining subsets of Caprace-Cornulier-Monod-Tessera. This machinery appl ies in particular to solvable groups with virtually cyclic abelianizations .\n\nIn this talk\, my goal is to explain how to extend this machinery to classify the hyperbolic actions of certain solvable groups with higher ran k abelianizations. We apply this extension to classify the hyperbolic acti ons of a family of groups related to Baumslag-Solitar groups.\n\nThe first half of the talk will cover the required preliminary information and some of the known results concerning the hyperbolic actions of certain solvabl e groups. In the second half\, I shall explain the techniques used to pro ve 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://researchseminars.org/talk/WienGAGT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Pierre Mutanguha (IAS) DTSTART:20211123T140000Z DTEND:20211123T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/4 DESCRIPTION:Title: Limit pretrees for free group automorphisms\nby Jean Pierre Mutanguha (IAS) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbst ract\nFree group automorphisms seem to share a lot with surface homeomorph isms. While tools for studying mapping class groups do not always have cou nterparts in the free group setting\, it has nevertheless been extremely f ruitful to mimic these tools as much as we can. This talk will describe ou r attempt to develop one important missing analogue. Nielsen--Thurston the ory gives a canonical representation of a surface homeomorphism's isotopy class. Currently\, no such canonical representation of free group outer au tomorphisms exists. \n\nIn the introductory talk\, I will describe the Nie lsen--Thurston theory in some detail and outline the proof of this canonic al representation. For the research talk\, I will discuss the main obstacl es to carrying out the same argument with free group automorphisms. Fortun ately\, it appears these obstacles are surmountable and I will discuss som e partial results in this direction.\n LOCATION:https://researchseminars.org/talk/WienGAGT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Zaremsky (SUNY Albany) DTSTART:20211130T140000Z DTEND:20211130T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/5 DESCRIPTION:Title: Higher virtual algebraic fibering of certain right-angled Coxeter groups< /a>\nby Matt Zaremsky (SUNY Albany) as part of Vienna Geometry and Analysi s on Groups Seminar\n\n\nAbstract\nA group is said to "virtually algebraic ally 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 algebraic ally F_n-fibers". Right-angled Coxeter groups (RACGs) are a class of group s for which the question of virtual algebraic F_n-fibering is of great int erest. In joint work with Eduard Schesler\, we introduce a new probabilist ic criterion for the defining flag complex that ensures a RACG virtually a lgebraically F_n-fibers. This expands on work of Jankiewicz--Norin--Wise\, who developed a way of applying Bestvina--Brady Morse theory to the Davis complex of a RACG to deduce virtual algebraic fibering. We apply our crit erion to the special case where the defining flag complex comes from a cer tain family of finite buildings\, and establish virtual algebraic F_n-fibe ring 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 always n =1\, and then in the second half I will get into the n>1 case and the spec ific examples.\n LOCATION:https://researchseminars.org/talk/WienGAGT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Cordes (ETH Zürich) DTSTART:20211207T140000Z DTEND:20211207T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/6 DESCRIPTION:Title: Coxeter groups with connected Morse boundary\nby Matt Cordes (ETH Zü rich) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstr act\nThe Morse boundary is a quasi-isometry invariant that encodes the pos sible "hyperbolic" directions of a group. The topology of the Morse bounda ry can be challenging to understand\, even for simple examples. In this ta lk\, I will focus on a basic topological property: connectivity and on a w ell-studied class of CAT(0) groups: Coxeter groups. I will discuss a crite ria that guarantees that the Morse boundary of a Coxeter group is connecte d. In particular\, when we restrict to the right-angled case\, we get a fu ll characterization of right-angled Coxeter groups with connected Morse bo undary. This is joint work with Ivan Levcovitz.\n LOCATION:https://researchseminars.org/talk/WienGAGT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:David Kerr (Münster) DTSTART:20220111T140000Z DTEND:20220111T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/7 DESCRIPTION:Title: Entropy\, orbit equivalence\, and sparse connectivity\nby David Kerr (Münster) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\n Abstract\nIt was shown a few years ago by Tim Austin that if an orbit equi valence between probability-measure-preserving actions of finitely generat ed amenable groups is integrable then it preserves entropy. I will discuss some joint work with Hanfeng Li in which we show that the same conclusion holds for the maximal sofic entropy when the acting groups are countable and sofic and contain an amenable w-normal subgroup which is not locally v irtually cyclic\, and that it is moreover enough to assume that the Shanno n entropy of the cocycle partitions is finite (what we call Shannon orbit equivalence). One consequence is that two Bernoulli actions of a group in the above class are Shannon orbit equivalent if and only if they are conju gate.\n LOCATION:https://researchseminars.org/talk/WienGAGT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Steinberg (CUNY) DTSTART:20220118T140000Z DTEND:20220118T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/8 DESCRIPTION:Title: Simplicity of Nekrashevych algebras of contracting self-similar groups\nby Benjamin Steinberg (CUNY) as part of Vienna Geometry and Analysis 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.\, regu lar rooted tree) by automorphisms in such a way that the self-similarity o f the tree is reflected in the group. The most common examples are generat ed by the states of a finite automaton. Many famous groups\, like Grigorch uk's 2-group of intermediate growth are of this form. Nekrashevych associa ted $C^*$-algebras and algebras with coefficients in a field to self-simil ar groups. In the case $G$ is trivial\, the algebra is the classical Leavi tt algebra\, a famous finitely presented simple algebra. Nekrashevych show ed that the algebra associated to the Grigorchuk group is not simple in ch aracteristic 2\, but Clark\, Exel\, Pardo\, Sims and Starling showed its N ekrashevych algebra is simple over all other fields. Nekrashevych then sho wed that the algebra associated to the Grigorchuk-Erschler group is not si mple over any field (the first such example). The Grigorchuk and Grigorchu k-Erschler groups are contracting self-similar groups. This important clas s of self-similar groups includes Gupta-Sidki p-groups and many iterated m onodromy groups like the Basilica group. Nekrashevych proved algebras asso ciated to contacting groups are finitely presented.\n\nIn this talk we dis cuss a recent result of the speaker and N. Szakacs (Manchester) characteri zing simplicity of Nekrashevych algebras of contracting groups. In particu lar\, we give an algorithm for deciding simplicity given an automaton gene rating the group. We apply our results to several families of contracting groups like Gupta-Sidki groups\, GGS groups and Sunic's generalizations of Grigorchuk's group associated to polynomials over finite fields.\n LOCATION:https://researchseminars.org/talk/WienGAGT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Triestino (Dijon) DTSTART:20220308T140000Z DTEND:20220308T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/9 DESCRIPTION:Title: Describing spaces of harmonic actions on the line\nby Michele Triesti no (Dijon) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\n Abstract\nConsidering actions of a given group on a manifold can be seen a s a nonlinear version of classical representation theory. In this context\ , there is a well-developed theory for actions on one-manifolds\, in contr ast to the situation for higher-dimensional manifolds\, where the situatio n is still at the level of exploration. This is mainly due to the tight re lation 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 harm onic actions\, whose existence is based on a result of Deroin-Kleptsyn-Nav as-Parwani. This turns out to be a compact space endowed with a translatio n flow\, whose space of orbits gives exactly the space of all semi-conjuga cy classes of actions on the line without global fixed points.\n\nWe are a ble to understand the space of harmonic actions for solvable groups and ma ny locally moving groups (including Thompson's F and generalizations): the actions of these groups which are not the obvious ones\, are all obtained from actions on planar real trees fixing a point at infinity. This talk i s based on a joint project with J Brum\, N Matte Bon and C Rivas.\n LOCATION:https://researchseminars.org/talk/WienGAGT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Ioana (UCSD) DTSTART:20220315T140000Z DTEND:20220315T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/10 DESCRIPTION:Title: Almost commuting matrices and stability for product groups\nby Adria n Ioana (UCSD) as part of Vienna Geometry and Analysis on Groups Seminar\n \n\nAbstract\nI will present a result showing that the direct product grou p \\(G=\\mathbb F_2\\times\\mathbb F_2\\)\, where \\(\\mathbb F_2\\) is th e free group on two generators\, is not Hilbert-Schmidt stable. This means that \\(G\\) admits a sequence of asymptotic homomorphisms (with respect to the normalized Hilbert-Schmidt norm) which are not perturbations of gen uine homomorphisms. While this result concerns unitary matrices\, its pro of relies on techniques and ideas from the theory of von Neumann algebras. I will also explain how this result can be used to settle in the negative a natural version of an old question of Rosenthal concerning almost commu ting matrices. More precisely\, we derive the existence of contraction mat rices \\(A\,B\\) such that \\(A\\) almost commutes with \\(B\\) and \\(B^* \\) (in the normalized Hilbert-Schmidt norm)\, but there are no matrices \ \(A’\,B’\\) close to \\(A\,B\\) such that \\(A’\\) commutes with \\( B’\\) and \\(B’*\\).\n LOCATION:https://researchseminars.org/talk/WienGAGT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Cameron Cinel (UCSD) DTSTART:20220322T140000Z DTEND:20220322T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/11 DESCRIPTION:Title: Sofic Lie Algebras\nby Cameron Cinel (UCSD) as part of Vienna Geomet ry and Analysis on Groups Seminar\n\n\nAbstract\nWe introduce a notion of soficity for Lie algebras\, similar to linear soficity for groups and asso ciative algebras. Sofic Lie algebras can be thought of as Lie algebras tha t locally are almost embeddable in \\(\\mathfrak{gl}_n(F)\\) for some \\(n \\). We provide equivalent characterizations for soficity via metric ultra products and local \\(\\varepsilon\\)-almost representations. We show that Lie algebras of subexponential growth are sofic and give explicit familie s of almost representations for specific Lie algebras. Finally we show tha t\, over fields of characteristic 0\, a Lie algebra is sofic if and only i f its universal enveloping algebra is linearly sofic.\n\n \n\n \n\nJoin Zo om meeting ID 641 2123 2568 or via the link below. Passcode: A group is ca lled an ________ group if it admits an invariant mean. (8 letters\, lowerc ase)\n LOCATION:https://researchseminars.org/talk/WienGAGT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Edletzberger (Vienna) DTSTART:20220329T130000Z DTEND:20220329T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/12 DESCRIPTION:Title: Quasi-Isometries for certain Right-Angled Coxeter Groups\nby Alexand ra Edletzberger (Vienna) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nWe will introduce a construction of a specific gra ph of groups\, the so-called JSJ tree of cylinders\, for certain right-ang led Coxeter groups (RACGs) in terms of the defining graph.\nWe will use th is as a tool in the hunt for a solution to the Quasi-Isometry Problem of c ertain RACGs\, because if there is a quasi-isometry between two RACGs\, th ere is an induced tree isomorphism between the respective JSJ trees of cyl inders. In particular\, this tree isomorphism preserves some additional st ructure of the JSJ tree of cylinders. With this fact at hand we can distin guish RACGs up to quasi-isometry.\nAdditionally\, we explain that in certa in cases this structure preserving tree isomorphism even provides a comple te quasi-isometry invariant.\n LOCATION:https://researchseminars.org/talk/WienGAGT/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Linton (Warwick) DTSTART:20220405T130000Z DTEND:20220405T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/13 DESCRIPTION:Title: Primitivity rank\, one-relator groups and hyperbolicity\nby Marco Li nton (Warwick) as part of Vienna Geometry and Analysis on Groups Seminar\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 th ere is a striking connection between this quantity and the subgroup struct ure of the one-relator group \\(F/\\langle\\langle w\\rangle\\rangle\\). I n this talk\, I will start by motivating the study of one-relator groups a nd survey some recent advancements. Then\, I will show that one-relator gr oups whose defining relation has primitivity rank at least 3 are hyperboli c\, confirming a conjecture of Louder and Wilton. Finally\, I will discuss the ingredients that go into proving this result.\n LOCATION:https://researchseminars.org/talk/WienGAGT/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Emmanuel Breuillard (Oxford) DTSTART:20220426T130000Z DTEND:20220426T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/14 DESCRIPTION:Title: Random character varieties\nby Emmanuel Breuillard (Oxford) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nConsider a random group \\(\\Gamma\\) with \\(k\\) generators and \\(r\\) random re lators of large length \\(N\\). We ask about the geometry of the character variety of \\(\\Gamma\\) with values in \\(\\mathrm{SL}(2\,\\mathbb{C})\\ ) or any semisimple Lie group \\(G\\). \nThis is the moduli space of group homomorphisms from \\(\\Gamma\\) to \\(G\\) up to conjugation. \nWe show that with an exponentially small proportion of exceptions the character va riety is empty\, \\(k\\lt r+1\\)\, finite and large\, \\(k=r+1\\)\, or irr educible of dimension \\((k-r-1) \\mathrm{dim}\\thinspace G\\)\, \\(k\\gt r+1\\). The proofs use new results on expander graphs for finite simple gr oups of Lie type and are conditional of the Riemann hypothesis.\n LOCATION:https://researchseminars.org/talk/WienGAGT/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Joseph Maher (CSI CUNY) DTSTART:20220503T130000Z DTEND:20220503T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/15 DESCRIPTION:Title: Random walks on WPD groups\nby Joseph Maher (CSI CUNY) as part of Vi enna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nWe'll introduc e the WPD property for groups\, which can be thought of as a discreteness property for the action of a group on a space which need not be locally co mpact. More precisely\, the action of a group on a Gromov hyperbolic space X is WPD if the action is coarsely discrete along the quasi-axis of a lox odromic isometry. We'll give some examples of WPD groups\, which include t he mapping class group of a surface and Out(F_n)\, and consider when the a ction of a group on a quotient of X might still satisfy the WPD property. We'll also show that WPD elements are generic for random walks on WPD gro ups. This includes joint work with Hidetoshi Masai\, Saul Schleimer and Gi ulio Tiozzo.\n LOCATION:https://researchseminars.org/talk/WienGAGT/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessandro Sisto (Heriot-Watt) DTSTART:20220510T130000Z DTEND:20220510T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/16 DESCRIPTION:Title: Morse boundaries are sometimes not that wild\nby Alessandro Sisto (H eriot-Watt) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\ nAbstract\nThe Morse boundary of a metric space X is a topological space t hat encodes the "hyperbolic directions" of X. When X is not hyperbolic\, i ts Morse boundary is not even metrisable\, which makes it sound like it sh ould be impossible to understand. As it turns out\, however\, there are va rious results that describe the Morse boundaries of various interesting gr oups\, some even giving complete descriptions of the homeomorphism type. T he talk will be an overview of these results.\n LOCATION:https://researchseminars.org/talk/WienGAGT/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Yves de Cornulier (Lyon) DTSTART:20220517T130000Z DTEND:20220517T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/17 DESCRIPTION:Title: Near group actions\nby Yves de Cornulier (Lyon) as part of Vienna Ge ometry and Analysis on Groups Seminar\n\n\nAbstract\nFor a group action\, every group element acts on a set as a permutation. We consider a similar setting where each group element acts a permutation "modulo indeterminacy on finite subsets". We will indicate various natural occurrences of near a ctions. We will discuss realizability notions: is a given near action indu ced by a genuine action?\n LOCATION:https://researchseminars.org/talk/WienGAGT/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Evetts (Manchester) DTSTART:20220524T130000Z DTEND:20220524T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/18 DESCRIPTION:Title: Equations\, rational sets and formal languages\nby Alex Evetts (Manc hester) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbs tract\nThe set of solutions to a system of equations over a group is known as an algebraic set. The study of such sets goes back to the 1970s and 19 80s and work of Makanin and Razborov. More recently\, there has been a sig nificant amount of effort to describe algebraic sets in various classes of groups using formal languages\, and in particular the class of EDT0L lang uages. I will explain what an EDT0L language is and describe some recent r esults on virtually abelian groups. Namely that their algebraic sets can b e represented by EDT0L languages (joint work with A. Levine)\, and that th e same is true for their rational sets\, those sets described by finite st ate automata (joint work with L. Ciobanu).\n LOCATION:https://researchseminars.org/talk/WienGAGT/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Pallavi Dani (LSU) DTSTART:20220531T130000Z DTEND:20220531T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/19 DESCRIPTION:Title: Divergence\, thickness\, and hypergraph index for Coxeter groups\nby Pallavi Dani (LSU) as part of Vienna Geometry and Analysis on Groups Semi nar\n\n\nAbstract\nDivergence and thickness are well studied quasi-isometr y invariants for finitely generated groups. In general\, they can be quit e difficult to compute. In the case of right-angled Coxeter groups\, Levc ovitz introduced the notion of hypergraph index\, which can be algorithmic ally computed from the defining graph\, and proved that it determines the thickness and divergence of the group. I will talk about joint work with Yusra Naqvi\, Ignat Soroko\, and Anne Thomas\, in which we propose a defin ition of hypergraph index for general Coxeter groups. We show that it det ermines the divergence and thickness in an infinite family of non-right-an gled Coxeter groups.\n LOCATION:https://researchseminars.org/talk/WienGAGT/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Sang-hyun Kim (KIAS) DTSTART:20220614T130000Z DTEND:20220614T150000Z DTSTAMP:20260422T225924Z 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 Vienna G eometry and Analysis on Groups Seminar\n\n\nAbstract\nFor each finite inde x subgroup \\(H\\) of the mapping class group of a closed hyperbolic surfa ce\, and for each real number \\(r>1\\) we prove that there does not exist a faithful \\(C^r\\)-action (in Hölder's sense) of \\(H\\) on a circle. For this\, we determine the allowed regularities of faithful actions by ma ny right-angled Artin groups on a circle. (Joint with Thomas Koberda and C ristobal Rivas)\n LOCATION:https://researchseminars.org/talk/WienGAGT/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrés Navas (Santiago de Chile) DTSTART:20220628T130000Z DTEND:20220628T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/21 DESCRIPTION:Title: Distorted diffeomorphisms\nby Andrés Navas (Santiago de Chile) as p art of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nAn el ement of a finitely-generated group is said to be distorted if the word-le ngth of its powers grows sublinearly. An element of a general group is sai d to be distorted if it is distorted inside a finitely-generated subgroup. This notion was introduced by Gromov and is worth studying in many framew orks. In this talk I will be interested in diffeomorphisms groups.\n

Cal egary and Freedman showed that many homeomorphisms are distorted\, However \, in general\, \\(C^1\\) diffeomorphisms are not\, for instance due to th e existence of hyperbolic fixed points. Studying similar phenomena in high er regularity turns out to be interesting in the context of elliptic dynam ics. In particular\, we may address the following question: Given \\(r>\ ;s>\;1\\)\, does there exist undistorted \\(C^r\\) diffeomorphisms that are distorted inside the group of \\(C^s\\) diffeomorphisms? After a gener al discussion\, we will focus on the 1–dimensional case of this question for \\(r=2\\) and \\(s=1\\)\, for which we solve it in the affirmative vi a the introduction of a new invariant\, namely the asymptotic variation.\n LOCATION:https://researchseminars.org/talk/WienGAGT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Florin Radulescu (IMAR and Rome) DTSTART:20220602T100000Z DTEND:20220602T104500Z DTSTAMP:20260422T225924Z UID:WienGAGT/22 DESCRIPTION:Title: Dimension formulae of Gelfand-Graev\, Jones and their relation to automo rphic forms and temperdness of quasiregular representations\nby Florin Radulescu (IMAR and Rome) as part of Vienna Geometry and Analysis on Grou ps Seminar\n\n\nAbstract\nVaughan Jones introduced a formula computing the von Neumann dimension for the restriction to a lattice of the left regula r representation of a semisimple Lie group.\n\nIt is a variant of a formul a by Atiah Schmidt computing the formal dimension in the Haris Chandra t race formula for discrete series. It is surprisingly similar (in the case of PSL(2\,Z)) to the dimension of the space of automorphic forms and is si milar to a formula proved by Gelfand\, Graev. We use an extension of this formula to provide a method for computing the formal trace of representat ions of PSL(2\,Q_p) (or more general situations)\, when analyzing the quas i regular representation on PSL(2\,R)/PSL(2\,Z). It provides a method to o btain estimates for eigenvalues of Hecke operators.\n LOCATION:https://researchseminars.org/talk/WienGAGT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Annette Karrer (McGill) DTSTART:20221004T130000Z DTEND:20221004T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/23 DESCRIPTION:Title: Contracting boundaries of right-angled Coxeter and Artin groups\nby Annette Karrer (McGill) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nA complete CAT(0) space has a topological space ass ociated to it called the contracting or Morse boundary. This boundary capt ures how similar the CAT(0) space is to a hyperbolic space. Charney--Sulta n proved this boundary is a quasi-isometry invariant\, i.e. it can be defi ned for CAT(0) groups. Interesting examples arise among contracting bounda ries of right-anlged Artin and Coxeter groups. \n\nThe talk will consist o f two parts. The first 45 minutes will be about the main result of my PhD project. We will study the question of how the contracting boundary of a r ight-connected Coxeter group changes when we glue certain graphs on its de fining graph. We will focus on the question of when the resulting graph co rresponds to a right-angled Coxeter group with totally disconnected contra cting boundary. \n\nAfter a short break\, we will see a second result of my PhD thesis concerning the question of what happens if we glue a path of length at least two to a defining graph of a RACG. Afterwards\, we will u se our insights to investigate contracting boundaries of certain RACGs t hat contain surprising circles. These examples are joint work with Marius Graeber\, Nir Lazarovich\, and Emily Stark. Finally\, we will transfer the ideas we saw before to RAAGs. This will result in a proof that all right- angled Artin groups have totally disconnected contracting boundaries\, rep roving a result of Charney--Cordes--Sisto.\n LOCATION:https://researchseminars.org/talk/WienGAGT/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Emmanuel Caprace (UC Louvain) DTSTART:20221011T130000Z DTEND:20221011T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/24 DESCRIPTION:Title: New Kazhdan groups with infinitely many alternating quotients\nby Pi erre-Emmanuel Caprace (UC Louvain) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nIntroductory talk: "Generating the alter nating groups"\n\nAbstract: The goal of this talk is to provide an overvie w of results and methods allowing one to build generating sets for the fin ite alternating groups. Some of those rely on the Classification of the Fi nite Simple Groups\, others don't. This theme will be motivated by open pr oblems concerning the construction of finite quotients of certain families of finitely generated infinite groups. \n\nResearch talk: "New Kazhdan gr oups with infinitely many alternating quotients"\n\nAbstract: I will intro duce a new class of infinite groups enjoying Kazhdan's property (T) and ad mitting alternating group quotients of arbitrarily large degree. Those gro ups are constructed as automorphism groups of the ring of polynomials in n indeterminates with coefficients in the finite field of order p\, generat ed by a suitable finite set of polynomial transvections. As an application \, we obtain the first examples of hyperbolic Kazdhan groups with infinite ly many alternating group quotients. We also obtain expander Cayley graphs of degree 4 for an infinite family of alternating groups. The talk is bas ed on joint work with Martin Kassabov.\n LOCATION:https://researchseminars.org/talk/WienGAGT/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Xabier Legaspi (ICMAT and IRMAR) DTSTART:20221018T130000Z DTEND:20221018T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/25 DESCRIPTION:Title: Constricting elements and the growth of quasi-convex subgroups\nby X abier Legaspi (ICMAT and IRMAR) as part of Vienna Geometry and Analysis on Groups Seminar\n\nLecture held in SR 10\, 2. OG.\, OMP 1.\n\nAbstract\nLe t \\(G\\) be a group acting properly on a metric space \\(X\\) and conside r a path system of \\(X\\). Assume that \\(G\\) contains a constricting el ement with respect to this path system\, i.e. a very general condition of non-positive curvature. This talk will be about the relative growth and th e coset growth of the quasi-convex subgroups of \\(G\\) with respect to th is path system. Through the triangle inequality\, we will see that we can determine that the first kind of growth rates are strictly smaller than th e growth rate of \\(G\\)\, while the second kind of growth rates coincide with the growth rate of \\(G\\). Applications include actions of relativel y hyperbolic groups\, CAT(0) groups with Morse elements and mapping class groups. This generalises work of Antolín\, Dahmani-Futer-Wise and Gitik-R ips.\n LOCATION:https://researchseminars.org/talk/WienGAGT/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Tullio Ceccherini-Silberstein (U. Sannio) DTSTART:20221025T130000Z DTEND:20221025T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/26 DESCRIPTION:Title: Sofic entropy and surjunctive dynamical systems\nby Tullio Ceccherin i-Silberstein (U. Sannio) as part of Vienna Geometry and Analysis on Group s Seminar\n\nLecture held in SR 10\, 2. OG.\, OMP 1.\n\nAbstract\nA dynami cal system is a pair \\((X\,G)\\)\, where \\(X\\) is a compact metrizable space and \\(G\\) is a countable group acting by homeomorphisms of \\(X\\) . An endomorphism of \\((X\,G)\\) is a continuous selfmap of \\(X\\) which commutes with the action of \\(G\\). A dynamical system \\((X\, G)\\) is said to be surjunctive if every injective endomorphism of \\((X\,G)\\) is surjective. When the group \\(G\\) is sofic\, the combination of suitable dynamical properties (such as expansivity\, nonnegative sofic topological entropy\, weak specification\, and strong topological Markov property) gua rantees that (X\,G) is surjunctive. I'll explain in detail all notions inv olved\, the motivations\, and outline the main ideas of the proof of this result obtained in collaboration with Michel Coornaert and Hanfeng Li.\n LOCATION:https://researchseminars.org/talk/WienGAGT/26/ END:VEVENT BEGIN:VEVENT SUMMARY:William Slofstra (Waterloo) DTSTART:20221108T140000Z DTEND:20221108T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/27 DESCRIPTION:Title: Group theory and nonlocal games\nby William Slofstra (Waterloo) as p art of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nNonlo cal games are simple games used in quantum information to explore the powe r of entanglement. They are closely connected with Bell inequalities\, whi ch have been in the news recently as the subject of this year's Nobel priz e in physics. In this talk\, I'll give an overview of a class of nonlocal games called linear system nonlocal games\, which are particularly interes ting from the point of view of group theory\, in that every linear system nonlocal games has an associated group which controls the perfect strategi es for the game. The associated groups are finite colimits of finite abeli an groups\, and exploring this class of groups from the perspective of non local games gives rise to a number of interesting results and problems in group theory. For the introductory talk\, I'll cover some of the backgroun d concepts that come up: pictures of groups\, residual finiteness\, and hy perlinearity (if time permits\, I may sketch the construction of a group w ith superpolynomial hyperlinear profile).\n LOCATION:https://researchseminars.org/talk/WienGAGT/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Motiejus Valiunas (Wrocław) DTSTART:20221213T140000Z DTEND:20221213T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/28 DESCRIPTION:Title: Biautomatic and hierarchically hyperbolic groups\nby Motiejus Valiun as (Wrocław) as part of Vienna Geometry and Analysis on Groups Seminar\n\ n\nAbstract\nBiautomatic groups arose as groups explaining formal language -theoretic aspects of geodesics in word-hyperbolic groups. Many classes o f non-positively curved finitely generated groups\, such as hyperbolic\, v irtually abelian\, cocompactly cubulated\, small cancellation and Coxeter groups\, are known to be biautomatic. On the other hand\, there are some other classes\, such as CAT(0) or hierarchically hyperbolic groups\, for w hich the relationship to biautomaticity is more complicated.\n\nIn the fir st half of the talk\, I will outline the notions of non-positive curvature appearing in group theory and their connection to biautomaticity. In par ticular\, I will overview recent results on the relationship between biaut omaticity\, hierarchical hyperbolicity and being CAT(0)\, as well as some constructions of non-biautomatic non-positively curved groups.\n\nThe goal of the second half of the talk is to construct a non-biautomatic hierarch ically hyperbolic group\, giving the first known example of such a group. Our group acts geometrically on the cartesian product of a tree and the h yperbolic plane\, and therefore satisfies many nice geometric properties. The proof of non-biautomaticity will rely on the study of geodesic curren ts on a closed hyperbolic surface. The talk is based on joint work with S am Hughes.\n LOCATION:https://researchseminars.org/talk/WienGAGT/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Koberda (Virginia) DTSTART:20221115T140000Z DTEND:20221115T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/29 DESCRIPTION:Title: Model theory of the curve graph\nby Thomas Koberda (Virginia) as par t of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nIntrodu ctory talk: Automorphisms of the curve graph and related objects\n\nAbstra ct: I will give a brief introduction to Ivanov's result on the automorphis m group of the curve graph\, and survey some related results.\n\nResearch talk: Model theory of the curve graph\n\nAbstract: I will describe some no vel approaches to investigating the combinatorial topology of surfaces thr ough model theoretic means. I will give a model theoretic explanation of h ow a myriad of objects that are naturally associated to a surface are inte rpretable inside of the curve graph\, and how this provides a new perspect ive on a certain metaconjecture due to Ivanov. I will also discuss some of the properties of the theory of the curve graph\, including stability and quantifier elimination. This talk represents joint work with V. Disarlo a nd J. de la Nuez Gonzalez.\n LOCATION:https://researchseminars.org/talk/WienGAGT/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Pilar Páez Guillán (Vienna) DTSTART:20230110T140000Z DTEND:20230110T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/30 DESCRIPTION:Title: Counterexamples to the Zassenhaus conjecture on simple modular Lie algeb ras\nby Pilar Páez Guillán (Vienna) as part of Vienna Geometry and A nalysis on Groups Seminar\n\n\nAbstract\nHistorically\, the study of the ( outer) automorphism group of a given group (free\, simple...) has interest ed group-theorists\, topologists and geometers\, and consequently it is al so of great importance in the Lie algebra theory. In this talk\, we will b riefly revise some of the connections between groups and Lie algebras befo re giving a quick overview of the simple Lie algebras of classical and Car tan type over fields of positive characteristic. After that\, we will comp are the Schreier and Zassenhaus conjectures on the solvability of \\(\\mat hrm{Out}(G)\\) (resp. \\(\\mathrm{Out}(L)\\))\, the group of outer automor phisms (resp. the Lie algebra of outer derivations) of a finite simple gro up \\(G\\) (resp. a finite-dimensional simple Lie algebra \\(L\\)). While the former is known to be true as a consequence of the classification of f inite simple groups\, the latter is false over fields of small characteris tic \\(p=2\,3\\). We will finish the talk by presenting a new family of co unterexamples to the Zassenhaus conjecture over fields of characteristic \ \(p=3\\)\, as well as commenting some advances for \\(p=2\\).\n LOCATION:https://researchseminars.org/talk/WienGAGT/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Christopher Cashen (Vienna) DTSTART:20221122T140000Z DTEND:20221122T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/31 DESCRIPTION:Title: Snowflakes\, cones\, and shortcuts\nby Christopher Cashen (Vienna) a s part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nA graph is strongly shortcut if there exists \\(K>1\\) and a bound on the le ngth of \\(K\\)-biLipschitz embedded cycles. A group is strongly shortcut if it acts geometrically on a strongly shortcut graph. This is a kind of n on-positive curvature condition enjoyed by hyperbolic and CAT(0) groups\, for example. Strongly shortcut groups are finitely presented and have all of their asymptotic cones simply connected (so have polynomial Dehn functi on).\n\n We look at an infinite family of snowflake groups\, which are kno wn to have polynomial Dehn function\, and show that all of their asymptoti c cones are simply connected. The usual ways to show that a group has all asymptotic cones simply connected are to show that it is either of polynom ial growth or has quadratic Dehn function\, but our groups have neither of these properties. We also show that the 'obvious' Cayley graph is not str ongly shortcut. This implies that some of its asymptotic cones contain iso metrically embedded circles\, so they have metrically nontrivial loops eve n though there are no topologically nontrivial loops. Here are two questio ns:\n\n 1. If a group has all of its asymptotic cones simply connected\, d oes that imply that it is \nstrongly shortcut? \n\n2. Is it true that one Cayley graph of a group is strongly shortcut if and only if every Cayley g raph of that group is strongly shortcut? \n\nOur snowflake examples show t hat the answer to one of these questions is 'no'. \n\nThis is joint work w ith Nima Hoda and Daniel Woohouse.\n LOCATION:https://researchseminars.org/talk/WienGAGT/31/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hume (Bristol) DTSTART:20230124T140000Z DTEND:20230124T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/32 DESCRIPTION:Title: Thick embeddings of graphs into symmetric spaces\nby David Hume (Bri stol) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstr act\nInspired by the work of Kolmogorov-Barzdin in the 60’s and more rec ently by Gromov-Guth on thick embeddings into Euclidean spaces\, we consid er thick embeddings of graphs into more general symmetric spaces. Roughly\ , a thick embedding is a topological embedding of a graph where disjoint p airs of edges and vertices are at least a uniformly controlled distance ap art (consistent with applications where vertices and edges are considered as having volume). The goal is to find thick embeddings with minimal “vo lume”.\n\nWe prove a dichotomy depending upon the rank of the non-compac t factor of the symmetric space. For rank at least 2\, there are thick emb eddings of \\(N\\)-vertex graphs with volume \\(\\leq C N\\log(N)\\) where \\(C\\) depends on the maximal degree of the graph. By contrast\, for ran k at most 1\, thick embeddings of expander graphs have volume \\(\\geq c N ^{1+a}\\) for some \\(a\\geq 0\\).\n\nThe key tool required for these resu lts is the notion of a coarse wiring\, which is a continuous embedding of one graph inside another satisfying some additional properties. We prove t hat the minimal “volume” of a coarse wiring into a symmetric space is equivalent to the minimal volume of a thick embedding. We obtain lower bou nds on the volume of coarse wirings by comparing the relative connectivity (as measured by the separation profile) of the domain and target\, and up per bounds by direct construction.\n\nThis is joint work with Benjamin Bar rett.\n LOCATION:https://researchseminars.org/talk/WienGAGT/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Alon Dogon (Weizmann Institute) DTSTART:20230117T140000Z DTEND:20230117T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/33 DESCRIPTION:Title: Hyperlinearity versus flexible Hilbert Schmidt stability for property (T ) groups\nby Alon Dogon (Weizmann Institute) as part of Vienna Geometr y and Analysis on Groups Seminar\n\n\nAbstract\nIn these two talks\, we wi ll present and illustrate a phenomenon\, commonly termed "stability vs. ap proximation"\, that has been present in several works in recent years. \nO n the one hand\, consider the following classical question: Given two almo st commuting matrices/permutations\, are they necessarily close to a pair of commuting matrices/permutations? This turns out to be a typical stabili ty question for groups\, which was introduced by G.N. Arzhantseva and L. P aunescu\, and since then considered in different scenarios for general gro ups. \n\nOn the other hand\, the well known subject of approximation for g roups is of central interest. Various metric approximation properties for groups have been defined by different mathematicians (including M. Gromov\ , A. Connes\, F. Radulescu\, E. Kirchberg....)\, resulting in notions such as sofic and hyperlinear groups\, which have gained importance since thei r inception. Surprisingly\, no counterexamples for failing soficity or hyp erlinearity are known. A somewhat simple observation shows that a group th at is both stable and approximable is residually finite. This yielded a su ccessful strategy for constructing certain non-approximable groups by givi ng ones that are stable but not residually finite. \n\nIn the introductory lecture we will discuss these notions precisely\, and in the research par t we will present classical residually finite groups\, for which establish ing (flexible Hilbert Schmidt) stability would still give non hyperlinear groups.\nThe same phenomenon is also shown to be generic for random groups in certain models.\n LOCATION:https://researchseminars.org/talk/WienGAGT/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Guillon (CNRS/Marseille) DTSTART:20230418T130000Z DTEND:20230418T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/34 DESCRIPTION:Title: Decidability and symbolic dynamics over groups\nby Pierre Guillon (C NRS/Marseille) as part of Vienna Geometry and Analysis on Groups Seminar\n \n\nAbstract\nShifts of finite type are sets of biinfinite words (sequence s of colors from a finite alphabet indexed in \\(\\mathbb{Z}\\)) that avoi d a finite collection of finite patterns. Their dynamical properties are v ery well understood thanks to their representation by matrices or finite g raphs. When changing \\(\\mathbb{Z}\\) into \\(\\mathbb{Z}^2\\)\, the defi nition stays coherent\, but most classical dynamical properties or invaria nts become intractable\; one way to understand this is to consider this ob ject as a computational model\, capable of some algorithmic behavior.
Now\, when changing \\(\\mathbb{Z}^2\\) into any finitely generated gro up\, it is not completely clear when the behavior is close to that of \\(\ \mathbb{Z}\\) or to that of \\(\\mathbb{Z}^2\\). I will try to give some i ntuition on this open problem\, survey what is known\, and sketch some ide as that could help approach a solution.\n LOCATION:https://researchseminars.org/talk/WienGAGT/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Lvzhou Chen (Purdue) DTSTART:20230516T130000Z DTEND:20230516T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/35 DESCRIPTION:Title: The Kervaire conjecture and the minimal complexity of surfaces\nby L vzhou Chen (Purdue) as part of Vienna Geometry and Analysis on Groups Semi nar\n\n\nAbstract\n

Talk 1

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Title: Weights of groups

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

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Talk 2

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Title: The Kervaire con jecture and the minimal complexity of surfaces

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

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\n LOCATION:https://researchseminars.org/talk/WienGAGT/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Lysenok (Steklov Institute) DTSTART:20230606T130000Z DTEND:20230606T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/36 DESCRIPTION:Title: A sample iterated small cancellation theory for groups of Burnside type< /a>\nby Igor Lysenok (Steklov Institute) as part of Vienna Geometry and An alysis on Groups Seminar\n\n\nAbstract\n

The free Burnside group \\(B(m\ ,n)\\) is the \\(m\\)-generated group defined by all relations of the form \\(x^n=1\\). Despite the simplicity of the definition\, obtaining a struc tural information about the free Burnside groups is known to be a difficul t problem. The primary question of this sort is whether \\(B(m\,n)\\) is f inite for given \\(m\, n \\ge 2\\). Starting from fundamental results of N ovikov and Adian\, it became known that \\(B(m\,n)\\) is infinite for all sufficiently large exponents \\(n\\). There are known several approaches t o prove this result and to establish other properties of groups \\(B(m\,n) \\) in the `infinite' case. However\, even simpler ones are quite technica l and require a large lower bound on the exponent \\(n\\) (as odd \\(n \\g t 10^{10}\\) in Ol'shanskii's approach).

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

\n LOCATION:https://researchseminars.org/talk/WienGAGT/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Monika Kudlinska (Oxford) DTSTART:20230523T130000Z DTEND:20230523T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/37 DESCRIPTION:Title: Profinite rigidity and free-by-cyclic groups\nby Monika Kudlinska (O xford) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbst ract\nIt is a natural question to ask how much algebraic information is en coded in the set of finite quotient of a given group. More precisely\, one tries to establish which properties of infinite\, discrete\, residually f inite groups are preserved under isomorphisms of their profinite completio ns. A group is said to be (absolutely) profinitely rigid if its isomorphis m type is completely determined by its profinite completion. The first tal k will focus on the history of this problem\, covering some classical resu lts as well as more recent work and open problems in the area. We will int roduce all the necessary background\, so no prior knowledge of the topic w ill be assumed.\n\nA variation of this problem involves restricting to a c ertain family of groups and trying to decide whether a group is profinitel y rigid relative to this family. Much work has been done towards solving t his problem for fundamental groups of 3-manifolds. In the second talk\, we will focus our attention on a related family of groups known as free-by-c yclic groups\, which have natural connections with 3-manifolds. We will se e that many properties of free-by-cyclic groups are invariants of their pr ofinite completion. As a consequence\, we obtain various profinite rigidit y results\, including the almost profinite rigidity of generic free-by-cyc lic groups amongst the class of all free-by-cyclic groups. \n\nThis is joi nt work with Sam Hughes.\n LOCATION:https://researchseminars.org/talk/WienGAGT/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Pansu (Paris-Saclay) DTSTART:20231114T140000Z DTEND:20231114T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/38 DESCRIPTION:Title: Computing homology robustly: from persistence to the geometry of normed chain complexes\nby Pierre Pansu (Paris-Saclay) as part of Vienna Geom etry and Analysis on Groups Seminar\n\n\nAbstract\nTopological Data Analys is uses homology as a feature for large data sets. It has successfully add ressed the issue of the robustness of computing homology. Nevertheless\, t he conditioning number suggests an alternative approach. When computing th e cohomology of a graph (or a simplicial complex)\, it has geometric signi ficance: it is known as Cheeger's constant or spectral gap. This indicates that (co-)chain complexes contain more information than their mere (co-)h omology. We turn the set of normed chain complexes into a metric space and study a compactness criterion.\n LOCATION:https://researchseminars.org/talk/WienGAGT/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Cantrell (Warwick) DTSTART:20240116T140000Z DTEND:20240116T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/39 DESCRIPTION:Title: Sparse spectrally rigid sets for negatively curved manifolds\nby Ste phen Cantrell (Warwick) as part of Vienna Geometry and Analysis on Groups Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WienGAGT/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Bogdan Nica (IUPUI) DTSTART:20240604T130000Z DTEND:20240604T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/40 DESCRIPTION:Title: Norms of averaging operators on hyperbolic groups\nby Bogdan Nica (I UPUI) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstr act\nConsider an infinite\, finitely generated group. A natural operator\, acting on complex-valued functions on the group\, is the averaging operat or 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 spherical averaging operators on Gromov hyperbolic groups. In order to provide some context\, the introductory part of the talk will be devoted to the propert y of Rapid Decay.\n LOCATION:https://researchseminars.org/talk/WienGAGT/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandros Eskenazis (Sorbonne) DTSTART:20241203T140000Z DTEND:20241203T153000Z DTSTAMP:20260422T225924Z UID:WienGAGT/41 DESCRIPTION:Title: Metric rigidity of nonpositive curvature\nby Alexandros Eskenazis (S orbonne) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAb stract\nWe shall present a novel rigidity theorem for metric transforms of nonpositively curved Alexandrov spaces. We will then use this result to c onstruct counterexamples to previously conjectured metric formulations of Kwapień's theorem from Banach space theory. Time permitting\, further geo metric and algorithmic applications will also be discussed. The talks will be based on joint work with M. Mendel (Open University of Israel) and A. Naor (Princeton).\n LOCATION:https://researchseminars.org/talk/WienGAGT/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Ewan Cassidy (Durham) DTSTART:20250114T140000Z DTEND:20250114T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/42 DESCRIPTION:Title: Random permutations\, word maps and Schreier graph expansion\nby Ewa n Cassidy (Durham) as part of Vienna Geometry and Analysis on Groups Semin ar\n\n\nAbstract\nGiven a word \\(w\\) in the free group on \\(r\\) genera tors\, one can obtain a word map for any finite group\, \\(w \\colon\\thin space G^r\\to G\\)\, by substitutions. By uniformly randomly sampling \\(r \\) random permutations in \\(S_n\\) and evaluating their image under this word map\, we obtain a '\\(w\\)-random permutation'. Recent studies of th ese random permutations have exposed some deep connections with various ot her areas of mathematics. I will discuss the current asymptotic bounds we have for the expected irreducible characters of \\(w\\)-random permutation s\, and an application towards showing that a large family of random Schre ier graphs have a near-optimal spectral gap with high probability.\n LOCATION:https://researchseminars.org/talk/WienGAGT/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Ignacio Vergara (University of Santiago de Chile) DTSTART:20250325T140000Z DTEND:20250325T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/43 DESCRIPTION:Title: Property (T) and actions on the real line\nby Ignacio Vergara (Unive rsity of Santiago de Chile) as part of Vienna Geometry and Analysis on Gro ups Seminar\n\n\nAbstract\nThis talk will focus on the class of countable groups admitting a faithful action on \\(\\mathbb{R}\\) by orientation-pre serving homeomorphisms. Equivalently\, these are the groups that admit a l eft-invariant order. The main question that we will address is how Propert y (T) -an analytic property defined in terms of unitary representations- i mposes restrictions on the kinds of action that a group can have on \\(\\m athbb{R}\\).\n\nThe first part of the talk will be devoted to basic defini tions and examples. In the second part\, I will present a result that link s the Lipschitz and Kazhdan constants associated to finite generating subs ets.\n LOCATION:https://researchseminars.org/talk/WienGAGT/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Agelos Georgakopoulos (Warwick) DTSTART:20250506T130000Z DTEND:20250506T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/44 DESCRIPTION:Title: A Notion of Dimension based on Probability on Groups\nby Agelos Geor gakopoulos (Warwick) as part of Vienna Geometry and Analysis on Groups Sem inar\n\n\nAbstract\nProbability on Groups studies how properties of a grou p \\(G\\)\, such as amenability or growth rate\, influence the outcome of random experiments\, such as random walk or percolation\, carried out on ( a Cayley graph of) \\(G\\). Can we learn something new about \\(G\\) by st udying such experiments? I will survey some results in the area and introd uce a notion of “dimension” of a group that arose from the hope to ans wer this question positively.
https://arxiv.org/abs/2404.17278

\n LOCATION:https://researchseminars.org/talk/WienGAGT/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Jintao Deng (SUNY at Buffalo) DTSTART:20250513T130000Z DTEND:20250513T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/45 DESCRIPTION:Title: Higher index theory and the large-scale geometry\nby Jintao Deng (SU NY at Buffalo) as part of Vienna Geometry and Analysis on Groups Seminar\n \n\nAbstract\nThe Novikov conjecture is an important problem in geometry a nd topology\, asserting the higher signatures of compact oriented smooth m anifolds are invariant under orientation-preserving homotopy equivalences. It has inspired a lot of beautiful mathematics\, including the developmen t of Kasparov’s KK-theory\, Connes’ cyclic cohomology theory\, Gromov- Connes-Moscovici theory of almost flat bundles\, Connes-Higson’s E-theor y\, and quantitative operator K-theory. Recent breakthroughs\, such as the works of Connes\, Kasparov\, Higson\, Yu and others\, have extended its v alidity to a large class of groups using techniques from geometric group t heory\, operator algebras\, and index theory. \n\nTo date\, the Novikov co njecture has been verified for a wide range of cases of groups with "good" large scale geometry including amenability\, Yu's Property A\, and coarse ly embeddability into Hilbert space. In the first part of the talk\, I wil l 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://researchseminars.org/talk/WienGAGT/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Cordes (Heriot-Watt) DTSTART:20250520T130000Z DTEND:20250520T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/46 DESCRIPTION:Title: Cannon-Thurston maps for the Morse boundary\nby Matthew Cordes (Heri ot-Watt) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAb stract\nFundamental to the study of hyperbolic groups is their Gromov boun daries. The classical Cannon--Thurston map for a closed fibered hyperbolic 3-manifolds relates two such boundaries: it gives a continuous surjection 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 hyperbol ic groups with hyperbolic normal subgroups. A generalization of the Gromov boundary to all finitely generated groups is called the Morse boundary. I t 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 wi th Ruth Charney\, Antoine Goldsborough\, Alessandro Sisto and Stefanie Zbi nden.\n LOCATION:https://researchseminars.org/talk/WienGAGT/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Hoang Thanh Nguyen (FPT University\, DaNang) DTSTART:20250603T130000Z DTEND:20250603T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/47 DESCRIPTION:Title: Quasi-redirecting boundaries of groups\nby Hoang Thanh Nguyen (FPT U niversity\, DaNang) as part of Vienna Geometry and Analysis on Groups Semi nar\n\n\nAbstract\nQing and Rafi recently introduced a new boundary for me tric spaces\, called the quasi-redirecting (QR) boundary. This boundary is quasi-isometry invariant\, often compact\, and contains the sublinearly M orse boundary as a topological subspace. While the existence of the QR bou ndary for all finitely generated groups remains an open question\, we esta blish well-defined QR boundaries for several well-studied classes of group s\, including relatively hyperbolic groups and all finitely generated 3-ma nifold groups.\n\nWe also demonstrate a connection between the QR boundary and the divergence of groups: groups with linear divergence have single-p oint QR boundaries\, whereas certain groups with quadratic divergence\, su ch as graph manifolds and CAT(0) admissible groups\, have QR posets of hei ght 2. Some open questions will be discussed if time permits.\n\nThis talk is based on joint work with Yulan Qing.\n LOCATION:https://researchseminars.org/talk/WienGAGT/47/ END:VEVENT BEGIN:VEVENT SUMMARY:John Mackay (Bristol) DTSTART:20251021T130000Z DTEND:20251021T150000Z DTSTAMP:20260422T225924Z UID:WienGAGT/48 DESCRIPTION:Title: Critical exponents for Poincaré profiles and conformal dimension\nb y John Mackay (Bristol) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nBenjamini\, Schramm and Timár quantified how well- connected an infinite \ngraph is in terms of its "separation profile"\, wh ere one considers the \ncut size of finite subgraphs. There is an "L^p" v ersion of this that \nuses Poincaré inequalities to measure the connectiv ity of finite \nsubgraphs. These "p-Poincaré profiles" were used in prev ious work with \nHume and Tessera to show a variety of non-embedding resul ts between \ngroups. I'll mainly talk about current work with Hume where we further \nstudy the connection between these profiles and the conformal dimension \nof the boundary at infinity of certain Gromov hyperbolic grou ps.\n LOCATION:https://researchseminars.org/talk/WienGAGT/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Eberhard (Warwick) DTSTART:20251104T140000Z DTEND:20251104T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/49 DESCRIPTION:Title: Growth gap of residually soluble groups\nby Sean Eberhard (Warwick) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nI f \\(G = \\langle X\\rangle\\) is a finitely generated group\, the growth function \\(\\gamma_G(n)\\) is the number of elements of \\(G\\) word leng th at most \\(n\\). We ignore the fine-scale detail of this function and f ocus on how fast it tends to infinity. The growth of a group is a fundamen tal quasi-isometric invariant\, but there are still many mysteries. It can be as slow as polynomial (e.g.\, for nilpotent groups)\, or as fast as ex ponential (e.g.\, for free groups)\, and nothing else was known until the 80's when Grigorchuk gave his famous example of a group of intermediate gr owth\, i.e.\, neither polynomial nor exponential\, and it is now known (Er schler--Zheng\, 2020) that this group has growth roughly \\(\\exp(n^{0.767 })\\). Grigorchuk's "gap conjecture" predicts that there is some constant \\(c > 0\\) such if the growth is slower than \\(\\exp(n^c)\\) then it sho uld be polynomial (which is equivalent to virtual nilpotence\, by a theore m of a Gromov). This is known for residually nilpotent groups with \\(c = 1/2\\)\, and Wilson (2011) showed that it holds for residually soluble gro ups 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 resi dually soluble and its growth is \\(< \\exp(\\frac{n^{1/4}}{100})\\) for l arge \\(n\\) then \\(G\\) is in fact virtually nilpotent. In this talk I w ill give an overview of this landsacpe\, including a basic introduction to the theory of growth\, and by the end of the talk I will give the whole p roof of a slightly weaker bound with exponent \\(\\frac{1}{4.16}\\).\n LOCATION:https://researchseminars.org/talk/WienGAGT/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne Lonjou (Paris-Saclay) DTSTART:20260113T140000Z DTEND:20260113T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/50 DESCRIPTION:Title: Cremona group and CAT(0) cube complexes\nby Anne Lonjou (Paris-Sacla y) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract \nThe Cremona group is the group of birational transformations of the proj ective plane\, namely isomorphisms between two dense open subsets. This gr oup acts on a CAT(0) cube complex that we constructed with Urech. After an introduction on Cremona group and CAT(0) cube complexes\, I will focus on fixed-point property for actions on CAT(0) cube complexes and explain how it is related to an open question for the Cremona group.\n LOCATION:https://researchseminars.org/talk/WienGAGT/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Sablik (Toulouse) DTSTART:20260127T140000Z DTEND:20260127T160000Z DTSTAMP:20260422T225924Z UID:WienGAGT/51 DESCRIPTION:Title: Self-simulable groups\nby Mathieu Sablik (Toulouse) as part of Vienn a Geometry and Analysis on Groups Seminar\n\n\nAbstract\nA configuration i s a colouring of a finitely generated group by a finite alphabet. A subshi ft of finite type is a set of configurations defined by a finite collectio n of forbidden patterns. Subshifts of finite type naturally arise in the s tudy 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\, we will address several questions that are classical in the case Z^2\, but which l ead to new and largely unexplored phenomena for general finitely generated groups. These include:\n- existence of a subshift of finite type containi ng at most one element of the alphabet.\n- existence of a subshift of fini te type containing only aperiodic configurations (local rules force global behaviour).\n- decidability of the emptiness problem for subshift of fini te type\, given the set of forbidden patterns as input.\n\nIn the second p art of the talk\, we introduce a new class of groups. A finitely generated group is said to be self-simulable if every computable action of the grou p on an effectively closed zero-dimensional space is a topological factor of a subshift of finite type over that group. In other words\, any “reas onable” group action can be encoded by local rules. We will show that su ch groups do exist\, and that the class of self-simulable groups is stable under commensurability and under quasi-isometries among finitely presente d groups. Finally\, we will present several examples of self-simulable gro ups\, 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://researchseminars.org/talk/WienGAGT/51/ END:VEVENT END:VCALENDAR