Cal egary and Freedman showed that many homeomorphisms are distorted\, However \, in general\, \\(C^1\\) diffeomorphisms are not\, for instance due to th e existence of hyperbolic fixed points. Studying similar phenomena in high er regularity turns out to be interesting in the context of elliptic dynam ics. In particular\, we may address the following question: Given \\(r>\ ;s>\;1\\)\, does there exist undistorted \\(C^r\\) diffeomorphisms that are distorted inside the group of \\(C^s\\) diffeomorphisms? After a gener al discussion\, we will focus on the 1–dimensional case of this question for \\(r=2\\) and \\(s=1\\)\, for which we solve it in the affirmative vi a the introduction of a new invariant\, namely the asymptotic variation.\n LOCATION:https://researchseminars.org/talk/WienGAGT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Florin Radulescu (IMAR and Rome) DTSTART;VALUE=DATE-TIME:20220602T100000Z DTEND;VALUE=DATE-TIME:20220602T104500Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/22 DESCRIPTION:Title: Dimension formulae of Gelfand-Graev\, Jones and their relation to automo rphic forms and temperdness of quasiregular representations\nby Florin Radulescu (IMAR and Rome) as part of Vienna Geometry and Analysis on Grou ps Seminar\n\n\nAbstract\nVaughan Jones introduced a formula computing the von Neumann dimension for the restriction to a lattice of the left regula r representation of a semisimple Lie group.\n\nIt is a variant of a formul a by Atiah Schmidt computing the formal dimension in the Haris Chandra t race formula for discrete series. It is surprisingly similar (in the case of PSL(2\,Z)) to the dimension of the space of automorphic forms and is si milar to a formula proved by Gelfand\, Graev. We use an extension of this formula to provide a method for computing the formal trace of representat ions of PSL(2\,Q_p) (or more general situations)\, when analyzing the quas i regular representation on PSL(2\,R)/PSL(2\,Z). It provides a method to o btain estimates for eigenvalues of Hecke operators.\n LOCATION:https://researchseminars.org/talk/WienGAGT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Annette Karrer (McGill) DTSTART;VALUE=DATE-TIME:20221004T130000Z DTEND;VALUE=DATE-TIME:20221004T150000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/23 DESCRIPTION:Title: Contracting boundaries of right-angled Coxeter and Artin groups\nby Annette Karrer (McGill) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nA complete CAT(0) space has a topological space ass ociated to it called the contracting or Morse boundary. This boundary capt ures how similar the CAT(0) space is to a hyperbolic space. Charney--Sulta n proved this boundary is a quasi-isometry invariant\, i.e. it can be defi ned for CAT(0) groups. Interesting examples arise among contracting bounda ries of right-anlged Artin and Coxeter groups. \n\nThe talk will consist o f two parts. The first 45 minutes will be about the main result of my PhD project. We will study the question of how the contracting boundary of a r ight-connected Coxeter group changes when we glue certain graphs on its de fining graph. We will focus on the question of when the resulting graph co rresponds to a right-angled Coxeter group with totally disconnected contra cting boundary. \n\nAfter a short break\, we will see a second result of my PhD thesis concerning the question of what happens if we glue a path of length at least two to a defining graph of a RACG. Afterwards\, we will u se our insights to investigate contracting boundaries of certain RACGs t hat contain surprising circles. These examples are joint work with Marius Graeber\, Nir Lazarovich\, and Emily Stark. Finally\, we will transfer the ideas we saw before to RAAGs. This will result in a proof that all right- angled Artin groups have totally disconnected contracting boundaries\, rep roving a result of Charney--Cordes--Sisto.\n LOCATION:https://researchseminars.org/talk/WienGAGT/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Emmanuel Caprace (UC Louvain) DTSTART;VALUE=DATE-TIME:20221011T130000Z DTEND;VALUE=DATE-TIME:20221011T150000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/24 DESCRIPTION:Title: New Kazhdan groups with infinitely many alternating quotients\nby Pi erre-Emmanuel Caprace (UC Louvain) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nIntroductory talk: "Generating the alter nating groups"\n\nAbstract: The goal of this talk is to provide an overvie w of results and methods allowing one to build generating sets for the fin ite alternating groups. Some of those rely on the Classification of the Fi nite Simple Groups\, others don't. This theme will be motivated by open pr oblems concerning the construction of finite quotients of certain families of finitely generated infinite groups. \n\nResearch talk: "New Kazhdan gr oups with infinitely many alternating quotients"\n\nAbstract: I will intro duce a new class of infinite groups enjoying Kazhdan's property (T) and ad mitting alternating group quotients of arbitrarily large degree. Those gro ups are constructed as automorphism groups of the ring of polynomials in n indeterminates with coefficients in the finite field of order p\, generat ed by a suitable finite set of polynomial transvections. As an application \, we obtain the first examples of hyperbolic Kazdhan groups with infinite ly many alternating group quotients. We also obtain expander Cayley graphs of degree 4 for an infinite family of alternating groups. The talk is bas ed on joint work with Martin Kassabov.\n LOCATION:https://researchseminars.org/talk/WienGAGT/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Xabier Legaspi (ICMAT and IRMAR) DTSTART;VALUE=DATE-TIME:20221018T130000Z DTEND;VALUE=DATE-TIME:20221018T150000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/25 DESCRIPTION:Title: Constricting elements and the growth of quasi-convex subgroups\nby X abier Legaspi (ICMAT and IRMAR) as part of Vienna Geometry and Analysis on Groups Seminar\n\nLecture held in SR 10\, 2. OG.\, OMP 1.\n\nAbstract\nLe t \\(G\\) be a group acting properly on a metric space \\(X\\) and conside r a path system of \\(X\\). Assume that \\(G\\) contains a constricting el ement with respect to this path system\, i.e. a very general condition of non-positive curvature. This talk will be about the relative growth and th e coset growth of the quasi-convex subgroups of \\(G\\) with respect to th is path system. Through the triangle inequality\, we will see that we can determine that the first kind of growth rates are strictly smaller than th e growth rate of \\(G\\)\, while the second kind of growth rates coincide with the growth rate of \\(G\\). Applications include actions of relativel y hyperbolic groups\, CAT(0) groups with Morse elements and mapping class groups. This generalises work of Antolín\, Dahmani-Futer-Wise and Gitik-R ips.\n LOCATION:https://researchseminars.org/talk/WienGAGT/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Tullio Ceccherini-Silberstein (U. Sannio) DTSTART;VALUE=DATE-TIME:20221025T130000Z DTEND;VALUE=DATE-TIME:20221025T150000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/26 DESCRIPTION:Title: Sofic entropy and surjunctive dynamical systems\nby Tullio Ceccherin i-Silberstein (U. Sannio) as part of Vienna Geometry and Analysis on Group s Seminar\n\nLecture held in SR 10\, 2. OG.\, OMP 1.\n\nAbstract\nA dynami cal system is a pair \\((X\,G)\\)\, where \\(X\\) is a compact metrizable space and \\(G\\) is a countable group acting by homeomorphisms of \\(X\\) . An endomorphism of \\((X\,G)\\) is a continuous selfmap of \\(X\\) which commutes with the action of \\(G\\). A dynamical system \\((X\, G)\\) is said to be surjunctive if every injective endomorphism of \\((X\,G)\\) is surjective. When the group \\(G\\) is sofic\, the combination of suitable dynamical properties (such as expansivity\, nonnegative sofic topological entropy\, weak specification\, and strong topological Markov property) gua rantees that (X\,G) is surjunctive. I'll explain in detail all notions inv olved\, the motivations\, and outline the main ideas of the proof of this result obtained in collaboration with Michel Coornaert and Hanfeng Li.\n LOCATION:https://researchseminars.org/talk/WienGAGT/26/ END:VEVENT BEGIN:VEVENT SUMMARY:William Slofstra (Waterloo) DTSTART;VALUE=DATE-TIME:20221108T140000Z DTEND;VALUE=DATE-TIME:20221108T160000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/27 DESCRIPTION:Title: Group theory and nonlocal games\nby William Slofstra (Waterloo) as p art of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nNonlo cal games are simple games used in quantum information to explore the powe r of entanglement. They are closely connected with Bell inequalities\, whi ch have been in the news recently as the subject of this year's Nobel priz e in physics. In this talk\, I'll give an overview of a class of nonlocal games called linear system nonlocal games\, which are particularly interes ting from the point of view of group theory\, in that every linear system nonlocal games has an associated group which controls the perfect strategi es for the game. The associated groups are finite colimits of finite abeli an groups\, and exploring this class of groups from the perspective of non local games gives rise to a number of interesting results and problems in group theory. For the introductory talk\, I'll cover some of the backgroun d concepts that come up: pictures of groups\, residual finiteness\, and hy perlinearity (if time permits\, I may sketch the construction of a group w ith superpolynomial hyperlinear profile).\n LOCATION:https://researchseminars.org/talk/WienGAGT/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Motiejus Valiunas (Wrocław) DTSTART;VALUE=DATE-TIME:20221213T140000Z DTEND;VALUE=DATE-TIME:20221213T160000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/28 DESCRIPTION:Title: Biautomatic and hierarchically hyperbolic groups\nby Motiejus Valiun as (Wrocław) as part of Vienna Geometry and Analysis on Groups Seminar\n\ n\nAbstract\nBiautomatic groups arose as groups explaining formal language -theoretic aspects of geodesics in word-hyperbolic groups. Many classes o f non-positively curved finitely generated groups\, such as hyperbolic\, v irtually abelian\, cocompactly cubulated\, small cancellation and Coxeter groups\, are known to be biautomatic. On the other hand\, there are some other classes\, such as CAT(0) or hierarchically hyperbolic groups\, for w hich the relationship to biautomaticity is more complicated.\n\nIn the fir st half of the talk\, I will outline the notions of non-positive curvature appearing in group theory and their connection to biautomaticity. In par ticular\, I will overview recent results on the relationship between biaut omaticity\, hierarchical hyperbolicity and being CAT(0)\, as well as some constructions of non-biautomatic non-positively curved groups.\n\nThe goal of the second half of the talk is to construct a non-biautomatic hierarch ically hyperbolic group\, giving the first known example of such a group. Our group acts geometrically on the cartesian product of a tree and the h yperbolic plane\, and therefore satisfies many nice geometric properties. The proof of non-biautomaticity will rely on the study of geodesic curren ts on a closed hyperbolic surface. The talk is based on joint work with S am Hughes.\n LOCATION:https://researchseminars.org/talk/WienGAGT/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Koberda (Virginia) DTSTART;VALUE=DATE-TIME:20221115T140000Z DTEND;VALUE=DATE-TIME:20221115T160000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/29 DESCRIPTION:Title: Model theory of the curve graph\nby Thomas Koberda (Virginia) as par t of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nIntrodu ctory talk: Automorphisms of the curve graph and related objects\n\nAbstra ct: I will give a brief introduction to Ivanov's result on the automorphis m group of the curve graph\, and survey some related results.\n\nResearch talk: Model theory of the curve graph\n\nAbstract: I will describe some no vel approaches to investigating the combinatorial topology of surfaces thr ough model theoretic means. I will give a model theoretic explanation of h ow a myriad of objects that are naturally associated to a surface are inte rpretable inside of the curve graph\, and how this provides a new perspect ive on a certain metaconjecture due to Ivanov. I will also discuss some of the properties of the theory of the curve graph\, including stability and quantifier elimination. This talk represents joint work with V. Disarlo a nd J. de la Nuez Gonzalez.\n LOCATION:https://researchseminars.org/talk/WienGAGT/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Pilar Páez Guillán (Vienna) DTSTART;VALUE=DATE-TIME:20230110T140000Z DTEND;VALUE=DATE-TIME:20230110T160000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/30 DESCRIPTION:Title: Counterexamples to the Zassenhaus conjecture on simple modular Lie algeb ras\nby Pilar Páez Guillán (Vienna) as part of Vienna Geometry and A nalysis on Groups Seminar\n\n\nAbstract\nHistorically\, the study of the ( outer) automorphism group of a given group (free\, simple...) has interest ed group-theorists\, topologists and geometers\, and consequently it is al so of great importance in the Lie algebra theory. In this talk\, we will b riefly revise some of the connections between groups and Lie algebras befo re giving a quick overview of the simple Lie algebras of classical and Car tan type over fields of positive characteristic. After that\, we will comp are the Schreier and Zassenhaus conjectures on the solvability of \\(\\mat hrm{Out}(G)\\) (resp. \\(\\mathrm{Out}(L)\\))\, the group of outer automor phisms (resp. the Lie algebra of outer derivations) of a finite simple gro up \\(G\\) (resp. a finite-dimensional simple Lie algebra \\(L\\)). While the former is known to be true as a consequence of the classification of f inite simple groups\, the latter is false over fields of small characteris tic \\(p=2\,3\\). We will finish the talk by presenting a new family of co unterexamples to the Zassenhaus conjecture over fields of characteristic \ \(p=3\\)\, as well as commenting some advances for \\(p=2\\).\n LOCATION:https://researchseminars.org/talk/WienGAGT/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Christopher Cashen (Vienna) DTSTART;VALUE=DATE-TIME:20221122T140000Z DTEND;VALUE=DATE-TIME:20221122T160000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/31 DESCRIPTION:Title: Snowflakes\, cones\, and shortcuts\nby Christopher Cashen (Vienna) a s part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nA graph is strongly shortcut if there exists \\(K>1\\) and a bound on the le ngth of \\(K\\)-biLipschitz embedded cycles. A group is strongly shortcut if it acts geometrically on a strongly shortcut graph. This is a kind of n on-positive curvature condition enjoyed by hyperbolic and CAT(0) groups\, for example. Strongly shortcut groups are finitely presented and have all of their asymptotic cones simply connected (so have polynomial Dehn functi on).\n\n We look at an infinite family of snowflake groups\, which are kno wn to have polynomial Dehn function\, and show that all of their asymptoti c cones are simply connected. The usual ways to show that a group has all asymptotic cones simply connected are to show that it is either of polynom ial growth or has quadratic Dehn function\, but our groups have neither of these properties. We also show that the 'obvious' Cayley graph is not str ongly shortcut. This implies that some of its asymptotic cones contain iso metrically embedded circles\, so they have metrically nontrivial loops eve n though there are no topologically nontrivial loops. Here are two questio ns:\n\n 1. If a group has all of its asymptotic cones simply connected\, d oes that imply that it is \nstrongly shortcut? \n\n2. Is it true that one Cayley graph of a group is strongly shortcut if and only if every Cayley g raph of that group is strongly shortcut? \n\nOur snowflake examples show t hat the answer to one of these questions is 'no'. \n\nThis is joint work w ith Nima Hoda and Daniel Woohouse.\n LOCATION:https://researchseminars.org/talk/WienGAGT/31/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hume (Bristol) DTSTART;VALUE=DATE-TIME:20230124T140000Z DTEND;VALUE=DATE-TIME:20230124T160000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z UID:WienGAGT/32 DESCRIPTION:Title: Thick embeddings of graphs into symmetric spaces\nby David Hume (Bri stol) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstr act\nInspired by the work of Kolmogorov-Barzdin in the 60’s and more rec ently by Gromov-Guth on thick embeddings into Euclidean spaces\, we consid er thick embeddings of graphs into more general symmetric spaces. Roughly\ , a thick embedding is a topological embedding of a graph where disjoint p airs of edges and vertices are at least a uniformly controlled distance ap art (consistent with applications where vertices and edges are considered as having volume). The goal is to find thick embeddings with minimal “vo lume”.\n\nWe prove a dichotomy depending upon the rank of the non-compac t factor of the symmetric space. For rank at least 2\, there are thick emb eddings of \\(N\\)-vertex graphs with volume \\(\\leq C N\\log(N)\\) where \\(C\\) depends on the maximal degree of the graph. By contrast\, for ran k at most 1\, thick embeddings of expander graphs have volume \\(\\geq c N ^{1+a}\\) for some \\(a\\geq 0\\).\n\nThe key tool required for these resu lts is the notion of a coarse wiring\, which is a continuous embedding of one graph inside another satisfying some additional properties. We prove t hat the minimal “volume” of a coarse wiring into a symmetric space is equivalent to the minimal volume of a thick embedding. We obtain lower bou nds on the volume of coarse wirings by comparing the relative connectivity (as measured by the separation profile) of the domain and target\, and up per bounds by direct construction.\n\nThis is joint work with Benjamin Bar rett.\n LOCATION:https://researchseminars.org/talk/WienGAGT/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Alon Dogon (Weizmann Institute) DTSTART;VALUE=DATE-TIME:20230117T140000Z DTEND;VALUE=DATE-TIME:20230117T160000Z DTSTAMP;VALUE=DATE-TIME:20230205T201932Z 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 END:VCALENDAR