BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Haluk Sengun (University of Sheffield) DTSTART:20201016T140000Z DTEND:20201016T150000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/1 DESCRIPTION:Title: Selberg trace formula in operator K-theory\nby Haluk Seng un (University of Sheffield) as part of Pure Mathematics Colloquium at Sou thampton\n\n\nAbstract\nAbstract: Selberg introduced his celebrated trace formula in 1956. Since\nthen\, the trace formula has become an indispensab le tool in number\ntheory\, with spectacular applications to the Langlands program. After an\nexposition of the trace formula\, I will present an id entity in the\nsetting of K-theory of group C*-algebras that is an analogu e of the\ntrace formula. Time remaining\, I will exhibit how one can deriv e the\nindex theoretic version of the trace formula (due to Barbasch and\n Moscovici) from our identity via the theory of higher indices.\n\nThis is joint work with Bram Mesland (Leiden) and Hang Wang (Shanghai).\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Wajid Mannan (QMUL) DTSTART:20201009T140000Z DTEND:20201009T150000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/2 DESCRIPTION:Title: An exotic group presentation\nby Wajid Mannan (QMUL) as p art of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nAbstract: The shape colloquially referred to as Nancy's toy can be pictured as bein g made of solid (3-dimensional) dough. It was conjectured in the early 200 0's that the shape could not be flattened by squeezing the dough\, in whic h case it would be the first with this property\, where there are no homol ogical obstructions to flattening it. However\, I and my colleague (Tomasz Popiel) flattened it\, leading instead to an unexpected group presentatio n of a quaternion group\, and the resolution of a question regarding the s pines of closed 3-manifolds.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Lukasz Grabowski (Lancaster University) DTSTART:20201023T140000Z DTEND:20201023T150000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/3 DESCRIPTION:Title: On the cost of Benjamini Schramm statistics with the Kazhdan property\nby Lukasz Grabowski (Lancaster University) as part of Pure M athematics Colloquium at Southampton\n\n\nAbstract\nThis talk is based on a joint work with Samuel Mellick.\nRecently Hutchcroft and Pete showed tha t the cost of any infinite\nKazhdan group is 1. We generalise this result to the context of\ngraphings. Our proof is noticably simpler than the orig inal proof of\nHutchcroft and Pete even for graphings arising from actio ns of\ncountable Kazhdan groups\, in particular our arguments do not use a ny\n"hard" probability theory. The main ingredient oin our approach is the \nanalysis of the connectivity properties of partitions of the vertex\nspa ce of graphings which are ``Cheeger-optimal''\, i.e.~minimise the\namount of edges present between the parts of a partition.\n\nWe work in the conte xt of Benjamini-Schramm statistics\, which are\nconvenient ``group-like'' objects roughly equivalent to ``invariant\nrandom subgroups''. In particul ar we give examples of Kazhdan\nBenjamini-Schramm statistics which do not arise from actions of\ncountable Kazhdan groups\, by considering point pro cesses on\nlattice-free Kazhdan Lie groups. Of some interest might be also a\nseemingly new characerisation of Kazhdan equivalence relations\, as\ns tudied by Mikael Pichot.\n\nThis work is partially motivated by the follow ing ``Lueck approximation\ntype'' question: Let $M_n$ be a seuqence of tri angulated compact\n3-manifolds\, such that the 1-skeleta of the triangulat ions have\nuniformly bounded vertex degrees and which converge to a triang ulation\nof R^3 in the sense of Benjamini-Schramm (informally speaking\, t his\nmeans that ``M_n is a sequence of compact manifolds with growing\ninj ectivity radia''). Is it true that the limit of\ndim H_1(M_n)/|M_n| =0 ? Here |M_n| is the number of vertices in the\ntriangulation of M_n.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Cashen (University of Vienna) DTSTART:20201030T150000Z DTEND:20201030T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/4 DESCRIPTION:Title: "Paging Dr. Frankenstein"\; or\, how to build monsters\nb y Chris Cashen (University of Vienna) as part of Pure Mathematics Colloqui um at Southampton\n\n\nAbstract\nI’ll talk about the use of small cancel lation theory to build the “monster groups” of Rips\, Olshanskii\, and Gromov. Then I’ll talk about work with Arzhantseva\, Gruber\, and Hume constructing Gromov monsters with further exotic properties.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Gareth Jones and Alexander Zvonkin (GAJ: U of Southampton\; AZ: La BRI\, U of Bordeaux) DTSTART:20201106T150000Z DTEND:20201106T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/5 DESCRIPTION:Title: Primes in geometric series and finite permutation groups\ nby Gareth Jones and Alexander Zvonkin (GAJ: U of Southampton\; AZ: LaBRI\ , U of Bordeaux) as part of Pure Mathematics Colloquium at Southampton\n\n \nAbstract\nAbstract: The classification of permutation groups of prime de gree is a very old problem\, going back to Galois and Burnside. As a conse quence of the classification of finite simple groups\, the classification is complete\, apart from the question of when the natural degree (q^n-1)/( q-1) of PSL_n(q) is prime. We present heuristic arguments and computationa l evidence to support a conjecture that there are infinitely many primes o f this form.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Johnny Nicholson (University College London) DTSTART:20201113T150000Z DTEND:20201113T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/6 DESCRIPTION:Title: Projective modules and exotic group presentations\nby Joh nny Nicholson (University College London) as part of Pure Mathematics Coll oquium at Southampton\n\n\nAbstract\nAbstract: Two presentations for a gr oup G which have the same deficiency are called exotic if the correspondin g presentation complexes are not homotopy equivalent. Despite early intere st by Cockroft-Swan and Dyer-Sieradski\, it was not until 1976 that the fi rst examples of exotic presentations were found by Dunwoody (for the trefo il group) and Metzler (for finite abelian groups). In recent years\, appli cations to Wall’s D2 problem and the classification of manifolds have sp arked renewed interest in this problem. In this talk\, we will discuss exo tic presentations for groups G with 4-periodic (group-)cohomology and thei r relation to the classification of projective ZG modules. This builds upo n recent work of Mannan-Popiel on exotic presentations for the quaternion group Q(28).\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Gerald Williams (University of Essex) DTSTART:20201120T150000Z DTEND:20201120T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/7 DESCRIPTION:Title: Hyperbolicity of cyclically presented groups\nby Gerald W illiams (University of Essex) as part of Pure Mathematics Colloquium at So uthampton\n\n\nAbstract\nCyclically presented groups are groups defined by presentations that admit a cyclic symmetry. Prominent examples include th e Higman group and the Fibonacci groups. I will discuss recent results tha t classify the T(6) (small cancellation) cyclically presented groups that are hyperbolic and present results concerning hyperbolicity of groups of F ibonacci type. This is joint work with Ihechukwu Chinyere.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Bin Sun (University of Oxford) DTSTART:20201127T150000Z DTEND:20201127T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/8 DESCRIPTION:Title: Groups acting acylindrically on hyperbolic metric spaces\ nby Bin Sun (University of Oxford) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nAbstract: I will talk about some recent deve lopments in the study of group actions on hyperbolic metric spaces. I will focus on the class of acylindrcially hyperbolic groups. This class is bro ad enough to include many examples of interest\, yet a significant part of the theory of hyperbolic and relatively hyperbolic groups can be generali zed in this context. In particular\, I will discuss group theoretic Dehn f illing and small cancellation theory in acylindrically hyperbolic groups. The talk will be accessible to graduate students.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Evington (University of Münster) DTSTART:20201204T150000Z DTEND:20201204T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/9 DESCRIPTION:Title: C*-Algebras and Dimension Theory\nby Sam Evington (Univer sity of Münster) as part of Pure Mathematics Colloquium at Southampton\n\ n\nAbstract\nI will begin with an elementary overview of the theory of C*- algebras\, discussing how they can be seen as a generalisation of both mat rix algebras and topological spaces. I will then look at covering dimensio n of topological spaces\, and how this can be generalised to the setting o f C*-algebras. Finally\, I will discuss my joint work with Castillejos\, Tikuisis\, White\, and Winter\, which restricts the possible values of dim ension for simple C*-algebras (i.e those with no non-trival ideals)\, and explain the connections to the classification programme for simple C*-alge bras.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Thom (Technische Universität Dresden) DTSTART:20201211T160000Z DTEND:20201211T170000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/10 DESCRIPTION:Title: (GGSE) Asymptotics of Cheeger constants and unitarisability of groups\nby Andreas Thom (Technische Universität Dresden) as part o f Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nGiven a group Γ\, we establish a connection between the unitarisability of its uniforml y bounded representations and the asymptotic behaviour of the isoperimetri c constants of Cayley graphs of Γ for increasingly large generating sets. \nThe connection hinges on an analytic invariant Lit(Γ)∈[0\,∞] which we call the Littlewood exponent. Finiteness\, amenability\, unitarisabilit y and the existence of free subgroups are related respectively to the thre sholds 0\,1\,2 and ∞ for Lit(Γ). Using graphical small cancellation the ory\, we prove that there exist groups Γ for which 1Groups and Geometry o n zoom" meeting.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Viveka Erlandsson (University of Bristol) DTSTART:20210108T150000Z DTEND:20210108T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/11 DESCRIPTION:Title: Mirzakhani’s curve counting theorem\nby Viveka Erlands son (University of Bristol) as part of Pure Mathematics Colloquium at Sout hampton\n\n\nAbstract\nAbstract: In her thesis\, Mirzakhani established th e asymptotic behavior of the number of simple closed geodesics of a given type in a hyperbolic surface. Here we say that two geodesics are of the sa me type if they differ by a homeomorphism. In this talk I will discuss thi s theorem\, the extension to geodesics which are not simple\, and some app lications.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacek Brodzki (University of Southampton) DTSTART:20210115T150000Z DTEND:20210115T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/12 DESCRIPTION:Title: Gyroscopes and topology\nby Jacek Brodzki (University of Southampton) as part of Pure Mathematics Colloquium at Southampton\n\n\nA bstract\nAbstract: In recent years\, physicists discovered materials whose properties and behaviour are controlled by the topology of their “band structure”\, that is the distribution of energy levels of their electron s. For example\, a topological insulator is a material that may conduct el ectricity on its surface\, but not in its interior. My talk will describe a recent mechanical demonstration by Nash et al of a system with topologic ally protected states in the form of a network of interacting gyroscopes. I will outline recent work in progress (in collaboration with Nigel Higson ) to understand the topological reasons for the behaviour of these excitin g systems.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Genevieve Walsh (Tufts University) DTSTART:20201211T133000Z DTEND:20201211T143000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/13 DESCRIPTION:Title: (GGSE) Incoherence of free-by-free and surface-by-free group s\nby Genevieve Walsh (Tufts University) as part of Pure Mathematics C olloquium at Southampton\n\n\nAbstract\nA group is coherent if every finit ely generated subgroup is finitely presented\, and incoherent otherwise. Many well-known groups are coherent: free groups\, surface groups\, and th e fundamental groups of compact 3-manifolds. We consider groups of the fo rm $F_m \\by F_n$ or $S_g \\by F_n$ where $S_g$ is the fundamental group of a closed surface of genus $g$. We show that all these groups are incoh erent whenever $g\, n$ are at least 2\, answering a question of D. Wise. One possible alternative method to prove incoherence would be to show th at these groups virtually algebraically fiber. We additionally show that not all groups covered by our methods virtually algebraically fiber. Thi s is joint work with Robert Kropholler and Stefano Vidussi.\n\nThis talk i s a part of "Groups and Geo metry on zoom" (GGSE) meeting.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Nima Hoda (ENS Paris) DTSTART:20201211T144500Z DTEND:20201211T154500Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/14 DESCRIPTION:Title: (GGSE) Crystallographic Helly Groups\nby Nima Hoda (ENS Paris) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract \nA Helly graph is a graph in which the metric balls form a Helly family: any pairwise intersecting collection of balls has nonempty total intersect ion. A Helly group is a group that acts properly and cocompactly on a Hel ly graph. Helly groups simultaneously generalize hyperbolic\, cocompactly cubulated and C(4)-T(4) graphical small cancellation groups while maintai ning nice properties\, such as biautomaticity. I will show that if a crys tallographic group is Helly then its point group preserves an L^{\\infinit y} metric on \\R^n. Thus we will obtain some new nonexamples of Helly gro ups\, including the 3-3-3 Coxeter group\, which is a systolic group. This answers a question posed by Chepoi during the recent Simons Semester on G eometric and Analytic Group Theory in Warsaw.\n\nThis talk is a part of "< a href="https://www.ucl.ac.uk/~ucahllo/ggse/">Groups and Geometry on zoom< /a>" (GGSE) meeting.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Liviu Pãunescu (Institute of Mathematics of the Romanian Academy) DTSTART:20210205T150000Z DTEND:20210205T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/15 DESCRIPTION:Title: Recent results on P-stability\nby Liviu Pãunescu (Insti tute of Mathematics of the Romanian Academy) as part of Pure Mathematics C olloquium at Southampton\n\n\nAbstract\nTwo permutations that almost commu te are close to two commuting permutations. The same question can be asked for other relations\, not only the commutant. We shall see that the answe r to this question depends only on the group that the equations describe. We then survey some recent results where this question is answered in posi tive or negative\, depending on the group.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Linckelmann (City University of London) DTSTART:20210226T150000Z DTEND:20210226T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/17 DESCRIPTION:Title: On the Lie algebra structure of outer derivations of finite group algebras\nby Markus Linckelmann (City University of London) as p art of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nVery few finite-dimensional algebras over a field are expected to arise as direct f actors of finite group algebras. In fact\, prominent finiteness conjecture s would imply that in any fixed dimension\, only finitely many isomorphism classes of algebras should arise in this way. Even in very small dimensio ns\, where this is known to hold\, this tends to require some substantial effort\, since it is generally very difficult to decide for any given alge bra whether it arises as a direct factor of some finite group algebra or n ot. Amongst many invariants which can be useful for this endeavour is the Lie algebra structure of the first Hochschild cohomology space - this is s imply the space of derivations on the algebra modulo inner derivations. We describe some progress in recent years. Time permitting\, we describe a construction principle for operators of degree -1 on Ext-spaces of modules which can be used to calculate the Lie algebra structure of the first Hoc hschild cohomology of certain finite p-group algebras. This is joint work with Radha Kessar and Dave Benson.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis Paris (Université de Bourgogne) DTSTART:20210305T150000Z DTEND:20210305T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/18 DESCRIPTION:Title: Artin groups of spherical type\nby Luis Paris (Universit é de Bourgogne) as part of Pure Mathematics Colloquium at Southampton\n\n \nAbstract\nAbstract: An Artin group is a group that has a presentation wi th relations of the form "aba... = bab..."\, the words on the right hand side and on the left hand side having the same length.\nThere are few resu lts proved for all Artin groups\, and the theory consists mainly in the st udy of more or less extended families. One of the most popular families\, in particular because of its implication in algebraic geometry\, is that o f Artin groups of spherical type\, that correspond to the finite Coxeter g roups. The talk will be an introduction to Artin groups of spherical type together with their different forms of classification.\n\nAs a direct cons equence of Coxeter's work\, dating from 1935\, we get an explicit classifi cation of the presentations of the Artin groups of spherical type. In 2004 I proved that two Artin groups of spherical type are isomorphic if and on ly if they have the same presentation. Very recently\, with Maria Cumplido \, we gave an almost complete classification up to commensurability. I can hardly say anything about the classification up to quasi-isometry.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Rudolf Zeidler (Universität Münster) DTSTART:20210312T150000Z DTEND:20210312T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/19 DESCRIPTION:Title: Scalar and mean curvature comparison via the Dirac operator< /a>\nby Rudolf Zeidler (Universität Münster) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nAbstract: In recent years\, Grom ov proposed studying the geometry of positive scalar curvature (``psc'') v ia various metric inequalities reminiscent of classical comparison geometr y. For instance\, he proposed the following conjecture: Let $M$ be a clos ed manifold of dimension $n-1$ which does not admit a metric of psc. Then with respect to any Riemannian metric of scalar curvature $\\geq n(n-1)$ o n the cylinder $V = M \\times [-1\,1]$\, the distance between the two boun dary components of $V$ is at most $2\\pi/n$. In this talk\, we will discus s how to address this and other related questions via Dirac operator techn iques on spin manifolds which have suitable non-vanishing index invariants . Using local boundary conditions\, we will refine these estimates using t he mean curvature of the boundary\, and we will explain that the extremal situation can only be realized by certain warped product metrics.\nThis is joint work with Simone Cecchini.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Jürgen Jost (Max-Planck-Institut Leipzig) DTSTART:20210319T150000Z DTEND:20210319T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/20 DESCRIPTION:Title: Graphs\, hypergraphs\, and network analysis\nby Jürgen Jost (Max-Planck-Institut Leipzig) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nEmpirical networks are often represented and analysed as graphs. These graphs are often qualitatively different from a nd typically less regular than those investigated in classical graph theor y. We have therefore developed tools from spectral theory and geometry. Th ese tools not only help us to understand empirical data\, but they also le ad to new mathematical problems and challenges. Also\, in many cases\, ran ging from chemical reactions to collaborations between scientists\, inter actions between more than two elements play important roles\, and therefor e\, we are also developing tools for hypergraph analysis\, and we currentl y explore the resulting mathematical structures.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Laurent Bartholdi (Universität Göttingen) DTSTART:20210430T140000Z DTEND:20210430T150000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/22 DESCRIPTION:Title: Dimension series and homotopy groups of spheres\nby Laur ent Bartholdi (Universität Göttingen) as part of Pure Mathematics Colloq uium at Southampton\n\n\nAbstract\nThe lower central series of a group $G$ is defined by $\\gamma_1=G$ and $\\gamma_n = [G\,\\gamma_{n-1}]$. The "di mension series"\, introduced by Magnus\, is defined using the group algebr a over the integers: $\\delta_n = \\{g: g-1\\text{ belongs to the $n$-th p ower of the augmentation ideal}\\}$.\n\nIt has been\, for the last 80 year s\, a fundamental problem of group theory to relate these two series. One always has $\\delta_n\\ge\\gamma_n$\, and a conjecture by Magnus\, with fa lse proofs by Cohn\, Losey\, etc.\, claims that they coincide\; but Rips c onstructed an example with $\\delta_4/\\gamma_4$ cyclic of order 2. On the positive side\, Sjogren showed that $\\delta_n/\\gamma_n$ is always a tor sion group\, of exponent bounded by a function of $n$. Furthermore\, it wa s believed (and falsely proven by Gupta) that only $2$-torsion may occur.\ n\nIn joint work with Roman Mikhailov\, we prove however that the torsion in the quotients $\\delta_n/\\gamma_n$ can be arbitrarily specified\; thus Sjogren's result is optimal.\n\nEven more interestingly\, I will show tha t the dimension quotient $\\delta_n/\\gamma_n$ is related to the differenc e between homotopy and homology: our construction is fundamentally based o n embedding the torsion of the homotopy group $\\pi_n(S^2\\vee S^2)$ in di mension quotients. We can even make this quite explicit on the order-$p$ e lement in $\\pi_{2p}(S^2)$ due to Serre.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Puschnigg (Institut de Mathématiques de Luminy\, Marseill e) DTSTART:20210416T140000Z DTEND:20210416T150000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/23 DESCRIPTION:Title: Operator-K-theory and cyclic homology\nby Michael Puschn igg (Institut de Mathématiques de Luminy\, Marseille) as part of Pure Mat hematics Colloquium at Southampton\n\n\nAbstract\nOperator-K-theory has tu rned out to be a key homological invariant of Banach algebras. Despite its simple definition it is usually very hard to calculate. Local cyclic homo logy is designed to provide a good approximation of K-theory while being c omputable by standard techniques. We outline the construction of this theo ry and discuss how much information is lost by passing from K-theory to lo cal cyclic homology. We stress the outstanding role played in this context by $C^*$-algebras of Gromov-hyperbolic groups with Kazhdan's property (T) .\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Li (University of Southampton) DTSTART:20210219T150000Z DTEND:20210219T160000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/24 DESCRIPTION:Title: Topological complexity of hyperbolic groups\nby Kevin Li (University of Southampton) as part of Pure Mathematics Colloquium at Sou thampton\n\n\nAbstract\nThe topological complexity TC(X) of a space X is a n integer-valued homotopy invariant which is similar in spirit to the clas sical Lusternik-Schnirelmann category. It was introduced by M. Farber in 2 003 in the context of robot motion planning\, measuring the "navigational complexity" of X\, but since then has been studied in its own right. One o btains an invariant of groups as usual by setting TC(G) to be TC(BG)\, the precise value of which is known only for a small class of groups. Farber- Grant-Lupton-Oprea have given a characterization of TC is terms of classif ying spaces for families of subgroups\, which was recently used by A. Dran ishnikov to compute TC for hyperbolic groups. We will present an alternati ve proof of Dranishnikov's result via the Lück-Weiermann construction and equivariant Bredon cohomology. Our proof has the advantage that it easily generalizes to certain toral relatively hyperbolic groups.\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Goulnara Arzhantseva (Universität Wien) DTSTART:20210514T140000Z DTEND:20210514T150000Z DTSTAMP:20260422T212929Z UID:SotonPureMathsColloq/25 DESCRIPTION:Title: Approximations of infinite groups\nby Goulnara Arzhantse va (Universität Wien) as part of Pure Mathematics Colloquium at Southampt on\n\n\nAbstract\nAbstract: We discuss various (still open) questions on a pproximations of finitely generated groups\, focusing on finite-dimensiona l approximations such as residual finiteness and soficity. We survey our r esults on the existence and stability of metric approximations. We suggest a few conjectures\, e.g. on Gromov hyperbolic groups and their infinite m onster limits.\n\nBased on joint work with Liviu Paunescu (Bucharest).\n LOCATION:https://researchseminars.org/talk/SotonPureMathsColloq/25/ END:VEVENT END:VCALENDAR