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:20260404T110744Z UID:SotonPureMathsColloq/1 DESCRIPTION:Title: Selberg trace formula in operator K-theory\nby Hal uk Sengun (University of Sheffield) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nAbstract: Selberg introduced his celebrated trace formula in 1956. Since\nthen\, the trace formula has become an indi spensable tool in number\ntheory\, with spectacular applications to the La nglands program. After an\nexposition of the trace formula\, I will presen t an identity in the\nsetting of K-theory of group C*-algebras that is an analogue of the\ntrace formula. Time remaining\, I will exhibit how one ca n derive the\nindex theoretic version of the trace formula (due to Barbasc h and\nMoscovici) from our identity via the theory of higher indices.\n\nT his is joint work with Bram Mesland (Leiden) and Hang Wang (Shanghai).\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Wajid Mannan (QMUL) DTSTART:20201009T140000Z DTEND:20201009T150000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/2 DESCRIPTION:Title: An exotic group presentation\nby Wajid Mannan (QMU L) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nAb stract: The shape colloquially referred to as Nancy's toy can be pictured as being made of solid (3-dimensional) dough. It was conjectured in the ea rly 2000's that the shape could not be flattened by squeezing the dough\, in which case it would be the first with this property\, where there are n o homological obstructions to flattening it. However\, I and my colleague (Tomasz Popiel) flattened it\, leading instead to an unexpected group pres entation of a quaternion group\, and the resolution of a question regardin g the spines of closed 3-manifolds.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Lukasz Grabowski (Lancaster University) DTSTART:20201023T140000Z DTEND:20201023T150000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/3 DESCRIPTION:Title: On the cost of Benjamini Schramm statistics with the K azhdan property\nby Lukasz Grabowski (Lancaster University) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nThis talk is ba sed on a joint work with Samuel Mellick.\nRecently Hutchcroft and Pete sho wed that the cost of any infinite\nKazhdan group is 1. We generalise this result to the context of\ngraphings. Our proof is noticably simpler than t he original proof of\nHutchcroft and Pete even for graphings arising from actions of\ncountable Kazhdan groups\, in particular our arguments do no t use any\n"hard" probability theory. The main ingredient oin our approach is the\nanalysis of the connectivity properties of partitions of the vert ex\nspace of graphings which are ``Cheeger-optimal''\, i.e.~minimise the\n amount of edges present between the parts of a partition.\n\nWe work in th e context of Benjamini-Schramm statistics\, which are\nconvenient ``group- like'' objects roughly equivalent to ``invariant\nrandom subgroups''. In p articular we give examples of Kazhdan\nBenjamini-Schramm statistics which do not arise from actions of\ncountable Kazhdan groups\, by considering po int processes on\nlattice-free Kazhdan Lie groups. Of some interest might be also a\nseemingly new characerisation of Kazhdan equivalence relations\ , as\nstudied by Mikael Pichot.\n\nThis work is partially motivated by the following ``Lueck approximation\ntype'' question: Let $M_n$ be a seuqence of triangulated compact\n3-manifolds\, such that the 1-skeleta of the tri angulations have\nuniformly bounded vertex degrees and which converge to a triangulation\nof R^3 in the sense of Benjamini-Schramm (informally speak ing\, this\nmeans that ``M_n is a sequence of compact manifolds with growi ng\ninjectivity 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://stable.researchseminars.org/talk/SotonPureMathsColloq/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Cashen (University of Vienna) DTSTART:20201030T150000Z DTEND:20201030T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/4 DESCRIPTION:Title: "Paging Dr. Frankenstein"\; or\, how to build monsters \nby Chris Cashen (University of Vienna) as part of Pure Mathematics C olloquium at Southampton\n\n\nAbstract\nI’ll talk about the use of small cancellation theory to build the “monster groups” of Rips\, Olshanski i\, and Gromov. Then I’ll talk about work with Arzhantseva\, Gruber\, an d Hume constructing Gromov monsters with further exotic properties.\n LOCATION:https://stable.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:20260404T110744Z UID:SotonPureMathsColloq/5 DESCRIPTION:Title: Primes in geometric series and finite permutation grou ps\nby Gareth Jones and Alexander Zvonkin (GAJ: U of Southampton\; AZ: LaBRI\, U of Bordeaux) as part of Pure Mathematics Colloquium at Southamp ton\n\n\nAbstract\nAbstract: The classification of permutation groups of p rime degree is a very old problem\, going back to Galois and Burnside. As a consequence of the classification of finite simple groups\, the classifi cation 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 compu tational evidence to support a conjecture that there are infinitely many p rimes of this form.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Johnny Nicholson (University College London) DTSTART:20201113T150000Z DTEND:20201113T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/6 DESCRIPTION:Title: Projective modules and exotic group presentations\ nby Johnny Nicholson (University College London) as part of Pure Mathemati cs Colloquium at Southampton\n\n\nAbstract\nAbstract: Two presentations f or a group G which have the same deficiency are called exotic if the corre sponding presentation complexes are not homotopy equivalent. Despite early interest by Cockroft-Swan and Dyer-Sieradski\, it was not until 1976 that the first examples of exotic presentations were found by Dunwoody (for th e trefoil group) and Metzler (for finite abelian groups). In recent years\ , applications to Wall’s D2 problem and the classification of manifolds have sparked renewed interest in this problem. In this talk\, we will disc uss exotic presentations for groups G with 4-periodic (group-)cohomology a nd their relation to the classification of projective ZG modules. This bui lds upon recent work of Mannan-Popiel on exotic presentations for the quat ernion group Q(28).\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Gerald Williams (University of Essex) DTSTART:20201120T150000Z DTEND:20201120T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/7 DESCRIPTION:Title: Hyperbolicity of cyclically presented groups\nby G erald Williams (University of Essex) as part of Pure Mathematics Colloquiu m at Southampton\n\n\nAbstract\nCyclically presented groups are groups def ined by presentations that admit a cyclic symmetry. Prominent examples inc lude the Higman group and the Fibonacci groups. I will discuss recent resu lts that classify the T(6) (small cancellation) cyclically presented group s that are hyperbolic and present results concerning hyperbolicity of grou ps of Fibonacci type. This is joint work with Ihechukwu Chinyere.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Bin Sun (University of Oxford) DTSTART:20201127T150000Z DTEND:20201127T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/8 DESCRIPTION:Title: Groups acting acylindrically on hyperbolic metric spac es\nby Bin Sun (University of Oxford) as part of Pure Mathematics Coll oquium at Southampton\n\n\nAbstract\nAbstract: I will talk about some rece nt developments in the study of group actions on hyperbolic metric spaces. I will focus on the class of acylindrcially hyperbolic groups. This class is broad enough to include many examples of interest\, yet a significant part of the theory of hyperbolic and relatively hyperbolic groups can be g eneralized in this context. In particular\, I will discuss group theoretic Dehn filling and small cancellation theory in acylindrically hyperbolic g roups. The talk will be accessible to graduate students.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Evington (University of Münster) DTSTART:20201204T150000Z DTEND:20201204T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/9 DESCRIPTION:Title: C*-Algebras and Dimension Theory\nby Sam Evington (University of Münster) as part of Pure Mathematics Colloquium at Southam pton\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 b oth matrix algebras and topological spaces. I will then look at covering d imension of topological spaces\, and how this can be generalised to the se tting of C*-algebras. Finally\, I will discuss my joint work with Castill ejos\, Tikuisis\, White\, and Winter\, which restricts the possible values of dimension for simple C*-algebras (i.e those with no non-trival ideals) \, and explain the connections to the classification programme for simple C*-algebras.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Thom (Technische Universität Dresden) DTSTART:20201211T160000Z DTEND:20201211T170000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/10 DESCRIPTION:Title: (GGSE) Asymptotics of Cheeger constants and unitarisa bility of groups\nby Andreas Thom (Technische Universität Dresden) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nGiven a group Γ\, we establish a connection between the unitarisability of its u niformly bounded representations and the asymptotic behaviour of the isope rimetric constants of Cayley graphs of Γ for increasingly large generatin g sets.\nThe connection hinges on an analytic invariant Lit(Γ)∈[0\,∞] which we call the Littlewood exponent. Finiteness\, amenability\, unitari sability and the existence of free subgroups are related respectively to t he thresholds 0\,1\,2 and ∞ for Lit(Γ). Using graphical small cancellat ion theory\, we prove that there exist groups Γ for which 1Groups and Geo metry on zoom" meeting.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Viveka Erlandsson (University of Bristol) DTSTART:20210108T150000Z DTEND:20210108T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/11 DESCRIPTION:Title: Mirzakhani’s curve counting theorem\nby Viveka Erlandsson (University of Bristol) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nAbstract: In her thesis\, Mirzakhani establi shed the 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 same type if they differ by a homeomorphism. In this talk I will disc uss this theorem\, the extension to geodesics which are not simple\, and s ome applications.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacek Brodzki (University of Southampton) DTSTART:20210115T150000Z DTEND:20210115T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/12 DESCRIPTION:Title: Gyroscopes and topology\nby Jacek Brodzki (Univer sity of Southampton) as part of Pure Mathematics Colloquium at Southampton \n\n\nAbstract\nAbstract: In recent years\, physicists discovered material s whose properties and behaviour are controlled by the topology of their “band structure”\, that is the distribution of energy levels of their electrons. For example\, a topological insulator is a material that may co nduct electricity on its surface\, but not in its interior. My talk will d escribe a recent mechanical demonstration by Nash et al of a system with t opologically protected states in the form of a network of interacting gyro scopes. I will outline recent work in progress (in collaboration with Nige l Higson) to understand the topological reasons for the behaviour of these exciting systems.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Genevieve Walsh (Tufts University) DTSTART:20201211T133000Z DTEND:20201211T143000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/13 DESCRIPTION:Title: (GGSE) Incoherence of free-by-free and surface-by-fre e groups\nby Genevieve Walsh (Tufts University) as part of Pure Mathem atics Colloquium at Southampton\n\n\nAbstract\nA group is coherent if ever y finitely generated subgroup is finitely presented\, and incoherent other wise. Many well-known groups are coherent: free groups\, surface groups\, and the fundamental groups of compact 3-manifolds. We consider groups of the form $F_m \\by F_n$ 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 ar e incoherent whenever $g\, n$ are at least 2\, answering a question of D. Wise. One possible alternative method to prove incoherence would be to show that these groups virtually algebraically fiber. We additionally sho w that not all groups covered by our methods virtually algebraically fiber . This is joint work with Robert Kropholler and Stefano Vidussi.\n\nThis talk is a part of "Groups and Geometry on zoom" (GGSE) meeting.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Nima Hoda (ENS Paris) DTSTART:20201211T144500Z DTEND:20201211T154500Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/14 DESCRIPTION:Title: (GGSE) Crystallographic Helly Groups\nby Nima Hod a (ENS Paris) as part of Pure Mathematics Colloquium at Southampton\n\n\nA bstract\nA Helly graph is a graph in which the metric balls form a Helly f amily: any pairwise intersecting collection of balls has nonempty total in tersection. A Helly group is a group that acts properly and cocompactly o n a Helly graph. Helly groups simultaneously generalize hyperbolic\, coco mpactly cubulated and C(4)-T(4) graphical small cancellation groups while maintaining nice properties\, such as biautomaticity. I will show that if a crystallographic group is Helly then its point group preserves an L^{\\ infinity} metric on \\R^n. Thus we will obtain some new nonexamples of He lly groups\, including the 3-3-3 Coxeter group\, which is a systolic group . This answers a question posed by Chepoi during the recent Simons Semest er on Geometric and Analytic Group Theory in Warsaw.\n\nThis talk is a par t of "Groups and Geometry o n zoom" (GGSE) meeting.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Liviu Pãunescu (Institute of Mathematics of the Romanian Academy) DTSTART:20210205T150000Z DTEND:20210205T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/15 DESCRIPTION:Title: Recent results on P-stability\nby Liviu Pãunescu (Institute of Mathematics of the Romanian Academy) as part of Pure Mathem atics Colloquium at Southampton\n\n\nAbstract\nTwo permutations that almos t commute are close to two commuting permutations. The same question can b e asked for other relations\, not only the commutant. We shall see that th e answer to this question depends only on the group that the equations des cribe. We then survey some recent results where this question is answered in positive or negative\, depending on the group.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Linckelmann (City University of London) DTSTART:20210226T150000Z DTEND:20210226T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/17 DESCRIPTION:Title: On the Lie algebra structure of outer derivations of finite group algebras\nby Markus Linckelmann (City University of Londo n) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nVe ry few finite-dimensional algebras over a field are expected to arise as d irect factors of finite group algebras. In fact\, prominent finiteness con jectures would imply that in any fixed dimension\, only finitely many isom orphism classes of algebras should arise in this way. Even in very small d imensions\, where this is known to hold\, this tends to require some subst antial effort\, since it is generally very difficult to decide for any giv en algebra whether it arises as a direct factor of some finite group algeb ra or not. Amongst many invariants which can be useful for this endeavour is the Lie algebra structure of the first Hochschild cohomology space - th is is simply the space of derivations on the algebra modulo inner derivati ons. We describe some progress in recent years. Time permitting\, we descr ibe 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 fi rst Hochschild cohomology of certain finite p-group algebras. This is join t work with Radha Kessar and Dave Benson.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis Paris (Université de Bourgogne) DTSTART:20210305T150000Z DTEND:20210305T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/18 DESCRIPTION:Title: Artin groups of spherical type\nby Luis Paris (Un iversité de Bourgogne) as part of Pure Mathematics Colloquium at Southamp ton\n\n\nAbstract\nAbstract: An Artin group is a group that has a presenta tion with relations of the form "aba... = bab..."\, the words on the righ t hand side and on the left hand side having the same length.\nThere are f ew results proved for all Artin groups\, and the theory consists mainly in the study of more or less extended families. One of the most popular fami lies\, in particular because of its implication in algebraic geometry\, is that of Artin groups of spherical type\, that correspond to the finite Co xeter groups. The talk will be an introduction to Artin groups of spherica l type together with their different forms of classification.\n\nAs a dire ct consequence of Coxeter's work\, dating from 1935\, we get an explicit c lassification 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 only if they have the same presentation. Very recently\, with Maria C umplido\, we gave an almost complete classification up to commensurability . I can hardly say anything about the classification up to quasi-isometry. \n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Rudolf Zeidler (Universität Münster) DTSTART:20210312T150000Z DTEND:20210312T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/19 DESCRIPTION:Title: Scalar and mean curvature comparison via the Dirac op erator\nby Rudolf Zeidler (Universität Münster) as part of Pure Math ematics Colloquium at Southampton\n\n\nAbstract\nAbstract: In recent years \, Gromov proposed studying the geometry of positive scalar curvature (``p sc'') via various metric inequalities reminiscent of classical comparison geometry. For instance\, he proposed the following conjecture: Let $M$ be a closed manifold of dimension $n-1$ which does not admit a metric of psc . Then with respect to any Riemannian metric of scalar curvature $\\geq n( n-1)$ on the cylinder $V = M \\times [-1\,1]$\, the distance between the t wo boundary components of $V$ is at most $2\\pi/n$. In this talk\, we will discuss how to address this and other related questions via Dirac operato r techniques on spin manifolds which have suitable non-vanishing index inv ariants. Using local boundary conditions\, we will refine these estimates using the mean curvature of the boundary\, and we will explain that the ex tremal situation can only be realized by certain warped product metrics.\n This is joint work with Simone Cecchini.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Jürgen Jost (Max-Planck-Institut Leipzig) DTSTART:20210319T150000Z DTEND:20210319T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/20 DESCRIPTION:Title: Graphs\, hypergraphs\, and network analysis\nby J ürgen Jost (Max-Planck-Institut Leipzig) as part of Pure Mathematics Coll oquium at Southampton\n\n\nAbstract\nEmpirical networks are often represen ted and analysed as graphs. These graphs are often qualitatively different from and typically less regular than those investigated in classical grap h theory. We have therefore developed tools from spectral theory and geome try. These tools not only help us to understand empirical data\, but they also lead to new mathematical problems and challenges. Also\, in many case s\, ranging from chemical reactions to collaborations between scientists\, interactions between more than two elements play important roles\, and t herefore\, we are also developing tools for hypergraph analysis\, and we c urrently explore the resulting mathematical structures.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Laurent Bartholdi (Universität Göttingen) DTSTART:20210430T140000Z DTEND:20210430T150000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/22 DESCRIPTION:Title: Dimension series and homotopy groups of spheres\n by Laurent Bartholdi (Universität Göttingen) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nThe lower central series of a gr oup $G$ is defined by $\\gamma_1=G$ and $\\gamma_n = [G\,\\gamma_{n-1}]$. The "dimension series"\, introduced by Magnus\, is defined using the group algebra over the integers: $\\delta_n = \\{g: g-1\\text{ belongs to the $ n$-th power of the augmentation ideal}\\}$.\n\nIt has been\, for the last 80 years\, a fundamental problem of group theory to relate these two serie s. One always has $\\delta_n\\ge\\gamma_n$\, and a conjecture by Magnus\, with false proofs by Cohn\, Losey\, etc.\, claims that they coincide\; but Rips constructed an example with $\\delta_4/\\gamma_4$ cyclic of order 2. On the positive side\, Sjogren showed that $\\delta_n/\\gamma_n$ is alway s a torsion group\, of exponent bounded by a function of $n$. Furthermore\ , it was believed (and falsely proven by Gupta) that only $2$-torsion may occur.\n\nIn joint work with Roman Mikhailov\, we prove however that the t orsion in the quotients $\\delta_n/\\gamma_n$ can be arbitrarily specified \; thus Sjogren's result is optimal.\n\nEven more interestingly\, I will s how that the dimension quotient $\\delta_n/\\gamma_n$ is related to the di fference between homotopy and homology: our construction is fundamentally based on embedding the torsion of the homotopy group $\\pi_n(S^2\\vee S^2) $ in dimension quotients. We can even make this quite explicit on the orde r-$p$ element in $\\pi_{2p}(S^2)$ due to Serre.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Puschnigg (Institut de Mathématiques de Luminy\, Marseill e) DTSTART:20210416T140000Z DTEND:20210416T150000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/23 DESCRIPTION:Title: Operator-K-theory and cyclic homology\nby Michael Puschnigg (Institut de Mathématiques de Luminy\, Marseille) as part of P ure Mathematics Colloquium at Southampton\n\n\nAbstract\nOperator-K-theory has turned out to be a key homological invariant of Banach algebras. Desp ite its simple definition it is usually very hard to calculate. Local cycl ic homology is designed to provide a good approximation of K-theory while being computable by standard techniques. We outline the construction of th is theory and discuss how much information is lost by passing from K-theor y to local cyclic homology. We stress the outstanding role played in this context by $C^*$-algebras of Gromov-hyperbolic groups with Kazhdan's prope rty (T).\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Li (University of Southampton) DTSTART:20210219T150000Z DTEND:20210219T160000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/24 DESCRIPTION:Title: Topological complexity of hyperbolic groups\nby K evin Li (University of Southampton) as part of Pure Mathematics Colloquium at Southampton\n\n\nAbstract\nThe topological complexity TC(X) of a space X is an integer-valued homotopy invariant which is similar in spirit to t he classical Lusternik-Schnirelmann category. It was introduced by M. Farb er in 2003 in the context of robot motion planning\, measuring the "naviga tional complexity" of X\, but since then has been studied in its own right . One obtains 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 classifying spaces for families of subgroups\, which was recently used by A. Dranishnikov to compute TC for hyperbolic groups. We will present an al ternative proof of Dranishnikov's result via the Lück-Weiermann construct ion and equivariant Bredon cohomology. Our proof has the advantage that it easily generalizes to certain toral relatively hyperbolic groups.\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Goulnara Arzhantseva (Universität Wien) DTSTART:20210514T140000Z DTEND:20210514T150000Z DTSTAMP:20260404T110744Z UID:SotonPureMathsColloq/25 DESCRIPTION:Title: Approximations of infinite groups\nby Goulnara Ar zhantseva (Universität Wien) as part of Pure Mathematics Colloquium at So uthampton\n\n\nAbstract\nAbstract: We discuss various (still open) questio ns on approximations of finitely generated groups\, focusing on finite-dim ensional approximations such as residual finiteness and soficity. We surve y our results on the existence and stability of metric approximations. We suggest a few conjectures\, e.g. on Gromov hyperbolic groups and their inf inite monster limits.\n\nBased on joint work with Liviu Paunescu (Buchares t).\n LOCATION:https://stable.researchseminars.org/talk/SotonPureMathsColloq/25/ END:VEVENT END:VCALENDAR