BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Federico Berlai (University of the Basque Country) DTSTART:20200605T050000Z DTEND:20200605T060000Z DTSTAMP:20260422T225724Z UID:SiN/1 DESCRIPTION:Title: From hyperbolicity to hierarchical hyperbolicity\nby Federico Berlai (Univ ersity of the Basque Country) as part of Symmetry in Newcastle\n\nAbstract : TBA\n LOCATION:https://researchseminars.org/talk/SiN/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Hagen (University of Bristol) DTSTART:20200605T063000Z DTEND:20200605T073000Z DTSTAMP:20260422T225724Z UID:SiN/2 DESCRIPTION:Title: Hier archical hyperbolicity from actions on simplicial complexes\nby Mark H agen (University of Bristol) as part of Symmetry in Newcastle\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SiN/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Verret (The University of Auckland\, New Zealand) DTSTART:20200918T050000Z DTEND:20200918T060000Z DTSTAMP:20260422T225724Z UID:SiN/3 DESCRIPTION:Title: Loca l actions in vertex-transitive graphs\nby Gabriel Verret (The Universi ty of Auckland\, New Zealand) as part of Symmetry in Newcastle\n\n\nAbstra ct\nA graph is vertex-transitive if its group of automorphism acts transit ively on its vertices. A very important concept in the study of these grap hs is that of local action\, that is\, the permutation group induced by a vertex-stabiliser on the corresponding neighbourhood. I will explain some of its importance and discuss some attempts to generalise it to the case o f directed graphs.\n LOCATION:https://researchseminars.org/talk/SiN/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Giudici (The University of Western Australia\, Australia) DTSTART:20200918T063000Z DTEND:20200918T073000Z DTSTAMP:20260422T225724Z UID:SiN/4 DESCRIPTION:Title: The synchronisation hierarchy for permutation groups\nby Michael Giudici ( The University of Western Australia\, Australia) as part of Symmetry in Ne wcastle\n\n\nAbstract\nThe concept of a synchronising permutation group wa s introduced nearly 15 years ago as a possible way of approaching The \\v{ C}ern\\'y Conjecture. Such groups must be primitive. In an attempt to unde rstand synchronising groups\, a whole hierarchy of properties for a permut ation group has been developed\, namely\, 2-transitive groups\, $\\mathbb{ Q}$I-groups\, spreading\, separating\, synchronising\, almost synchronisin g and primitive. Many surprising connections with other areas of mathemat ics such as finite geometry\, graph theory\, and design theory have arisen in the study of these properties. In this survey talk I will give an over view of the hierarchy and discuss what is known about which groups lie whe re.\n LOCATION:https://researchseminars.org/talk/SiN/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandra Garrido (Universidad Autónoma de Madrid) DTSTART:20201002T060000Z DTEND:20201002T070000Z DTSTAMP:20260422T225724Z UID:SiN/5 DESCRIPTION:Title: When is a piecewise (a.k.a topological) full group locally compact?\nby Al ejandra Garrido (Universidad Autónoma de Madrid) as part of Symmetry in N ewcastle\n\n\nAbstract\nQuestion: When is a piecewise (a.k.a topological) full group locally compact? \n\nAnswer: Only when it's an ample group in t he sense of Krieger (in particular\, discrete\, countable and locally fini te) and has a Bratteli diagram satisfying certain conditions. \n\nComplain t: Wait\, isn't Neretin's group a non-discrete\, locally compact\, topolog ical full group? \n\nRetort: It is\, but you need to use the correct topol ogy!\n\nA fleshed-out version of the above conversation will be given in t he talk. Based on joint work with Colin Reid.\n LOCATION:https://researchseminars.org/talk/SiN/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Feyisayo Olukoya (University of Aberdeen) DTSTART:20201002T073000Z DTEND:20201002T083000Z DTSTAMP:20260422T225724Z UID:SiN/6 DESCRIPTION:Title: The group of automorphisms of the shift dynamical system and the Higman-Thomps on groups\nby Feyisayo Olukoya (University of Aberdeen) as part of Sym metry in Newcastle\n\n\nAbstract\nWe give a survey of recent results explo ring connections between the Higman-Thompson groups and their automorphism groups and the group of automorphisms of the shift dynamical system. Our survey takes us from dynamical systems to group theory via groups of homeo morphisms with a segue through combinatorics\, in particular\, de Bruijn g raphs.\n\nJoint work with Collin Bleak and Peter Cameron.\n LOCATION:https://researchseminars.org/talk/SiN/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Skipper (Ohio State University) DTSTART:20201015T230000Z DTEND:20201016T000000Z DTSTAMP:20260422T225724Z UID:SiN/7 DESCRIPTION:Title: Maxi mal Subgroups of Thompson's group V\nby Rachel Skipper (Ohio State Uni versity) as part of Symmetry in Newcastle\n\n\nAbstract\nThere has been a long interest in embedding and non-embedding results for groups in the Tho mpson family. One way to get at results of this form is to classify maxima l subgroups. In this talk\, we will define certain labelings of binary tre es and use them to produce a large family of new maximal subgroups of Thom pson's group V. We also relate them to a conjecture about Thompson's group T.\nThis is joint\, ongoing work with Jim Belk\, Collin Bleak\, and Marty n Quick at the University of Saint Andrews.\n LOCATION:https://researchseminars.org/talk/SiN/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Lawrence Reeves (The University of Melbourne) DTSTART:20201016T003000Z DTEND:20201016T013000Z DTSTAMP:20260422T225724Z UID:SiN/8 DESCRIPTION:Title: Irra tional-slope versions of Thompson’s groups T and V\nby Lawrence Reev es (The University of Melbourne) as part of Symmetry in Newcastle\n\n\nAbs tract\nWe consider irrational slope versions of T and V\, We give infinite presentations for these groups and show how they can be represented by tr ee-pair diagrams. We also show that they have index-2 normal subgroups tha t are simple. \nThis is joint work with Brita Nucinkis and Pep Burillo.\n LOCATION:https://researchseminars.org/talk/SiN/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Bradford (University of Cambridge) DTSTART:20201109T090000Z DTEND:20201109T100000Z DTSTAMP:20260422T225724Z UID:SiN/9 DESCRIPTION:Title: Quan titative LEF and topological full groups\nby Henry Bradford (Universit y of Cambridge) as part of Symmetry in Newcastle\n\n\nAbstract\nTopologica l full groups of minimal subshifts are an important source of exotic examp les in geometric group theory\, as well as being powerful invariants of sy mbolic dynamical systems. In 2011\, Grigorchuk and Medynets proved that TF Gs are LEF\, that is\, every finite subset of the multiplication table occ urs in the multiplication table of some finite group. In this talk we expl ore some ways in which asymptotic properties of the finite groups which oc cur reflect asymptotic properties of the associated subshift. Joint work w ith Daniele Dona.\n LOCATION:https://researchseminars.org/talk/SiN/9/ END:VEVENT BEGIN:VEVENT SUMMARY:William Hautekiet (Université libre de Bruxelles\, Belgium) DTSTART:20201123T073000Z DTEND:20201123T083000Z DTSTAMP:20260422T225724Z UID:SiN/10 DESCRIPTION:Title: Aut omorphism groups of transcendental field extensions\nby William Hautek iet (Université libre de Bruxelles\, Belgium) as part of Symmetry in Newc astle\n\n\nAbstract\nIt is well-known that the Galois group of an (infinit e) algebraic field extension is a profinite group. When the extension is t ranscendental\, the automorphism group is no longer compact\, but has a to tally disconnected locally compact structure (TDLC for short). The study o f TDLC groups was initiated by van Dantzig in 1936 and then restarted by W illis in 1994. In this talk some of Willis' concepts\, such as tidy subgro ups\, the scale function\, flat subgroups and directions are introduced an d applied to examples of automorphism groups of transcendental field exten sions. It remains unknown whether there exist conditions that a TDLC group must satisfy to be a Galois group. A suggestion of such a condition is ma de.\n LOCATION:https://researchseminars.org/talk/SiN/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Florian Breuer (University of Newcastle\, Australia) DTSTART:20201123T090000Z DTEND:20201123T100000Z DTSTAMP:20260422T225724Z UID:SiN/11 DESCRIPTION:Title: Rea lising general linear groups as Galois groups\nby Florian Breuer (Univ ersity of Newcastle\, Australia) as part of Symmetry in Newcastle\n\n\nAbs tract\nI will show how to construct field extensions with Galois groups is omorphic to general linear groups (with entries in various rings and field s) from the torsion of elliptic curves and Drinfeld modules. No prior know ledge of these structures is assumed.\n LOCATION:https://researchseminars.org/talk/SiN/11/ END:VEVENT BEGIN:VEVENT SUMMARY:François Le Maître (Université de Paris) DTSTART:20210125T073000Z DTEND:20210125T083000Z DTSTAMP:20260422T225724Z UID:SiN/12 DESCRIPTION:Title: Den se totipotent free subgroups of full groups\nby François Le Maître ( Université de Paris) as part of Symmetry in Newcastle\n\n\nAbstract\nIn t his talk\, we will be interested in measure-preserving actions of countabl e groups on standard probability spaces\, and more precisely in the partit ions of the space into orbits that they induce\, also called measure-prese rving equivalence relations. In 2000\, Gaboriau obtained a characterizatio n of the ergodic equivalence relations which come from non-free actions of the free group on $n > 1$ generators: these are exactly the equivalence r elations of cost less than n. A natural question is: how non-free can thes e actions be made\, and what does the action on each orbit look like? We w ill obtain a satisfactory answer by showing that the action on each orbit can be made totipotent\, which roughly means "as rich as possible"\, and f urthermore that the free group can be made dense in the ambient full group of the equivalence relation.\n\nThis is joint work with Alessandro Carder i and Damien Gaboriau.\n LOCATION:https://researchseminars.org/talk/SiN/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Cox (University of Bristol) DTSTART:20210125T090000Z DTEND:20210125T100000Z DTSTAMP:20260422T225724Z UID:SiN/13 DESCRIPTION:Title: Spr ead and infinite groups\nby Charles Cox (University of Bristol) as par t of Symmetry in Newcastle\n\n\nAbstract\nMy recent work has involved taki ng questions asked for finite groups and considering them for infinite gro ups. There are various natural directions with this. In finite group theor y\, there exist many beautiful results regarding generation properties. On e such notion is that of spread\, and Scott Harper and Casey Donoven have raised several intriguing questions for spread for infinite groups (in htt ps://arxiv.org/abs/1907.05498). A group $G$ has spread $k$ if for every $g _1\, \\dots\, g_k \\in G$ we can find an $h \\in G$ such that $\\langle g_ i\, h \\rangle = G$. For any group we can say that if it has a proper quot ient that is non-cyclic\, then it has spread 0. In the finite world there is then the astounding result - which is the work of many authors - that t his condition on proper quotients is not just a necessary condition for po sitive spread\, but is also a sufficient one. Harper-Donoven’s first que stion is therefore: is this the case for infinite groups? Well\, no. But t hat’s for the trivial reason that we have infinite simple groups that ar e not 2-generated (and they point out that 3-generated examples are also k nown). But if we restrict ourselves to 2-generated groups\, what happens? In this talk we’ll see the answer to this question. The arguments will b e concrete (*) and accessible to a general audience.\n\n(*) at the risk of ruining the punchline\, we will find a 2-generated group that has every p roper quotient cyclic but that has spread zero.\n LOCATION:https://researchseminars.org/talk/SiN/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Henry-Leemann (University of Neuchatel) DTSTART:20210222T073000Z DTEND:20210222T083000Z DTSTAMP:20260422T225724Z UID:SiN/14 DESCRIPTION:Title: Cay ley graphs with few automorphisms\nby Paul Henry-Leemann (University o f Neuchatel) as part of Symmetry in Newcastle\n\n\nAbstract\nLet G be a gr oup and S a generating set. Then the group G naturally acts on the Cayley graph Cay(G\,S) by left multiplications. The group G is said to be rigid i f there exists an S such that the only automorphisms of Cay(G\,S) are the ones coming from the action of G.\nWhile the classification of finite rigi d groups was achieved in 1981\, few results were known about infinite grou ps. In a recent work\, with M. de la Salle we gave a complete classificati on of infinite finitely generated rigid groups. As a consequence\, we also obtain that every finitely generated group admits a Cayley graph with cou ntable automorphism group.\n LOCATION:https://researchseminars.org/talk/SiN/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Giles Gardam (WWU Muenster) DTSTART:20210222T090000Z DTEND:20210222T100000Z DTSTAMP:20260422T225724Z UID:SiN/15 DESCRIPTION:Title: Kap lansky's conjectures\nby Giles Gardam (WWU Muenster) as part of Symmet ry in Newcastle\n\n\nAbstract\nKaplansky made various related conjectures about group rings\, especially for torsion-free groups. For example\, the zero divisors conjecture predicts that if K is a field and G is a torsion- free group\, then the group ring K[G] has no zero divisors. I will survey what is known about the conjectures\, including their relationships to eac h other and to other group properties such as orderability\, and present s ome recent progress.\n LOCATION:https://researchseminars.org/talk/SiN/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Zoe Chatzidakis (CNRS - ENS) DTSTART:20210419T063000Z DTEND:20210419T073000Z DTSTAMP:20260422T225724Z UID:SiN/16 DESCRIPTION:Title: A n ew invariant for difference fields\nby Zoe Chatzidakis (CNRS - ENS) as part of Symmetry in Newcastle\n\n\nAbstract\nIf $(K\,f)$ is a difference field\, and a is a finite tuple in some difference field extending $K$\, a nd such that $f(a)$ in $K(a)^{alg}$\, then we define $dd(a/K)=\\mathop{lim }[K(f^k(a)\,a):K(a)]^{1/k}$\, the distant degree of $a$ over $K$. This is an invariant of the difference field extension $K(a)^{alg}/K$. We show tha t there is some $b$ in the difference field generated by $a$ over $K$\, wh ich is equi-algebraic with $a$ over $K$\, and such that $dd(a/K)=[K(f(b)\, b):K(b)]$\, i.e.: for every $k>0$\, $f(b) \\in K(b\,f^k(b))$.\n\nViewing $ \\mathop{Aut}(K(a)^{alg}/K)$ as a locally compact group\, this result is c onnected to results of Goerge Willis on scales of automorphisms of locally compact totally disconnected groups. I will explicit the correspondence b etween the two sets of results.\n(Joint with E. Hrushovski)\n LOCATION:https://researchseminars.org/talk/SiN/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Ciobanu (Herriot Watt) DTSTART:20210419T080000Z DTEND:20210419T090000Z DTSTAMP:20260422T225724Z UID:SiN/17 DESCRIPTION:Title: Fre e group homomorphisms and the Post Correspondence Problem\nby Laura Ci obanu (Herriot Watt) as part of Symmetry in Newcastle\n\n\nAbstract\nThe P ost Correspondence Problem (PCP) is a classical problem in computer scienc e that can be stated as: is it decidable whether given two morphisms $g$ a nd $h$ between two free semigroups $A$ and $B$\, there is any nontrivial $ x$ in $A$ such that $g(x)=h(x)$? This question can be phrased in terms of equalisers\, asked in the context of free groups\, and expanded: if the `e qualiser' of $g$ and $h$ is defined to be the subgroup consisting of all $ x$ where $g(x)=h(x)$\, it is natural to wonder not only whether the equali ser is trivial\, but what its rank or basis might be.\n\nWhile the PCP for semigroups is famously insoluble and acts as a source of undecidability i n many areas of computer science\, the PCP for free groups is open\, as ar e the related questions about rank\, basis\, or further generalisations. H owever\, in this talk we will show that there are links and surprising equ ivalences between these problems in free groups\, and classes of maps for which we can give complete answers. This is joint work with Alan Logan.\n LOCATION:https://researchseminars.org/talk/SiN/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Yago Antolin (Universidad Complutense de Madrid) DTSTART:20210510T063000Z DTEND:20210510T073000Z DTSTAMP:20260422T225724Z UID:SiN/18 DESCRIPTION:Title: Geo metry and Complexity of positive cones in groups.\nby Yago Antolin (Un iversidad Complutense de Madrid) as part of Symmetry in Newcastle\n\n\nAbs tract\nA positive cone on a group $G$ is a subsemigroup $P$\, such that $G $ is the disjoint union of $P$\, $P^{-1}$ and the trivial element. Positiv e cones codify naturally $G$-left-invariant total orders on $G$. When $G$ is a finitely generated group\, we will discuss whether or not a positive cone can be described by a regular language over the generators and how th e ambient geometry of $G$ influences the geometry of a positive cone.\n\nT his will be based on joint works with Juan Alonso\, Joaquin Brum\, Cristob al Rivas and Hang Lu Su.\n LOCATION:https://researchseminars.org/talk/SiN/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Kropholler (Universität Münster) DTSTART:20210510T080000Z DTEND:20210510T090000Z DTSTAMP:20260422T225724Z UID:SiN/19 DESCRIPTION:Title: Gro ups of type FP_2 over fields but not over the integers\nby Robert Krop holler (Universität Münster) as part of Symmetry in Newcastle\n\n\nAbstr act\nBeing of type $\\mathop{FP}_2$ is an algebraic shadow of being finite ly presented. A long standing question was whether these two classes are e quivalent. This was shown to be false in the work of Bestvina and Brady. M ore recently\, there are many new examples of groups of type $\\mathop{FP} _2$ coming with various interesting properties. I will begin with an intro duction to the finiteness property $\\mathop{FP}_2$. I will end by giving a construction to find groups that are of type $\\mathop{FP}_2(F)$ for all fields $F$ but not $\\mathop{FP}_2(\\mathbb{Z})$\n LOCATION:https://researchseminars.org/talk/SiN/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Libor Barto (Charles University in Prague) DTSTART:20210524T063000Z DTEND:20210524T073000Z DTSTAMP:20260422T225724Z UID:SiN/20 DESCRIPTION:Title: CSP s and Symmetries\nby Libor Barto (Charles University in Prague) as par t of Symmetry in Newcastle\n\n\nAbstract\nHow difficult is to solve a give n computational problem? In a large class of computational problems\, incl uding the fixed-template Constraint Satisfaction Problems (CSPs)\, this fu ndamental question has a simple and beautiful answer: the more symmetrical the problem is\, the easier is to solve it. The tight connection between the complexity of a CSP and a certain concept that captures its symmetry h as fueled much of the progress in the area in the last 20 years. I will ta lk about this connection and some of the many tools that have been used to analyze the symmetries. The tools involve rather diverse areas of mathema tics including algebra\, analysis\, combinatorics\, logic\, probability\, and topology.\n LOCATION:https://researchseminars.org/talk/SiN/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Zoe Chatzidakis (CNRS - ENS) DTSTART:20210524T080000Z DTEND:20210524T090000Z DTSTAMP:20260422T225724Z UID:SiN/21 DESCRIPTION:Title: A n ew invariant for difference fields\nby Zoe Chatzidakis (CNRS - ENS) as part of Symmetry in Newcastle\n\n\nAbstract\nIf $(K\,f)$ is a difference field\, and $a$ is a finite tuple in some difference field extending $K$\, and such that $f(a) \\in K(a)^{alg}$\, then we define $dd(a/K)=\\lim[K(f^ k(a)\,a):K(a)]^{1/k}$\, the distant degree of $a$ over $K$. This is an inv ariant of the difference field extension $K(a)^{alg}/K$. We show that ther e is some $b$ in the difference field generated by $a$ over $K$\, which is equi-algebraic with $a$ over $K$\, and such that $dd(a/K)=[K(f(b)\,b):K(b )]$\, i.e.: for every $k>0$\, $f(b) \\in K(b\,f^k(b))$.\n\nViewing $\\math op{Aut}(K(a)^{alg}/K)$ as a locally compact group\, this result is connect ed to results of Goerge Willis on scales of automorphisms of locally compa ct totally disconnected groups. I will explicit the correspondence between the two sets of results.\n(Joint with E. Hrushovski)\n LOCATION:https://researchseminars.org/talk/SiN/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Waldemar Hołubowski (Silesian University of Technology) DTSTART:20210607T063000Z DTEND:20210607T073000Z DTSTAMP:20260422T225724Z UID:SiN/22 DESCRIPTION:Title: Nor mal subgroups in the group of column-finite infinite matrices\nby Wald emar Hołubowski (Silesian University of Technology) as part of Symmetry i n Newcastle\n\n\nAbstract\nThe classical result\, due to Jordan\, Burnside \, Dickson\, says that every normal subgroup of $GL(n\, K)$ ($K$ - a field \, $n \\geq 3$) which is not contained in the center\, contains $SL(n\, K) $. A. Rosenberg gave description of normal subgroups of $GL(V)$\, where $V $ is a vector space of any infinite cardinality dimension over a division ring. However\, when he considers subgroups of the direct product of the c enter and the group of linear transformations $g$ such that $g-id_V$ has f inite dimensional range the proof is not complete. We fill this gap for co untably dimensional $V$ giving description of the lattice of normal subgro ups in the group of infinite column-finite matrices indexed by positive in tegers over any field. Similar results for Lie algebras of matrices will b e surveyed.\n\nThe talks is based on results presented in https://arxiv.or g/abs/1808.06873 and https://arxiv.org/abs/1806.01099.\n\n(joint work with Martyna Maciaszczyk and Sebastian Zurek.)\n LOCATION:https://researchseminars.org/talk/SiN/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Yves Stadler (Université Clermont Auvergne) DTSTART:20210621T063000Z DTEND:20210621T073000Z DTSTAMP:20260422T225724Z UID:SiN/23 DESCRIPTION:Title: Hig hly transitive groups among groups acting on trees\nby Yves Stadler (U niversité Clermont Auvergne) as part of Symmetry in Newcastle\n\n\nAbstra ct\nHighly transitive groups\, i.e. groups admitting an embedding in Sym(N ) with dense image\, form a wide class of groups. For instance\, M. Hull a nd D. Osin proved that it contains all countable acylindrically hyperbolic groups with trivial finite radical. After an introduction to high transit iviy\, I will present a theorem (from joint work with P. Fima\, F. Le Maî tre and S. Moon) showing that many groups acting on trees are highly trans itive. On the one hand\, this theorem gives new examples of highly transit ive groups. On the other hand\, it is sharp because of results by A. Le Bo udec and N. Matte Bon.\n LOCATION:https://researchseminars.org/talk/SiN/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilaria Castellano (University of Milan - Bicoca) DTSTART:20210621T080000Z DTEND:20210621T090000Z DTSTAMP:20260422T225724Z UID:SiN/24 DESCRIPTION:Title: The Euler characteristic and the zeta-functions of a totally disconnected loc ally compact group\nby Ilaria Castellano (University of Milan - Bicoca ) as part of Symmetry in Newcastle\n\n\nAbstract\nThe Euler characteristic and the zeta-functions of a totally disconnected locally compact group\nA bstract: The Euler-Poincaré characteristic of a discrete group is an impo rtant (but also quite mysterious) invariant. It is usually just an integer or a rational number and reflects many quite significant properties. The realm of totally disconnected locally compact groups admits an analogue of the Euler-Poincaré characteristic which surprisingly is no longer just a n integer\, or a rational number\, but a rational multiple of a Haar measu re. Warning: in order to gain such an invariant the group has to be unimod ular and satisfy some cohomological finiteness conditions. Examples of gro ups satisfying these additional conditions are the fundamental groups of f inite trees of profinite groups. What arouses our curiosity is the fact th at - in some cases - the Euler-Poincaré characteristic turns out to be mi raculously related to a zeta-function. A large part of the talk will be de voted to the introduction of the just-cited objects. We aim at concluding the presentation by facing the concrete example of the group of F-points o f a split semisimple simply connected algebraic group G over F (where F de notes a non-archimedean locally compact field of residue characteristic p) .\nJoint work with Gianmarco Chinello and Thomas Weigel.\n LOCATION:https://researchseminars.org/talk/SiN/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Lancelot Semal (UC Louvain) DTSTART:20200705T080000Z DTEND:20200705T090000Z DTSTAMP:20260422T225724Z UID:SiN/25 DESCRIPTION:Title: Uni tary representations of totally disconnected locally compact groups satisf ying Ol'shanskii's factorization\nby Lancelot Semal (UC Louvain) as pa rt of Symmetry in Newcastle\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SiN/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Lancelot Semal (UC Louvain) DTSTART:20210705T080000Z DTEND:20210705T090000Z DTSTAMP:20260422T225724Z UID:SiN/26 DESCRIPTION:Title: Uni tary representations of totally disconnected locally compact groups satisf ying Ol'shanskii's factorization\nby Lancelot Semal (UC Louvain) as pa rt of Symmetry in Newcastle\n\n\nAbstract\nWe provide a new axiomatic fram ework\, inspired by the work of Ol'shanskii\, to describe explicitly certa in irreducible unitary representations of second-countable non-discrete un imodular totally disconnected locally compact groups. We show that this se tup applies to various families of automorphism groups of locally finite s emiregular trees and right-angled buildings.\n\nThe talk is based on mater ial presented in https://arxiv.org/abs/2106.05730\n LOCATION:https://researchseminars.org/talk/SiN/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Sven Raum (Stockholm University) DTSTART:20210809T063000Z DTEND:20210809T073000Z DTSTAMP:20260422T225724Z UID:SiN/27 DESCRIPTION:Title: Loc ally compact groups acting on trees\, the type I conjecture and non-amenab le von Neumann algebras\nby Sven Raum (Stockholm University) as part o f Symmetry in Newcastle\n\n\nAbstract\nn the 90's\, Nebbia conjectured tha t a group of tree automorphisms acting transitively on the tree's boundary must be of type I\, that is\, its unitary representations can in principa l be classified. For key examples\, such as Burger-Mozes groups\, this co njecture is verified. Aiming for a better understanding of Nebbia's conje cture and a better understanding of representation theory of groups acting on trees\, it is natural to ask whether there is a characterisation of ty pe I groups acting on trees. In 2016\, we introduced in collaboration with Cyril Houdayer a refinement of Nebbia's conjecture to a trichotomy\, oppo sing type I groups with groups whose von Neumann algebra is non-amenable. For large classes of groups\, including Burger-Mozes groups\, we could ve rify this trichotomy.\nIn this talk\, I will motivate and introduce the co njecture trichotomy for groups acting on tress and explain how von Neumann algebraic techniques enter the picture.\n LOCATION:https://researchseminars.org/talk/SiN/27/ END:VEVENT BEGIN:VEVENT SUMMARY:James Parkinson (University of Sydney) DTSTART:20210809T080000Z DTEND:20210809T090000Z DTSTAMP:20260422T225724Z UID:SiN/28 DESCRIPTION:Title: Aut omata for Coxeter groups\nby James Parkinson (University of Sydney) as part of Symmetry in Newcastle\n\n\nAbstract\nIn 1993 Brink and Howlett pr oved that finitely generated Coxeter groups are automatic. In particular\, they constructed a finite state automaton recognising the language of red uced words in the Coxeter group. This automaton is constructed in terms of the remarkable set of "elementary roots" in the associated root system.\n In this talk we outline the construction of Brink and Howlett. We also des cribe the minimal automaton recognising the language of reduced words\, an d prove necessary and sufficient conditions for the Brink-Howlett automato n to coincide with this minimal automaton. This resolves a conjecture of H ohlweg\, Nadeau\, and Williams\, and is joint work with Yeeka Yau.\n LOCATION:https://researchseminars.org/talk/SiN/28/ END:VEVENT BEGIN:VEVENT SUMMARY:George Willis (University of Newcastle) DTSTART:20210830T080000Z DTEND:20210830T090000Z DTSTAMP:20260422T225724Z UID:SiN/29 DESCRIPTION:Title: Con structing groups with flat-rank greater than 1\nby George Willis (Univ ersity of Newcastle) as part of Symmetry in Newcastle\n\n\nAbstract\nThe c ontraction subgroup for $x$ in the locally compact group\, $G$\, $\\mathop {con}(x) = \\left\\{ g\\in G \\mid x^ngx^{-n} \\to 1\\text{ as }n\\to\\inf ty \\right\\}$\, and the Levi subgroup is $\\mathop{lev}(x) = \\left\\{ g\ \in G \\mid \\{x^ngx^{-n}\\}_{n\\in\\mathbb{Z}} \\text{ has compact closur e}\\right\\}$. The following will be shown.\n\nLet $G$ be a totally discon nected\, locally compact group and $x\\in G$. Let $y\\in{\\sf lev}(x)$. Th en there are $x'\\in G$ and a compact subgroup\, $K\\leq G$ such that: $K$ is normalised by $x'$ and $y$\, $\\mathop{con}(x') = \\mathop{con}(x)$ an d $\\mathop{lev}(x') = \\mathop{lev}(x)$\, and the group $\\langle x'\,y\, K\\rangle$ is abelian modulo $K$\, and hence flat.\n\n\nIf no compact open subgroup of $G$ normalised by $x$ and no compact open subgroup of $\\math op{lev}(x)$ normalised by $y$\, then the flat-rank of $\\langle x'\,y\,K\\ rangle$ is equal to $2$.\n LOCATION:https://researchseminars.org/talk/SiN/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Siegfried Echterhoff (University of Münster) DTSTART:20210927T063000Z DTEND:20210927T073000Z DTSTAMP:20260422T225724Z UID:SiN/30 DESCRIPTION:Title: Ame nable group actions on C*-algebras and the weak containment problem\nb y Siegfried Echterhoff (University of Münster) as part of Symmetry in New castle\n\n\nAbstract\nThe notion of amenable actions by discrete groups on C*-algebras has been introduced by Claire Amantharaman-Delaroche more tha n thirty years ago\, and has become a well understood theory with many app lications. So it is somewhat surprising that an established theory of amen able actions by general locally compact groups has been missed for a very long time. We now present a theory which extends the discrete case and uni fies several notions of approximation properties of actions which have bee n discussed in the literature. We also discuss the weak containment proble m which asks wether an action $\\alpha:G\\to \\Aut(A)$ is amenable if and only if the maximal and reduced crossed products coincide.\n\nIn this lect ure we report on joint work with Alcides Buss and Rufus Willett\n LOCATION:https://researchseminars.org/talk/SiN/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Tim de Laat (University of Münster) DTSTART:20210927T080000Z DTEND:20210927T090000Z DTSTAMP:20260422T225724Z UID:SiN/31 DESCRIPTION:Title: Gel fand pairs\, spherical functions and exotic group C*-algebras\nby Tim de Laat (University of Münster) as part of Symmetry in Newcastle\n\n\nAbs tract\nFor a non-amenable group $G$\, there can be many group C*-algebras that lie naturally between the universal and the reduced C*-algebra of $G$ . These are called exotic group C*-algebras. After a short introduction\, I will explain that if $G$ is a simple Lie group or an appropriate locally compact group acting on a tree\, the $L^p$-integrability properties of di fferent spherical functions on $G$ (relative to a maximal compact subgroup ) can be used to distinguish between exotic group C*-algebras. This recove rs results of Samei and Wiersma. Additionally\, I will explain that under certain natural assumptions\, the aforementioned exotic group C*-algebras are the only ones coming from $G$-invariant ideals in the Fourier-Stieltje s algebra of $G$.\n\nThis is based on joint work with Dennis Heinig and Ti mo Siebenand.\n LOCATION:https://researchseminars.org/talk/SiN/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Sanghyun Kim (KIAS) DTSTART:20211101T063000Z DTEND:20211101T073000Z DTSTAMP:20260422T225724Z UID:SiN/32 DESCRIPTION:Title: Opt imal regularity of mapping class group actions on the circle\nby Sangh yun Kim (KIAS) as part of Symmetry in Newcastle\n\n\nAbstract\nWe prove th at for each finite index subgroup $H$ of the mapping class group of a clos ed hyperbolic surface\, and for each real number $r>0$ there does not exis t a faithful $C^{1+r}$--action of $H$ on a circle. (Joint with Thomas Kobe rda and Cristobal Rivas)\n LOCATION:https://researchseminars.org/talk/SiN/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Francois Thilmany (UC Louvain) DTSTART:20211101T080000Z DTEND:20211101T090000Z DTSTAMP:20260422T225724Z UID:SiN/33 DESCRIPTION:Title: Uni form discreteness of arithmetic groups and the Lehmer conjecture\nby F rancois Thilmany (UC Louvain) as part of Symmetry in Newcastle\n\n\nAbstra ct\nThe famous Lehmer problem asks whether there is a gap between 1 and th e Mahler measure of algebraic integers which are not roots of unity. Asked in 1933\, this deep question concerning number theory has since then been connected to several other subjects. After introducing the concepts invol ved\, we will briefly describe a few of these connections with the theory of linear groups. Then\, we will discuss the equivalence of a weak form of the Lehmer conjecture and the "uniform discreteness" of cocompact lattice s in semisimple Lie groups (conjectured by Margulis).\n\nJoint work with L am Pham.\n LOCATION:https://researchseminars.org/talk/SiN/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne Thomas (University of Sydney) DTSTART:20220204T010000Z DTEND:20220204T020000Z DTSTAMP:20260422T225724Z UID:SiN/34 DESCRIPTION:Title: A g allery model for affine flag varieties via chimney retractions\nby Ann e Thomas (University of Sydney) as part of Symmetry in Newcastle\n\nLectur e held in SR118\, Callaghan Campus.\n\nAbstract\nA gallery model for affin e flag varieties via chimney retractions\nWe provide a unified combinatori al framework to study orbits in affine flag varieties via the associated B ruhat-Tits buildings. We first formulate\, for arbitrary affine buildings\ , the notion of a chimney retraction. This simultaneously generalises the two well-known notions of retractions in affine buildings: retractions fro m chambers at infinity and retractions from alcoves. We then present a rec ursive formula for computing the images of certain minimal galleries in th e building under chimney retractions\, using purely combinatorial tools as sociated to the underlying affine Weyl group. Finally\, for Bruhat-Tits bu ildings\, we relate these retractions and their effect on certain minimal galleries to double coset intersections in the corresponding affine flag v ariety. This is joint work with Elizabeth Milicevic\, Yusra Naqvi and Petr a Schwer.\n LOCATION:https://researchseminars.org/talk/SiN/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Bischof (Uni Giesen) DTSTART:20220204T033000Z DTEND:20220204T043000Z DTSTAMP:20260422T225724Z UID:SiN/35 DESCRIPTION:Title: (Tw in) Buildings and groups\nby Sebastian Bischof (Uni Giesen) as part of Symmetry in Newcastle\n\nLecture held in SR118\, Callaghan Campus.\n\nAbs tract\nBuildings have been introduced by Tits in order to study semi-simpl e algebraic groups from a geometrical point of view. One of the most impor tant results in the theory of buildings is the classification of thick irr educible spherical buildings of rank at least 3. In particular\, any such building comes from an RGD-system. The decisive tool in this classificatio n is the Extension theorem for spherical buildings\, i.e. a local isometry extends to the whole building.\nTwin buildings were introduced by Ronan a nd Tits in the late 1980s. Their definition was motivated by the theory of Kac-Moody groups over fields. Each such group acts naturally on a pair of buildings and the action preserves an opposition relation between the cha mbers of the two buildings. This opposition relation shares many important properties with the opposition relation on the chambers of a spherical bu ilding. Thus\, twin buildings appear to be natural generalizations of sphe rical buildings with infinite Weyl group. Since the notion of RGD-systems exists not only in the spherical case\, one can ask whether any twin build ing (satisfying some further conditions) comes from an RGD-system. In 1992 Tits proves several results that are inspired by his strategy in the sphe rical case and he discusses several obstacles for obtaining a similar Exte nsion theorem for twin buildings. In this talk I will speak about the hist ory and developments of the Extension theorem for twin buildings.\n LOCATION:https://researchseminars.org/talk/SiN/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Michal Ferov (University of Newcastle) DTSTART:20220304T010000Z DTEND:20220304T020000Z DTSTAMP:20260422T225724Z UID:SiN/36 DESCRIPTION:Title: Aut omorphism groups of Cayley graphs of Coxeter groups: when are they discret e?\nby Michal Ferov (University of Newcastle) as part of Symmetry in N ewcastle\n\nLecture held in SR118\, University Drive\, Callaghan.\n\nAbstr act\nGroup of automorphisms of a connected locally finite graph is natural ly a totally disconnected locally compact topological group\, when equippe d with the permutation topology. It therefore makes sense to ask for which graphs is the topology not discrete. We show that in case of Cayley graph s of Coxeter groups\, one can fully characterise the discrete ones in term s of the symmetries of the corresponding Coxeter system. Joint work with F ederico Berlai.\n LOCATION:https://researchseminars.org/talk/SiN/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeroen Schillewaert (The University of Auckland) DTSTART:20220304T033000Z DTEND:20220304T043000Z DTSTAMP:20260422T225724Z UID:SiN/37 DESCRIPTION:Title: The geometries of the Freudenthal-Tits magic square\nby Jeroen Schillewae rt (The University of Auckland) as part of Symmetry in Newcastle\n\nLectur e held in SR118\, University Drive\, Callaghan.\n\nAbstract\nI will give a n overview of a programme investigating projective embeddings of (exceptio nal) geometries which Hendrik Van Maldeghem and I started in 2010.\n LOCATION:https://researchseminars.org/talk/SiN/37/ END:VEVENT BEGIN:VEVENT SUMMARY:James Parkinson (University of Sydney) DTSTART:20220304T050000Z DTEND:20220304T060000Z DTSTAMP:20260422T225724Z UID:SiN/38 DESCRIPTION:Title: Aut omorphisms and opposition in spherical buildings.\nby James Parkinson (University of Sydney) as part of Symmetry in Newcastle\n\nLecture held in SR118\, University Drive\, Callaghan.\n\nAbstract\nThe geometry of elemen ts fixed by an automorphism of a spherical building is a rich and well-stu died object\, intimately connected to the theory of Galois descent in buil dings. In recent years\, a complementary theory has emerged investigating the geometry of elements mapped onto opposite elements by a given automorp hism. In this talk we will give an overview of this theory. This work is j oint primarily with Hendrik Van Maldeghem (along with others).\n LOCATION:https://researchseminars.org/talk/SiN/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Max Carter (University of Newcastle) DTSTART:20220401T010000Z DTEND:20220401T020000Z DTSTAMP:20260422T225724Z UID:SiN/39 DESCRIPTION:Title: Uni tary representations and the type I property of groups acting on trees \nby Max Carter (University of Newcastle) as part of Symmetry in Newcastle \n\n\nAbstract\nUnitary representations are a classical and useful tool fo r studying locally compact groups: motivated in part by quantum mechanics\ , they have been studied in detail since the early-mid 1900’s with much success\, and they enable group theorists to employ functional analytic te chniques in the study of locally compact groups. The algebras that unitary representations generate play an important role in not only understanding the representation theory of a locally compact group\, but also in unders tanding properties pertaining to the group itself. This talk will give a b rief introduction to some of the basics of the unitary representation theo ry of locally compact groups\, with focus placed on the associated operato r algebraic structures/properties. In particular\, `type I groups' and `CC R groups' will be the main focus. As an application\, I will discuss some current research interests in the unitary representation theory of groups acting on trees\, including work of myself on the unitary representation t heory of `scale groups’.\n LOCATION:https://researchseminars.org/talk/SiN/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Camila Sehnem (Victoria University of Wellington) DTSTART:20220401T033000Z DTEND:20220401T043000Z DTSTAMP:20260422T225724Z UID:SiN/40 DESCRIPTION:Title: Equ ilibrium on Toeplitz extensions of higher dimensional noncommutative tori< /a>\nby Camila Sehnem (Victoria University of Wellington) as part of Symme try in Newcastle\n\n\nAbstract\nThe C*-algebra generated by the left-regul ar representation of $\\mathbb{N}^n$ twisted by a $2$-cocycle is a Toeplit z extension of an $n$-dimensional noncommutative torus\, on which each vec tor $r \\in [0\,\\infty)^n$ determines a one-parameter subgroup of the gau ge action. I will report on joint work with Z. Afsar\, J. Ramagge and M. L aca\, in which we show that the equilibrium states of the resulting C*-dyn amical system are parametrised by tracial states of the noncommutative tor us corresponding to the restriction of the cocycle to the vanishing coordi nates of $r$. These in turn correspond to probability measures on a classi cal torus whose dimension depends on a certain degeneracy index of the res tricted cocycle. Our results generalise the phase transition on the Toepli tz noncommutative tori used as building blocks in work of Brownlowe\, Haw kins and Sims\, and of Afsar\, an Huef\, Raeburn and Sims.\n LOCATION:https://researchseminars.org/talk/SiN/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Roozbeh Hazrat (University of Western Sydney) DTSTART:20220401T050000Z DTEND:20220401T060000Z DTSTAMP:20260422T225724Z UID:SiN/41 DESCRIPTION:Title: San dpile models and Leavitt algebras\nby Roozbeh Hazrat (University of We stern Sydney) as part of Symmetry in Newcastle\n\n\nAbstract\nSandpile mod els are about how things spread along a grid (think of Covid!) and Leavitt algebras are algebras associated to graphs. We relate these two subjects! \n LOCATION:https://researchseminars.org/talk/SiN/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudio Bravo (University of Chile) DTSTART:20220701T000000Z DTEND:20220701T010000Z DTSTAMP:20260422T225724Z UID:SiN/42 DESCRIPTION:Title: Quo tients of the Bruhat-Tits tree function filed analogs of the Hecke congrue nce subgroups\nby Claudio Bravo (University of Chile) as part of Symme try in Newcastle\n\nLecture held in Lambert Lounge\, US 321.\n\nAbstract\n Let C be a smooth\, projective\, and geometrically connected curve defined over a finite field F. For each closed point P_infty of C\, let R be the ring of functions that are regular outside P_infty\, and let K be the comp letion path P_infty of the function field of C. In order to study group of the form GL_2(R)\, Serre describes the quotient graph GL_2(R)\\T\, where T is the Bruhat-Tits tree defined from SL_2(K). In particular\, Serre show s that GL_2(R)\\T is the union of a finite graph and a finite number of ra y shaped subgraphs\, which are called cusps. It is not hard to see that fi nite index subgroups inherit this property.\nIn this exposition we describ e the quotient graph H\\T defined from the action on T of the group H cons isting of matrices that are upper triangular modulo I\, where I is an idea l R. More specifically\, we give an explicit formula for the cusp number H \\T. Then By\, using Bass-Serre theory\, we describe the combinatorial str ucture of H. These groups play\, in the function field context\, the same role as the Hecke Congruence subgroups of SL_2(Z). Moreover\, not that the groups studied by Serre correspond to the case where the ideal I coincide s with the ring R.\n LOCATION:https://researchseminars.org/talk/SiN/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Conder (University of Auckland) DTSTART:20220701T013000Z DTEND:20220701T023000Z DTSTAMP:20260422T225724Z UID:SiN/43 DESCRIPTION:Title: Dis crete two-generator subgroups of PSL(2\,Q_p)\nby Matthew Conder (Unive rsity of Auckland) as part of Symmetry in Newcastle\n\nLecture held in Lam bert Lounge\, US 321.\n\nAbstract\nDue to work of Gilman\, Rosenberger\, P urzitsky and many others\, discrete two-generator subgroups of PSL(2\,R) h ave been completely classified by studying their action by Möbius transfo rmations on the hyperbolic plane. Here we aim to classify discrete two-gen erator subgroups of PSL(2\,Q_p) by studying their action by isometries on the Bruhat-Tits tree. We first give a general structure theorem for two-ge nerator groups acting by isometries on a tree\, which relies on certain Kl ein-Maskit combination theorems. We will then discuss how this theorem can be applied to determine discreteness of a two-generator subgroup of PSL(2 \,Q_p). This is ongoing work in collaboration with Jeroen Schillewaert.\n LOCATION:https://researchseminars.org/talk/SiN/43/ END:VEVENT BEGIN:VEVENT SUMMARY:George Willis (University of Newcastle) DTSTART:20220701T040000Z DTEND:20220701T050000Z DTSTAMP:20260422T225724Z UID:SiN/44 DESCRIPTION:Title: Gro ups acting on regular trees and t.d.l.c. groups\nby George Willis (Uni versity of Newcastle) as part of Symmetry in Newcastle\n\nLecture held in Lambert Lounge\, US 321.\n\nAbstract\nGroups acting on regular trees and t .d.l.c. groups\nAbstract: Groups of automorphisms of regular trees are an important source of examples of and intuition about totally disconnected\, locally compact (t.d.l.c.) groups. Indeed\, Pierre-Emmanuel Caprice has c alled them a microcosm the general theory of t.d.l.c. groups. Although muc h is know about them\, many questions remain open.\nThis talk will survey some of what is known about groups of tree automorphisms and how it relate s to the general theory.\n LOCATION:https://researchseminars.org/talk/SiN/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Kane Townsend (University of Technology Sydney) DTSTART:20221007T010000Z DTEND:20221007T020000Z DTSTAMP:20260422T225724Z UID:SiN/45 DESCRIPTION:Title: Hyp erbolic groups with $k$-geodetic Cayley graphs\nby Kane Townsend (Univ ersity of Technology Sydney) as part of Symmetry in Newcastle\n\n\nAbstrac t\nA locally-finite simple connected graph is said to be $k$-geodetic for some $k\\geq1$\, if there is at most $k$ distinct geodesics between any tw o vertices of the graph. We investigate the properties of hyperbolic group s with $k$-geodetic Cayley graphs. To begin\, we show that $k$-geodetic gr aphs cannot have a "ladder-like" geodesic structure with unbounded length. Using this bound\, we generalise a well-known result of Papasoglu that st ates hyperbolic groups with $1$-geodetic Cayley graphs are virtually-free. We then investigate which elements of the hyperbolic group with $k$-geode tic Cayley graph commute with a given infinite order element.\n LOCATION:https://researchseminars.org/talk/SiN/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Freden (Southern Utah University) DTSTART:20221007T033000Z DTEND:20221007T043000Z DTSTAMP:20260422T225724Z UID:SiN/46 DESCRIPTION:Title: Asp ects of growth in Baumslag-Solitar groups\nby Eric Freden (Southern Ut ah University) as part of Symmetry in Newcastle\n\n\nAbstract\nIn 1997\, G rigorchuk and de la Harpe suggested computing the growth series for the Ba umslag-Solitar group BS(2\,3). After 25 years\, this is still an open prob lem. In fact\, the growth of only the solvable groups BS(1\,n) and automat ic groups BS(n\,n) are known. In this talk I will review what has since be en discovered about these remarkable groups and conclude with new unpublis hed results concerning the exponents of growth for the subfamily BS(2\,2n) .\n LOCATION:https://researchseminars.org/talk/SiN/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Volker Diekert (Universität Stuttgart) DTSTART:20221007T050000Z DTEND:20221007T060000Z DTSTAMP:20260422T225724Z UID:SiN/47 DESCRIPTION:Title: Dec idability of membership problems for $2\\times 2$ matrices over $\\mathbb{ Q}$\nby Volker Diekert (Universität Stuttgart) as part of Symmetry in Newcastle\n\n\nAbstract\nMy talk is based on a joint work with Igor Potap ov and Pavel Semukhin (Liverpool\, UK).\nWe consider membership problems i n matrix semigroups. Using symbolic algorithms on words and finite automat a\, we prove various new decidability results for $2\\times 2$ matrices ov er $\\mathbb{Q}$.\nFor that\, we introduce the concept of flat rational se ts: if $M$ is a monoid and $N$ is\na submonoid\, then \\emph{flat rational sets of $M$ over $N$} are finite unions of the form $L_0g_1L_1 \\cdots g_ t L_t$ where all $L_i$'s are rational subsets of $N$ and $g_i\\in M$. We g ive quite general sufficient conditions under which flat rational sets for m an effective relative Boolean algebra. As a corollary\, we obtain that t he emptiness problem for Boolean combinations of flat rational subsets of $\\mathrm{GL}(2\,\\mathbb{Q})$ over $\\mathrm{GL}(2\,\\mathbb{Z})$ is deci dable (in singly exponential time). It is possible that such a strong deci dability result cannot be pushed any further for groups sitting between\n$ \\mathrm{GL}(2\,\\mathbb{Z})$ and $\\mathrm{GL}(2\,\\mathbb{Q})$.\n\nWe al so show a dichotomy for nontrivial group extension of $\\mathrm{GL}(2\,\\m athbb{Z})$ in $\\mathrm{GL}(2\,\\mathbb{Q})$: if $G$ is a f.g.~group such that $\\mathrm{GL}(2\,\\mathbb{Z}) < G \\leq \\mathrm{GL}(2\,\\mathbb{Q})$ \, then either $G\\cong \\mathrm{GL}(2\,\\mathbb{Z})\\times \\mathbb{Z}^k$ \, for\nsome $k\\geq 1$\, or $G$ contains an extension of the Baumslag-Sol itar group $\\mathop\\mathrm{BS}(1\,q)$\, with $q\\geq\n2$\, of infinite i ndex. In the first case of the dichotomy the membership problem for $G$ is \ndecidable but the equality problem for rational subsets of $G$ is undeci dable. In the second case\,\ndecidability of the membership problem for ra tional subsets in $G$ is open.\n\nOur improves various natural decidabili ty results for $2 \\times 2$ matrices with rational entries\, and it also\ nsupports them with concrete complexity bounds for the first time.\n LOCATION:https://researchseminars.org/talk/SiN/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Hulpke (Colorado State University) DTSTART:20221104T030000Z DTEND:20221104T040000Z DTSTAMP:20260422T225724Z UID:SiN/48 DESCRIPTION:Title: Con structing Perfect Groups\nby Alexander Hulpke (Colorado State Universi ty) as part of Symmetry in Newcastle\n\n\nAbstract\nThe construction of pe rfect groups of a given order can be considered as the prototype of constr uction of nonsolvable groups of a given order.\nI will describe a recent p roject to enumerate\, up to isomorphism\, the perfect groups of order up t o 2*10^6. It crucially relies on new tools for calculating cohmology\, as well as improved implementations for isomorphism test.\n\nThis work extend s results of Holt and Plesken from 1989 and illustrates the scope of algor ithmic improvements over the past decades.\n LOCATION:https://researchseminars.org/talk/SiN/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Conder (University of Auckland) DTSTART:20221124T230000Z DTEND:20221125T000000Z DTSTAMP:20260422T225724Z UID:SiN/49 DESCRIPTION:Title: Two -generator subgroups of SL2 over local fields\nby Matthew Conder (Univ ersity of Auckland) as part of Symmetry in Newcastle\n\n\nAbstract\nIn thi s talk\, we will give an overview of some results and open problems relati ng to two-generator subgroups of SL2 over a local field K. We first consid er the archimedean setting\, where certain discrete and/or free two-genera tor subgroups of SL(2\,R) and SL(2\,C) can be identified by investigating their respective actions by Möbius transformations on the upper half plan e and Riemann sphere. We then outline some recent results in the non-archi medean setting\, obtained by studying the analogous action of SL(2\,K) by isometries on the corresponding Bruhat-Tits tree. Finally\, we discuss an application of this work to the problem of deciding whether a two-generato r subgroup of SL(2\,K) is dense.\n LOCATION:https://researchseminars.org/talk/SiN/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Armin Weiß (Universität Stuttgart) DTSTART:20230125T040000Z DTEND:20230125T050000Z DTSTAMP:20260422T225724Z UID:SiN/50 DESCRIPTION:Title: An Automaton Group with PSPACE-Complete Word Problem\nby Armin Weiß (Uni versität Stuttgart) as part of Symmetry in Newcastle\n\n\nAbstract\nFinit e automata pose an interesting alternative way to present groups and \nsem igroups. Some of these automaton groups became famous for their peculiar \ nproperties and have been extensively studied. \n\nOne aspect of this rese arch is the study of algorithmic properties of \nautomaton groups and semi groups. While many natural algorithmic decision \nproblems have been prove n or are generally suspected to be undecidable for \nthese classes\, the w ord problem forms a notable exception. In the group case\, \nit asks wheth er a given word in the generators is equal to the neutral element \nin the group in question and is well-known to be decidable for automaton \ngroup s. In fact\, it was observed in a work by Steinberg published in 2015 that \nit can be solved in nondeterministic linear space using a straight-forw ard \nguess and check algorithm. In the same work\, he conjectured that th ere is an \nautomaton group with a PSPACE-complete word problem.\n\nIn a r ecent paper presented at STACS 2020\, Jan Philipp Wächter and myself coul d\nprove that there indeed is such an automaton group. To achieve this\, w e combined\ntwo ideas. The first one is a construction introduced by D'Ang eli\, Rodaro and\nWächter to show that there is an inverse automaton semi group with a \nPSPACE-complete word problem and the second one is an idea already used \nby Barrington in 1989 to encode NC¹ circuits in the group of even permutation \nover five elements. In the talk\, we will discuss ho w Barrington's idea can be \napplied in the context of automaton groups\, which will allow us to prove that \nthe uniform word problem for automaton groups (were the generating automaton \nand\, thus\, the group is part of the input) is PSPACE- complete. Afterwards\, we \nwill also discuss the i deas underlying the construction to simulate a PSPACE-\nmachine with an in vertible automaton\, which allow for extending the result to \nthe non-uni form case. Finally\, we will briefly look at related problems such \nas th e compressed word problem for automaton groups and the special case of\nau tomaton group of polynomial activity.\n LOCATION:https://researchseminars.org/talk/SiN/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Brownlowe (University of Sydney) DTSTART:20230217T000000Z DTEND:20230217T010000Z DTSTAMP:20260422T225724Z UID:SiN/51 DESCRIPTION:Title: C*- algebraic approaches to self-similarity\nby Nathan Brownlowe (Universi ty of Sydney) as part of Symmetry in Newcastle\n\n\nAbstract\nIn this talk I will go through the basics of self-similar actions and some of their ge neralisations. I will then introduce C*-algebras\, before surveying the li terature on how we build C*-algebras to model self-similarity.\n LOCATION:https://researchseminars.org/talk/SiN/51/ END:VEVENT BEGIN:VEVENT SUMMARY:David Robertson (University of New England) DTSTART:20230217T023000Z DTEND:20230217T033000Z DTSTAMP:20260422T225724Z UID:SiN/52 DESCRIPTION:Title: Sel f-similar quantum groups\nby David Robertson (University of New Englan d) as part of Symmetry in Newcastle\n\n\nAbstract\nQuantum automorphism gr oups originated in the work of Wang in the mid 90s as an answer to questio n of Connes: what are the quantum automorphisms of a space? Wang showed th at for a finite set with at least 4 points there are an infinite number of quantum permutations. Since then\, work on quantum automorphism groups ha s progressed in many different directions\, including the construction of the quantum automorphism group of a finite graph by Bichon in 2004 and qua ntum automorphisms of locally finite graphs by Rollier and Vaes in 2022. In a recent preprint with Nathan Brownlowe\, we have shown that the quant um automorphism group of a homogeneous rooted tree is a compact quantum gr oup\, and defined when a quantum subgroup is self-similar. In this talk I will give an overview of this construction\, and construct a number of ex amples through an analogue of the notion of a finitely constrained self-si milar group defined by Sunic in 2011.\n LOCATION:https://researchseminars.org/talk/SiN/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Aidan Sims (University of Wollongong) DTSTART:20230217T040000Z DTEND:20230217T050000Z DTSTAMP:20260422T225724Z UID:SiN/53 DESCRIPTION:Title: K-t heoretic duality for self-similar groupoids\nby Aidan Sims (University of Wollongong) as part of Symmetry in Newcastle\n\n\nAbstract\nA K-theore tic duality for C*-algebras is\, roughly speaking\, a particularly nice is omorphism of the K-theory groups of each with the K-homology groups of the other. They are generalisations of Poincare duality for manifolds\, and i n that vein\, they often help to compute algebraic or analytic K-theory in variants in terms of more-tractable topological information. Under some te chnical hypotheses\, Nekrashevych established a K-theoretic duality betwee n the C*-algebra of a self-similar group and a related C*-algebra associat ed to a limit space that resembles the way that real numbers are represent ed by decimal expansions. I will discuss how Nekrashevych’s limit space is constructed\, focussing on elementary but instructive examples to keep things concrete\, and sketch out how to use it to describe a K-theoretic d uality that helps in computing K-theory for self-similar groupoid C*-algeb ras. I won’t assume any background in any of this stuff. This is joint w ork with Brownlowe\, Buss\, Goncalves\, Hume and Whittaker.\n LOCATION:https://researchseminars.org/talk/SiN/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Wibmer (TU Graz) DTSTART:20230525T060000Z DTEND:20230525T070000Z DTSTAMP:20260422T225724Z UID:SiN/54 DESCRIPTION:Title: Dif ference algebraic groups\nby Michael Wibmer (TU Graz) as part of Symme try in Newcastle\n\n\nAbstract\nDifference algebraic groups are a generali zation of algebraic groups. Instead of just algebraic equations\, one allo ws difference algebraic equations as the defining equations. Here one can think of a difference equation as a discrete version of a differential equ ation. Besides their intrinsic beauty\, one of the main motivations for st udying difference algebraic groups is that they occur as Galois groups in certain Galois theories.\n\nThis talk will be an introduction to differenc e algebraic groups.\n LOCATION:https://researchseminars.org/talk/SiN/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Wibmer (TU Graz) DTSTART:20230525T073000Z DTEND:20230525T083000Z DTSTAMP:20260422T225724Z UID:SiN/55 DESCRIPTION:Title: Exp ansive endomorphisms of profinite groups\nby Michael Wibmer (TU Graz) as part of Symmetry in Newcastle\n\n\nAbstract\nÉtale algebraic groups ov er a field k are equivalent to finite groups with a continuous action of t he absolute Galois group of k. The difference version of this well-know re sult asserts that étale difference algebraic groups over a difference fie ld k (i.e.\, a field equipped with an endomorphism) are equivalent to prof inite groups equipped with an expansive endomorphism and a certain compati ble difference Galois action. In any case\, understanding the structure of expansive endomorphisms of profinite groups seems a worthwhile endeavor a nd that's what this talk is about.\n LOCATION:https://researchseminars.org/talk/SiN/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Dilshan Wijesena (University of New South Wales) DTSTART:20230809T040000Z DTEND:20230809T050000Z DTSTAMP:20260422T225724Z UID:SiN/56 DESCRIPTION:Title: Irr educible Pythagorean representations of Thompson’s groups\nby Dilsha n Wijesena (University of New South Wales) as part of Symmetry in Newcastl e\n\n\nAbstract\nRichard Thompson’s groups $F$\, $T$ and $V$ are one of the most fascinating discrete infinite groups for their several unusual pr operties and their analytical properties have been challenging experts for many decades. One reason for this is because very little is known about i ts representation theory. Luckily\, thanks to the novel technology of Jone s\, a rich family of so-called Pythagorean unitary representation of Thomp son’s groups can be constructed by simply specifying a pair of finite-di mensional operators satisfying a certain equality. These representations c an even be extended to the celebrated Cuntz algebra and carry a powerful d iagrammatic calculus which we use to develop techniques to study their pro perties. This permits to reduce very difficult questions concerning irredu cibility and equivalence of infinite-dimensional representations into prob lems in finite-dimensional linear algebra. This provides a new rich class of irreducible representations of $F$. Moreover\, we introduce the Pythago rean dimension which is a new invariant for all representations of the Cun tz algebra and Pythagorean representations of $F\,T\,V$. For each dimensio n $d$\, we show the irreducible classes form a moduli space of a real mani fold of dimension $2d^2+1$.\n LOCATION:https://researchseminars.org/talk/SiN/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Merlin Incerti-Medici (Universität Wien) DTSTART:20240125T070000Z DTEND:20240125T080000Z DTSTAMP:20260422T225724Z UID:SiN/57 DESCRIPTION:Title: Aut omorphism groups of cocompact CAT(0) cube complexes\nby Merlin Incerti -Medici (Universität Wien) as part of Symmetry in Newcastle\n\n\nAbstract \nGiven a cocompact CAT(0) cube complex\, we study the group of its cubica l isometries\, which frequently forms a non-discrete tdlc group. We presen t a method to study these groups that is focused on our ability to underst and the stabilizer subgroups. We demonstrate the potency of this method by introducing a finite\, topologically generating set and discuss an import ant simple subgroup. If there is time\, we discuss some open questions reg arding the placement of these groups among non-discrete tdlc groups.\n LOCATION:https://researchseminars.org/talk/SiN/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Glasby (University of Western Australia) DTSTART:20240320T010000Z DTEND:20240320T020000Z DTSTAMP:20260422T225724Z UID:SiN/58 DESCRIPTION:Title: Cla ssifying groups with three automorphism orbits\nby Stephen Glasby (Uni versity of Western Australia) as part of Symmetry in Newcastle\n\nLecture held in VG10.\n\nAbstract\nWe call a group $G$ a $k$-orbit group if its a utomorphism group $Aut(G)$ acting naturally on $G$ has \nprecisely $k$ orb its. I will describe the classification of finite 3-orbit groups after sur veying\nwork to classify $k$-orbit groups for small $k$ when $G$ is finite or infinite. The finite 3-orbit groups that are not $p$-groups are easy t o classify. Apart from $Q_8$\, the finite non-abelian 3-orbit 2-groups are a subset of the Suzuki 2-groups which Graham Higman [2] classified in 196 3. Determining which subset turns out to be far from easy as the automorph ism groups of Suzuki 2-groups are mysterious.\nAlex Bors and I classified the finite 3-orbit 2-groups in [1]. In 2024 Li and Zhu [3]\, unaware of ou r work\nand using different methods\, classified the finite groups $G$ whe re $Aut(G)$ is transitive on elements of order $p$. Their groups include t he 3-orbit Suzuki 2-groups\, the homocyclic groups $C_{p^n}^m$ of exponent $p^2$ and the generalised quaternion group $Q_{2^{n+1}}$.\n\nI was able t o classify all finite 3-orbit groups (including $p>2$) using Hering's Theo rem and some representation theory. However\, to my surprise Li and Zhu [4 ] in March 2024 did the same.\n\n[1] Alexander Bors and S.P. Glasby\,\nFin ite 2-groups with exactly three automorphism orbits\, https://arxiv.org/ab s/2011.13016v1 (2020).\n\n[2] G. Higman\, Suzuki 2-groups\, Illinois J.~Ma th. 7 (1963)\, 79--96.\n\n[3] Cai Heng Li and Yan Zhou Zhu\, A Proof of Gr oss' Conjecture on 2-Automorphic 2-Groups\,\nhttps://arxiv.org/abs/2312.16 416 (2024).\n\n[4] Cai Heng Li and Yan Zhou Zhu\,\nThe finite groups with three automorphism orbits\, https://arxiv.org/abs/2403.01725 (2024).\n LOCATION:https://researchseminars.org/talk/SiN/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Roman Gorazd (unaffiliated) DTSTART:20260415T053000Z DTEND:20260415T063000Z DTSTAMP:20260422T225724Z UID:SiN/59 DESCRIPTION:Title: An explicit solution to the isomorphism problem of Higman-Thompson groups usi ng gluing diagrams\nby Roman Gorazd (unaffiliated) as part of Symmetry in Newcastle\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SiN/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthias Chan (University of Auckland) DTSTART:20260415T070000Z DTEND:20260415T080000Z DTSTAMP:20260422T225724Z UID:SiN/60 DESCRIPTION:Title: $(P _k)$-Closed Groups Acting on Trees\nby Matthias Chan (University of Au ckland) as part of Symmetry in Newcastle\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SiN/60/ END:VEVENT END:VCALENDAR